Daily Papers

Recent advances in test-time compute scaling have enabled Large Language Models (LLMs) to tackle deep reasoning tasks by generating a chain-of-thought (CoT) that includes trial and error, backtracking, and intermediate reasoning steps before producing the final answer. However, these techniques have been applied predominantly to popular languages, such as English, leaving reasoning in low-resource languages underexplored and misaligned. In this work, we investigate the multilingual mechanism by which LLMs internally operate in a latent space biased toward their inherently dominant language. To leverage this phenomenon for low-resource languages, we train models to generate the CoT in English while outputting the final response in the target language, given input in the low-resource language. Our experiments demonstrate that this approach, named English-Pivoted CoT Training, outperforms other baselines, including training to generate both the CoT and the final response solely in the target language, with up to 28.33% improvement. Further analysis provides novel insights into the relationships between reasoning and multilinguality of LLMs, prompting for better approaches in developing multilingual large reasoning models

Enabling LLMs to improve their outputs by using more test-time computation is a critical step towards building generally self-improving agents that can operate on open-ended natural language. In this paper, we study the scaling of inference-time computation in LLMs, with a focus on answering the question: if an LLM is allowed to use a fixed but non-trivial amount of inference-time compute, how much can it improve its performance on a challenging prompt? Answering this question has implications not only on the achievable performance of LLMs, but also on the future of LLM pretraining and how one should tradeoff inference-time and pre-training compute. Despite its importance, little research attempted to understand the scaling behaviors of various test-time inference methods. Moreover, current work largely provides negative results for a number of these strategies. In this work, we analyze two primary mechanisms to scale test-time computation: (1) searching against dense, process-based verifier reward models; and (2) updating the model's distribution over a response adaptively, given the prompt at test time. We find that in both cases, the effectiveness of different approaches to scaling test-time compute critically varies depending on the difficulty of the prompt. This observation motivates applying a "compute-optimal" scaling strategy, which acts to most effectively allocate test-time compute adaptively per prompt. Using this compute-optimal strategy, we can improve the efficiency of test-time compute scaling by more than 4x compared to a best-of-N baseline. Additionally, in a FLOPs-matched evaluation, we find that on problems where a smaller base model attains somewhat non-trivial success rates, test-time compute can be used to outperform a 14x larger model.

By utilizing more computational resources at test-time, large language models (LLMs) can improve without additional training. One common strategy uses verifiers to evaluate candidate outputs. In this work, we propose a novel scaling dimension for test-time compute: scaling the number of verifiers. We introduce Multi-Agent Verification (MAV) as a test-time compute paradigm that combines multiple verifiers to improve performance. We propose using Aspect Verifiers (AVs), off-the-shelf LLMs prompted to verify different aspects of outputs, as one possible choice for the verifiers in a MAV system. AVs are a convenient building block for MAV since they can be easily combined without additional training. Moreover, we introduce BoN-MAV, a simple multi-agent verification algorithm that combines best-of-n sampling with multiple verifiers. BoN-MAV demonstrates stronger scaling patterns than self-consistency and reward model verification, and we demonstrate both weak-to-strong generalization, where combining weak verifiers improves even stronger LLMs, and self-improvement, where the same base model is used to both generate and verify outputs. Our results establish scaling the number of verifiers as a promising new dimension for improving language model performance at test-time.

We construct evaluation tasks where extending the reasoning length of Large Reasoning Models (LRMs) deteriorates performance, exhibiting an inverse scaling relationship between test-time compute and accuracy. Our evaluation tasks span four categories: simple counting tasks with distractors, regression tasks with spurious features, deduction tasks with constraint tracking, and advanced AI risks. We identify five distinct failure modes when models reason for longer: 1) Claude models become increasingly distracted by irrelevant information; 2) OpenAI o-series models resist distractors but overfit to problem framings; 3) models shift from reasonable priors to spurious correlations; 4) all models show difficulties in maintaining focus on complex deductive tasks; and 5) extended reasoning may amplify concerning behaviors, with Claude Sonnet 4 showing increased expressions of self-preservation. These findings suggest that while test-time compute scaling remains promising for improving model capabilities, it may inadvertently reinforce problematic reasoning patterns. Our results demonstrate the importance of evaluating models across diverse reasoning lengths to identify and address these failure modes in LRMs.

Recent advancements in software engineering agents have demonstrated promising capabilities in automating program improvements. However, their reliance on closed-source or resource-intensive models introduces significant deployment challenges in private environments, prompting a critical question: How can personally deployable open-source LLMs achieve comparable code reasoning performance? To this end, we propose a unified Test-Time Compute scaling framework that leverages increased inference-time computation instead of larger models. Our framework incorporates two complementary strategies: internal TTC and external TTC. Internally, we introduce a development-contextualized trajectory synthesis method leveraging real-world software repositories to bootstrap multi-stage reasoning processes, such as fault localization and patch generation. We further enhance trajectory quality through rejection sampling, rigorously evaluating trajectories along accuracy and complexity. Externally, we propose a novel development-process-based search strategy guided by reward models and execution verification. This approach enables targeted computational allocation at critical development decision points, overcoming limitations of existing "end-point only" verification methods. Evaluations on SWE-bench Verified demonstrate our 32B model achieves a 46\% issue resolution rate, surpassing significantly larger models such as DeepSeek R1 671B and OpenAI o1. Additionally, we provide the empirical validation of the test-time scaling phenomenon within SWE agents, revealing that models dynamically allocate more tokens to increasingly challenging problems, effectively enhancing reasoning capabilities. We publicly release all training data, models, and code to facilitate future research. https://github.com/yingweima2022/SWE-Reasoner

Recent studies have demonstrated that test-time compute scaling effectively improves the performance of small language models (sLMs). However, prior research has mainly examined test-time compute scaling with an additional larger model as a verifier, leaving self-verification by sLMs underexplored. In this work, we investigate whether sLMs can reliably self-verify their outputs under test-time scaling. We find that even with knowledge distillation from larger verifiers, sLMs struggle with verification tasks requiring memorization, such as numerical calculations and fact-checking. To address this limitation, we propose Tool-integrated self-verification (T1), which delegates memorization-heavy verification steps to external tools, such as a code interpreter. Our theoretical analysis shows that tool integration reduces memorization demands and improves test-time scaling performance. Experiments on the MATH benchmark demonstrate that, with T1, a Llama-3.2 1B model under test-time scaling outperforms the significantly larger Llama-3.1 8B model. Moreover, T1 generalizes effectively to both mathematical (MATH500) and multi-domain knowledge-intensive tasks (MMLU-Pro). Our findings highlight the potential of tool integration to substantially improve the self-verification abilities of sLMs.

Reasoning is a core capability of large language models, yet understanding how they learn and perform multi-step reasoning remains an open problem. In this study, we explore how different architectures and training methods affect model multi-step reasoning capabilities within a cellular automata framework. By training on state sequences generated with random Boolean functions for random initial conditions to exclude memorization, we demonstrate that most neural architectures learn to abstract the underlying rules. While models achieve high accuracy in next-state prediction, their performance declines sharply if multi-step reasoning is required. We confirm that increasing model depth plays a crucial role for sequential computations. We demonstrate that an extension of the effective model depth with recurrence, memory, and test-time compute scaling substantially enhances reasoning capabilities.

Prevalent reinforcement learning~(RL) methods for fine-tuning LLM reasoners, such as GRPO or Leave-one-out PPO, abandon the learned value function in favor of empirically estimated returns. This hinders test-time compute scaling that relies on using the value-function for verification. In this work, we propose RL^V that augments any ``value-free'' RL method by jointly training the LLM as both a reasoner and a generative verifier using RL-generated data, adding verification capabilities without significant overhead. Empirically, RL^V boosts MATH accuracy by over 20\% with parallel sampling and enables 8-32times efficient test-time compute scaling compared to the base RL method. RL^V also exhibits strong generalization capabilities for both easy-to-hard and out-of-domain tasks. Furthermore, RL^V achieves 1.2-1.6times higher performance when jointly scaling parallel and sequential test-time compute with a long reasoning R1 model.

Recent advances in Large Language Models (LLMs) have been driven by test-time compute scaling - a strategy that improves reasoning by generating longer, sequential thought processes. While effective, this approach encounters a significant bottleneck as computation increases, where further computation offers only marginal performance gains. We argue this ceiling is not an inherent limit of the model's capability but a flaw in the scaling strategy itself, a phenomenon we term "Tunnel Vision", where a model's imperfect initial steps lock it into a suboptimal reasoning path. To overcome this, we introduce a new scaling paradigm: native thought parallelism. We present ParaThinker, an end-to-end framework that trains an LLM to generate multiple, diverse reasoning paths in parallel and synthesize them into a superior final answer. By exploring different lines of thoughts simultaneously, ParaThinker effectively sidesteps the Tunnel Vision issue and unlocks the model's latent reasoning potential. Our approach demonstrates that scaling compute in parallel (width) is a more effective and efficient way to superior reasoning than simply scaling sequentially (depth). On challenging reasoning benchmarks, ParaThinker achieves substantial accuracy improvements over sequential LLMs (12.3% for 1.5B and 7.5% for 7B models on average with 8 parallel paths), while adding only negligible latency overhead (7.1%). This enables smaller models to surpass much larger counterparts and establishes parallel thinking as a critical, efficient dimension for scaling future LLMs.

Test-time compute scaling has emerged as a new axis along which to improve model accuracy, where additional computation is used at inference time to allow the model to think longer for more challenging problems. One promising approach for test-time compute scaling is search against a process reward model, where a model generates multiple potential candidates at each step of the search, and these partial trajectories are then scored by a separate reward model in order to guide the search process. The diversity of trajectories in the tree search process affects the accuracy of the search, since increasing diversity promotes more exploration. However, this diversity comes at a cost, as divergent trajectories have less KV sharing, which means they consume more memory and slow down the search process. Previous search methods either do not perform sufficient exploration, or else explore diverse trajectories but have high latency. We address this challenge by proposing Efficient Tree Search (ETS), which promotes KV sharing by pruning redundant trajectories while maintaining necessary diverse trajectories. ETS incorporates a linear programming cost model to promote KV cache sharing by penalizing the number of nodes retained, while incorporating a semantic coverage term into the cost model to ensure that we retain trajectories which are semantically different. We demonstrate how ETS can achieve 1.8times reduction in average KV cache size during the search process, leading to 1.4times increased throughput relative to prior state-of-the-art methods, with minimal accuracy degradation and without requiring any custom kernel implementation. Code is available at: https://github.com/SqueezeAILab/ETS.

Large language models have demonstrated remarkable progress in mathematical reasoning, leveraging chain-of-thought and test-time compute scaling. However, many open questions remain regarding the interplay between reasoning token usage and accuracy gains. In particular, when comparing models across generations, it is unclear whether improved performance results from longer reasoning chains or more efficient reasoning. We systematically analyze chain-of-thought length across o1-mini and o3-mini variants on the Omni-MATH benchmark, finding that o3-mini (m) achieves superior accuracy without requiring longer reasoning chains than o1-mini. Moreover, we show that accuracy generally declines as reasoning chains grow across all models and compute settings, even when controlling for difficulty of the questions. This accuracy drop is significantly smaller in more proficient models, suggesting that new generations of reasoning models use test-time compute more effectively. Finally, we highlight that while o3-mini (h) achieves a marginal accuracy gain over o3-mini (m), it does so by allocating substantially more reasoning tokens across all problems, even the ones that o3-mini (m) can already solve. These findings provide new insights into the relationship between model capability and reasoning length, with implications for efficiency, scaling, and evaluation methodologies.

The ability to organically reason over and with both text and images is a pillar of human intelligence, yet the ability of Multimodal Large Language Models (MLLMs) to perform such multimodal reasoning remains under-explored. Existing benchmarks often emphasize text-dominant reasoning or rely on shallow visual cues, failing to adequately assess integrated visual and textual reasoning. We introduce EMMA (Enhanced MultiModal reAsoning), a benchmark targeting organic multimodal reasoning across mathematics, physics, chemistry, and coding. EMMA tasks demand advanced cross-modal reasoning that cannot be addressed by reasoning independently in each modality, offering an enhanced test suite for MLLMs' reasoning capabilities. Our evaluation of state-of-the-art MLLMs on EMMA reveals significant limitations in handling complex multimodal and multi-step reasoning tasks, even with advanced techniques like Chain-of-Thought prompting and test-time compute scaling underperforming. These findings underscore the need for improved multimodal architectures and training paradigms to close the gap between human and model reasoning in multimodality.

Existing large language models (LLMs) face challenges of following complex instructions, especially when multiple constraints are present and organized in paralleling, chaining, and branching structures. One intuitive solution, namely chain-of-thought (CoT), is expected to universally improve capabilities of LLMs. However, we find that the vanilla CoT exerts a negative impact on performance due to its superficial reasoning pattern of simply paraphrasing the instructions. It fails to peel back the compositions of constraints for identifying their relationship across hierarchies of types and dimensions. To this end, we propose a systematic method to boost LLMs in dealing with complex instructions via incentivizing reasoning for test-time compute scaling. First, we stem from the decomposition of complex instructions under existing taxonomies and propose a reproducible data acquisition method. Second, we exploit reinforcement learning (RL) with verifiable rule-centric reward signals to cultivate reasoning specifically for instruction following. We address the shallow, non-essential nature of reasoning under complex instructions via sample-wise contrast for superior CoT enforcement. We also exploit behavior cloning of experts to facilitate steady distribution shift from fast-thinking LLMs to skillful reasoners. Extensive evaluations on seven comprehensive benchmarks confirm the validity of the proposed method, where a 1.5B LLM achieves 11.74% gains with performance comparable to a 8B LLM. Codes and data are available at https://github.com/yuleiqin/RAIF.

In this paper, we propose a simple and efficient method for value model training on long-context reasoning traces. Compared to existing process reward models (PRMs), our method does not require a fine-grained notion of "step," which is difficult to define for long-context reasoning models. By collecting a dataset of 2.5 million reasoning traces, we train a 1.5B token-level value model and apply it to DeepSeek models for improved performance with test-time compute scaling. We find that block-wise value-guided search (VGS) with a final weighted majority vote achieves better test-time scaling than standard methods such as majority voting or best-of-n. With an inference budget of 64 generations, VGS with DeepSeek-R1-Distill-1.5B achieves an average accuracy of 45.7% across four competition math benchmarks (AIME 2024 & 2025, HMMT Feb 2024 & 2025), reaching parity with o3-mini-medium. Moreover, VGS significantly reduces the inference FLOPs required to achieve the same performance of majority voting. Our dataset, model and codebase are open-sourced.

Reinforcement learning fine-tuning (RLFT) is a dominant paradigm for improving pretrained policies for downstream tasks. These pretrained policies, trained on large datasets, produce generations with a broad range of promising but unrefined behaviors. Often, a critical failure mode of RLFT arises when policies lose this diversity and collapse into a handful of easily exploitable outputs. This convergence hinders exploration, which is essential for expanding the capabilities of the pretrained policy and for amplifying the benefits of test-time compute scaling. To address this, we introduce an objective for policy gradient methods that explicitly enforces the exploration and refinement of diverse generations, which we call a polychromic objective. We then show how proximal policy optimization (PPO) can be adapted to optimize this objective. Our method (1) employs vine sampling to collect on-policy rollouts and (2) modifies the advantage function to reflect the advantage under our new objective. Experiments on BabyAI, Minigrid, and Algorithmic Creativity show that our method improves success rates by reliably solving a larger set of environment configurations and generalizes better under large perturbations. Moreover, when given multiple attempts in pass@k experiments, the policy achieves substantially higher coverage, demonstrating its ability to maintain and exploit a diverse repertoire of strategies.

Recent generative reasoning breakthroughs have transformed how large language models (LLMs) tackle complex problems by dynamically retrieving and refining information while generating coherent, multi-step thought processes. Techniques such as inference-time scaling, reinforcement learning, supervised fine-tuning, and distillation have been successfully applied to models like DeepSeek-R1, OpenAI's o1 & o3, GPT-4o, Qwen-32B, and various Llama variants, resulting in enhanced reasoning capabilities. In this paper, we provide a comprehensive analysis of the top 27 LLM models released between 2023 and 2025 (including models such as Mistral AI Small 3 24B, DeepSeek-R1, Search-o1, QwQ-32B, and phi-4). Then, we present an extensive overview of training methodologies that spans general training approaches, mixture-of-experts (MoE) and architectural innovations, retrieval-augmented generation (RAG), chain-of-thought and self-improvement techniques, as well as test-time compute scaling, distillation, and reinforcement learning (RL) methods. Finally, we discuss the key challenges in advancing LLM capabilities, including improving multi-step reasoning without human supervision, overcoming limitations in chained tasks, balancing structured prompts with flexibility, and enhancing long-context retrieval and external tool integration.

Test-Time Scaling (TTS) improves large language models (LLMs) by allocating additional computation during inference, typically through parallel, sequential, or hybrid scaling. However, prior studies often assume fixed collaboration architectures (e.g., topologies) and single-model usage, overlooking that optimal architectures and model combinations can vary across tasks. Therefore, we study the novel problem of searching for compute-optimal model combinations and architectures in TTS under a fixed budget. We formalize it as a multi-LLM collaboration graph, where nodes encode roles and LLM model assignments, and edges capture information flow. This problem is challenging because (i) the combinatorial search space is prohibitively large, and (ii) task-specific requirements demand tailored designs. To address these, we reformulate the problem as probabilistic graph optimization and, through pilot experiments, derive three empirical insights into TTS collaboration graphs. Guided by these insights, we propose Agent-REINFORCE, an LLM-agent-augmented framework that mirrors the REINFORCE pipeline by mapping sampling-gradient-update to sampling-feedback-update, where feedback serves as a textual gradient to update the probabilistic graph and efficiently search for optimal multi-LLM collaboration graphs. Experiments show that Agent-REINFORCE outperforms both traditional and LLM-based baselines in sample efficiency and search performance, and effectively identifies optimal graphs under joint objectives of accuracy and inference latency.

Test-time scaling (TTS) enhances the performance of large language models (LLMs) by allocating additional compute resources during inference. However, existing research primarily investigates TTS in single-stage tasks; while many real-world problems are multi-stage complex tasks, composed of a sequence of heterogeneous subtasks with each subtask requires LLM of specific capability. Therefore, we study a novel problem: the test-time compute-optimal scaling in multi-stage complex tasks, aiming to select suitable models and allocate budgets per subtask to maximize overall performance. TTS in multi-stage tasks introduces two fundamental challenges: (i) The combinatorial search space of model and budget allocations, combined with the high cost of inference, makes brute-force search impractical. (ii) The optimal model and budget allocations across subtasks are interdependent, increasing the complexity of the compute-optimal search. To address this gap, we conduct extensive pilot experiments on four tasks across six datasets, deriving three empirical insights characterizing the behavior of LLMs in multi-stage complex tasks. Informed by these insights, we propose AgentTTS, an LLM-agent-based framework that autonomously searches for compute-optimal allocations through iterative feedback-driven interactions with the execution environment. Experimental results demonstrate that AgentTTS significantly outperforms traditional and other LLM-based baselines in search efficiency, and shows improved robustness to varying training set sizes and enhanced interpretability.

Scaling test-time compute has emerged as a key ingredient for enabling large language models (LLMs) to solve difficult problems, but comes with high latency and inference cost. We introduce sleep-time compute, which allows models to "think" offline about contexts before queries are presented: by anticipating what queries users might ask and pre-computing useful quantities, we can significantly reduce the compute requirements at test-time. To demonstrate the efficacy of our method, we create modified versions of two reasoning tasks - Stateful GSM-Symbolic and Stateful AIME. We find that sleep-time compute can reduce the amount of test-time compute needed to achieve the same accuracy by ~ 5x on Stateful GSM-Symbolic and Stateful AIME and that by scaling sleep-time compute we can further increase accuracy by up to 13% on Stateful GSM-Symbolic and 18% on Stateful AIME. Furthermore, we introduce Multi-Query GSM-Symbolic, which extends GSM-Symbolic by including multiple related queries per context. By amortizing sleep-time compute across related queries about the same context using Multi-Query GSM-Symbolic, we can decrease the average cost per query by 2.5x. We then conduct additional analysis to understand when sleep-time compute is most effective, finding the predictability of the user query to be well correlated with the efficacy of sleep-time compute. Finally, we conduct a case-study of applying sleep-time compute to a realistic agentic SWE task.

Recent advancements in Large Language Models (LLMs) have shown that it is promising to utilize Process Reward Models (PRMs) as verifiers to enhance the performance of LLMs. However, current PRMs face three key challenges: (1) limited process supervision and generalization capabilities, (2) dependence on scalar value prediction without leveraging the generative abilities of LLMs, and (3) inability to scale the test-time compute of PRMs. In this work, we introduce GenPRM, a generative process reward model that performs explicit Chain-of-Thought (CoT) reasoning with code verification before providing judgment for each reasoning step. To obtain high-quality process supervision labels and rationale data, we propose Relative Progress Estimation (RPE) and a rationale synthesis framework that incorporates code verification. Experimental results on ProcessBench and several mathematical reasoning tasks show that GenPRM significantly outperforms prior PRMs with only 23K training data from MATH dataset. Through test-time scaling, a 1.5B GenPRM outperforms GPT-4o, and a 7B GenPRM surpasses Qwen2.5-Math-PRM-72B on ProcessBench. Additionally, GenPRM demonstrates strong abilities to serve as a critic model for policy model refinement. This work establishes a new paradigm for process supervision that bridges the gap between PRMs and critic models in LLMs. Our code, model, and data will be available in https://ryanliu112.github.io/GenPRM.

Despite substantial advances in scaling test-time compute, an ongoing debate in the community is how it should be scaled up to enable continued and efficient improvements with scaling. There are largely two approaches: first, distilling successful search or thinking traces; and second, using verification (e.g., 0/1 outcome rewards, reward models, or verifiers) to guide reinforcement learning (RL) and search algorithms. In this paper, we prove that finetuning LLMs with verifier-based (VB) methods based on RL or search is far superior to verifier-free (VF) approaches based on distilling or cloning search traces, given a fixed amount of compute/data budget. Further, we show that as we scale test-time compute (measured as the output token length) and training data, suboptimality of VF methods scales poorly compared to VB when the base pre-trained LLM presents a heterogeneous distribution over correct solution traces (e.g., different lengths, styles, etc.) and admits a non-sharp distribution over rewards on traces sampled from it. We formalize this condition using anti-concentration [Erdos, 1945]. This implies a stronger result that VB methods scale better asymptotically, with the performance gap between VB and VF methods widening as test-time budget grows. We corroborate our theory empirically on both didactic and math reasoning problems with 3/8/32B-sized pre-trained LLMs, where we find verification is crucial for scaling test-time compute.

Scaling test time compute has shown remarkable success in improving the reasoning abilities of large language models (LLMs). In this work, we conduct the first systematic exploration of applying test-time scaling methods to language agents and investigate the extent to which it improves their effectiveness. Specifically, we explore different test-time scaling strategies, including: (1) parallel sampling algorithms; (2) sequential revision strategies; (3) verifiers and merging methods; (4)strategies for diversifying rollouts.We carefully analyze and ablate the impact of different design strategies on applying test-time scaling on language agents, and have follow findings: 1. Scaling test time compute could improve the performance of agents. 2. Knowing when to reflect is important for agents. 3. Among different verification and result merging approaches, the list-wise method performs best. 4. Increasing diversified rollouts exerts a positive effect on the agent's task performance.

Scaling test-time compute is a promising axis for improving LLM capabilities. However, test-time compute can be scaled in a variety of ways, and effectively combining different approaches remains an active area of research. Here, we explore this problem in the context of solving real-world GitHub issues from the SWE-bench dataset. Our system, named CodeMonkeys, allows models to iteratively edit a codebase by jointly generating and running a testing script alongside their draft edit. We sample many of these multi-turn trajectories for every issue to generate a collection of candidate edits. This approach lets us scale "serial" test-time compute by increasing the number of iterations per trajectory and "parallel" test-time compute by increasing the number of trajectories per problem. With parallel scaling, we can amortize up-front costs across multiple downstream samples, allowing us to identify relevant codebase context using the simple method of letting an LLM read every file. In order to select between candidate edits, we combine voting using model-generated tests with a final multi-turn trajectory dedicated to selection. Overall, CodeMonkeys resolves 57.4% of issues from SWE-bench Verified using a budget of approximately 2300 USD. Our selection method can also be used to combine candidates from different sources. Selecting over an ensemble of edits from existing top SWE-bench Verified submissions obtains a score of 66.2% and outperforms the best member of the ensemble on its own. We fully release our code and data at https://scalingintelligence.stanford.edu/pubs/codemonkeys.

Large Language Models (LLMs) have shown remarkable abilities across various language tasks, but solving complex reasoning problems remains a challenge. While existing methods like Chain-of-Thought (CoT) and Tree-of-Thought (ToT) enhance reasoning by decomposing problems or structuring prompts, they typically perform a single pass of reasoning and may fail to revisit flawed paths, compromising accuracy. To address this, we propose a novel reasoning framework called Forest-of-Thought (FoT), which integrates multiple reasoning trees to leverage collective decision-making for solving complex logical problems. FoT utilizes sparse activation strategies to select the most relevant reasoning paths, improving both efficiency and accuracy. Additionally, we introduce a dynamic self-correction strategy that enables real-time error correction and learning from past mistakes, as well as consensus-guided decision making strategies to optimize correctness and computational resources. Experimental results demonstrate that the FoT framework, combined with these strategies, significantly enhances the reasoning capabilities of LLMs, enabling them to solve complex tasks with greater precision and efficiency.

We introduce MiniMax-M1, the world's first open-weight, large-scale hybrid-attention reasoning model. MiniMax-M1 is powered by a hybrid Mixture-of-Experts (MoE) architecture combined with a lightning attention mechanism. The model is developed based on our previous MiniMax-Text-01 model, which contains a total of 456 billion parameters with 45.9 billion parameters activated per token. The M1 model natively supports a context length of 1 million tokens, 8x the context size of DeepSeek R1. Furthermore, the lightning attention mechanism in MiniMax-M1 enables efficient scaling of test-time compute. These properties make M1 particularly suitable for complex tasks that require processing long inputs and thinking extensively. MiniMax-M1 is trained using large-scale reinforcement learning (RL) on diverse problems including sandbox-based, real-world software engineering environments. In addition to M1's inherent efficiency advantage for RL training, we propose CISPO, a novel RL algorithm to further enhance RL efficiency. CISPO clips importance sampling weights rather than token updates, outperforming other competitive RL variants. Combining hybrid-attention and CISPO enables MiniMax-M1's full RL training on 512 H800 GPUs to complete in only three weeks, with a rental cost of just $534,700. We release two versions of MiniMax-M1 models with 40K and 80K thinking budgets respectively, where the 40K model represents an intermediate phase of the 80K training. Experiments on standard benchmarks show that our models are comparable or superior to strong open-weight models such as the original DeepSeek-R1 and Qwen3-235B, with particular strengths in complex software engineering, tool utilization, and long-context tasks. We publicly release MiniMax-M1 at https://github.com/MiniMax-AI/MiniMax-M1.

We study a novel language model architecture that is capable of scaling test-time computation by implicitly reasoning in latent space. Our model works by iterating a recurrent block, thereby unrolling to arbitrary depth at test-time. This stands in contrast to mainstream reasoning models that scale up compute by producing more tokens. Unlike approaches based on chain-of-thought, our approach does not require any specialized training data, can work with small context windows, and can capture types of reasoning that are not easily represented in words. We scale a proof-of-concept model to 3.5 billion parameters and 800 billion tokens. We show that the resulting model can improve its performance on reasoning benchmarks, sometimes dramatically, up to a computation load equivalent to 50 billion parameters.

Recent studies have shown that making a model spend more time thinking through longer Chain of Thoughts (CoTs) enables it to gain significant improvements in complex reasoning tasks. While current researches continue to explore the benefits of increasing test-time compute by extending the CoT lengths of Large Language Models (LLMs), we are concerned about a potential issue hidden behind the current pursuit of test-time scaling: Would excessively scaling the CoT length actually bring adverse effects to a model's reasoning performance? Our explorations on mathematical reasoning tasks reveal an unexpected finding that scaling with longer CoTs can indeed impair the reasoning performance of LLMs in certain domains. Moreover, we discover that there exists an optimal scaled length distribution that differs across different domains. Based on these insights, we propose a Thinking-Optimal Scaling strategy. Our method first uses a small set of seed data with varying response length distributions to teach the model to adopt different reasoning efforts for deep thinking. Then, the model selects its shortest correct response under different reasoning efforts on additional problems for self-improvement. Our self-improved models built upon Qwen2.5-32B-Instruct outperform other distillation-based 32B o1-like models across various math benchmarks, and achieve performance on par with QwQ-32B-Preview.

Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how should model training be modified to optimize performance under a subsequent test-time compute strategy and budget? To explore this, we focus on pass@N, a simple test-time strategy that searches for a correct answer in N independent samples. We show, surprisingly, that training with cross-entropy (CE) loss can be {it misaligned} with pass@N in that pass@N accuracy {it decreases} with longer training. We explain the origins of this misalignment in terms of model overconfidence induced by CE, and experimentally verify our prediction of overconfidence as an impediment to scaling test-time compute via pass@N. Furthermore we suggest a principled, modified training loss that is better aligned to pass@N by limiting model confidence and rescuing pass@N test performance. Our algorithm demonstrates improved mathematical reasoning on MATH and MiniF2F benchmarks under several scenarios: (1) providing answers to math questions; and (2) proving theorems by searching over proof trees of varying shapes. Overall our work underscores the importance of co-designing two traditionally separate phases of LLM development: training-time protocols and test-time search and reasoning strategies.

Recent advances in large language models (LLMs) have enabled near-human performance on software coding benchmarks, but their effectiveness in RTL code generation remains limited due to the scarcity of high-quality training data. While prior efforts have fine-tuned LLMs for RTL tasks, they do not fundamentally overcome the data bottleneck and lack support for test-time scaling due to their non-reasoning nature. In this work, we introduce ScaleRTL, the first reasoning LLM for RTL coding that scales up both high-quality reasoning data and test-time compute. Specifically, we curate a diverse set of long chain-of-thought reasoning traces averaging 56K tokens each, resulting in a dataset of 3.5B tokens that captures rich RTL knowledge. Fine-tuning a general-purpose reasoning model on this corpus yields ScaleRTL that is capable of deep RTL reasoning. Subsequently, we further enhance the performance of ScaleRTL through a novel test-time scaling strategy that extends the reasoning process via iteratively reflecting on and self-correcting previous reasoning steps. Experimental results show that ScaleRTL achieves state-of-the-art performance on VerilogEval and RTLLM, outperforming 18 competitive baselines by up to 18.4% on VerilogEval and 12.7% on RTLLM.

We propose a general two-stage algorithm that enjoys a provable scaling law for the test-time compute of large language models (LLMs). Given an input problem, the proposed algorithm first generates N candidate solutions, and then chooses the best one via a multiple-round knockout tournament where each pair of candidates are compared for K times and only the winners move on to the next round. In a minimalistic implementation, both stages can be executed with a black-box LLM alone and nothing else (e.g., no external verifier or reward model), and a total of N times (K + 1) highly parallelizable LLM calls are needed for solving an input problem. Assuming that a generated candidate solution is correct with probability p_{gen} > 0 and a comparison between a pair of correct and incorrect solutions identifies the right winner with probability p_{comp} > 0.5 (i.e., better than a random guess), we prove theoretically that the failure probability of the proposed algorithm decays to zero exponentially with respect to N and K: $P(final output is incorrect) le (1 - p_{gen})^N + lceil log_2 N rceil e^{-2 K (p_{comp} - 0.5)^2}.$ Our empirical results with the challenging MMLU-Pro benchmark validate the technical assumptions, as well as the efficacy of the proposed algorithm and the gains from scaling up its test-time compute.

Increasing test-time compute for LLMs shows promise across domains but remains underexplored in code generation, despite extensive study in math. In this paper, we propose S*, the first hybrid test-time scaling framework that substantially improves the coverage and selection accuracy of generated code. S* extends the existing parallel scaling paradigm with sequential scaling to push performance boundaries. It further leverages a novel selection mechanism that adaptively generates distinguishing inputs for pairwise comparison, combined with execution-grounded information to robustly identify correct solutions. We evaluate across 12 Large Language Models and Large Reasoning Model and show: (1) S* consistently improves performance across model families and sizes, enabling a 3B model to outperform GPT-4o-mini; (2) S* enables non-reasoning models to surpass reasoning models - GPT-4o-mini with S* outperforms o1-preview by 3.7% on LiveCodeBench; (3) S* further boosts state-of-the-art reasoning models - DeepSeek-R1-Distill-Qwen-32B with S* achieves 85.7% on LiveCodeBench, approaching o1 (high) at 88.5%. Code will be available under https://github.com/NovaSky-AI/SkyThought.

Test-time scaling is a promising new approach to language modeling that uses extra test-time compute to improve performance. Recently, OpenAI's o1 model showed this capability but did not publicly share its methodology, leading to many replication efforts. We seek the simplest approach to achieve test-time scaling and strong reasoning performance. First, we curate a small dataset s1K of 1,000 questions paired with reasoning traces relying on three criteria we validate through ablations: difficulty, diversity, and quality. Second, we develop budget forcing to control test-time compute by forcefully terminating the model's thinking process or lengthening it by appending "Wait" multiple times to the model's generation when it tries to end. This can lead the model to double-check its answer, often fixing incorrect reasoning steps. After supervised finetuning the Qwen2.5-32B-Instruct language model on s1K and equipping it with budget forcing, our model s1 exceeds o1-preview on competition math questions by up to 27% (MATH and AIME24). Further, scaling s1 with budget forcing allows extrapolating beyond its performance without test-time intervention: from 50% to 57% on AIME24. Our model, data, and code are open-source at https://github.com/simplescaling/s1.

Scaling the test-time compute of large language models has demonstrated impressive performance on reasoning benchmarks. However, existing evaluations of test-time scaling make the strong assumption that a reasoning system should always give an answer to any question provided. This overlooks concerns about whether a model is confident in its answer, and whether it is appropriate to always provide a response. To address these concerns, we extract confidence scores during reasoning for thresholding model responses. We find that increasing compute budget at inference time not only helps models answer more questions correctly, but also increases confidence in correct responses. We then extend the current paradigm of zero-risk responses during evaluation by considering settings with non-zero levels of response risk, and suggest a recipe for reporting evaluations under these settings.

The new paradigm of test-time scaling has yielded remarkable breakthroughs in Large Language Models (LLMs) (e.g. reasoning models) and in generative vision models, allowing models to allocate additional computation during inference to effectively tackle increasingly complex problems. Despite the improvements of this approach, an important limitation emerges: the substantial increase in computation time makes the process slow and impractical for many applications. Given the success of this paradigm and its growing usage, we seek to preserve its benefits while eschewing the inference overhead. In this work we propose one solution to the critical problem of integrating test-time scaling knowledge into a model during post-training. Specifically, we replace reward guided test-time noise optimization in diffusion models with a Noise Hypernetwork that modulates initial input noise. We propose a theoretically grounded framework for learning this reward-tilted distribution for distilled generators, through a tractable noise-space objective that maintains fidelity to the base model while optimizing for desired characteristics. We show that our approach recovers a substantial portion of the quality gains from explicit test-time optimization at a fraction of the computational cost. Code is available at https://github.com/ExplainableML/HyperNoise

We rethink test-time scaling laws from a practical efficiency perspective, revealing that the effectiveness of smaller models is significantly overestimated. Prior work, grounded in compute-optimality, overlooks critical memory access bottlenecks introduced by inference-time strategies (e.g., Best-of-N, long CoTs). Our holistic analysis, spanning models from 0.6B to 32B parameters, reveals a new Kinetics Scaling Law that better guides resource allocation by incorporating both computation and memory access costs. Kinetics Scaling Law suggests that test-time compute is more effective when used on models above a threshold than smaller ones. A key reason is that in TTS, attention, rather than parameter count, emerges as the dominant cost factor. Motivated by this, we propose a new scaling paradigm centered on sparse attention, which lowers per-token cost and enables longer generations and more parallel samples within the same resource budget. Empirically, we show that sparse attention models consistently outperform dense counterparts, achieving over 60 points gains in low-cost regimes and over 5 points gains in high-cost regimes for problem-solving accuracy on AIME, encompassing evaluations on state-of-the-art MoEs. These results suggest that sparse attention is essential for realizing the full potential of test-time scaling because, unlike training, where parameter scaling saturates, test-time accuracy continues to improve through increased generation. The code is available at https://github.com/Infini-AI-Lab/Kinetics.

With the scale capability of increasing training data, model size, and computational cost, video generation has achieved impressive results in digital creation, enabling users to express creativity across various domains. Recently, researchers in Large Language Models (LLMs) have expanded the scaling to test-time, which can significantly improve LLM performance by using more inference-time computation. Instead of scaling up video foundation models through expensive training costs, we explore the power of Test-Time Scaling (TTS) in video generation, aiming to answer the question: if a video generation model is allowed to use non-trivial amount of inference-time compute, how much can it improve generation quality given a challenging text prompt. In this work, we reinterpret the test-time scaling of video generation as a searching problem to sample better trajectories from Gaussian noise space to the target video distribution. Specifically, we build the search space with test-time verifiers to provide feedback and heuristic algorithms to guide searching process. Given a text prompt, we first explore an intuitive linear search strategy by increasing noise candidates at inference time. As full-step denoising all frames simultaneously requires heavy test-time computation costs, we further design a more efficient TTS method for video generation called Tree-of-Frames (ToF) that adaptively expands and prunes video branches in an autoregressive manner. Extensive experiments on text-conditioned video generation benchmarks demonstrate that increasing test-time compute consistently leads to significant improvements in the quality of videos. Project page: https://liuff19.github.io/Video-T1

Effective reasoning is crucial to solving complex mathematical problems. Recent large language models (LLMs) have boosted performance by scaling test-time computation through long chain-of-thought reasoning. However, transformer-based models are inherently limited in extending context length due to their quadratic computational complexity and linear memory requirements. In this paper, we introduce a novel hybrid linear RNN reasoning model, M1, built on the Mamba architecture, which allows memory-efficient inference. Our approach leverages a distillation process from existing reasoning models and is further enhanced through RL training. Experimental results on the AIME and MATH benchmarks show that M1 not only outperforms previous linear RNN models but also matches the performance of state-of-the-art Deepseek R1 distilled reasoning models at a similar scale. We also compare our generation speed with a highly performant general purpose inference engine, vLLM, and observe more than a 3x speedup compared to a same size transformer. With throughput speedup, we are able to achieve higher accuracy compared to DeepSeek R1 distilled transformer reasoning models under a fixed generation time budget using self-consistency voting. Overall, we introduce a hybrid Mamba reasoning model and provide a more effective approach to scaling test-time generation using self-consistency or long chain of thought reasoning.

As language model (LM) outputs get more and more natural, it is becoming more difficult than ever to evaluate their quality. Simultaneously, increasing LMs' "thinking" time through scaling test-time compute has proven an effective technique to solve challenging problems in domains such as math and code. This raises a natural question: can an LM's evaluation capability also be improved by spending more test-time compute? To answer this, we investigate employing reasoning models-LMs that natively generate long chain-of-thought reasoning-as evaluators. Specifically, we examine methods to leverage more test-time compute by (1) using reasoning models, and (2) prompting these models to evaluate not only the response as a whole (i.e., outcome evaluation) but also assess each step in the response separately (i.e., process evaluation). In experiments, we observe that the evaluator's performance improves monotonically when generating more reasoning tokens, similar to the trends observed in LM-based generation. Furthermore, we use these more accurate evaluators to rerank multiple generations, and demonstrate that spending more compute at evaluation time can be as effective as using more compute at generation time in improving an LM's problem-solving capability.

Large reasoning models (LRMs) have exhibited the capacity of enhancing reasoning performance via internal test-time scaling. Building upon this, a promising direction is to further scale test-time compute to unlock even greater reasoning capabilities. However, as we push these scaling boundaries, systematically understanding the practical limits and achieving optimal resource allocation becomes a critical challenge. In this paper, we investigate the scaling Pareto of test-time scaling and introduce the Test-Time Scaling Performance Model (TTSPM). We theoretically analyze two fundamental paradigms for such extended scaling, parallel scaling and sequential scaling, from a probabilistic modeling perspective. Our primary contribution is the derivation of the saturation point on the scaling budget for both strategies, identifying thresholds beyond which additional computation yields diminishing returns. Remarkably, despite their distinct mechanisms, both paradigms converge to a unified mathematical structure in their upper bounds. We empirically validate our theoretical findings on challenging reasoning benchmarks, including AIME, MATH-500, and GPQA, demonstrating the practical utility of these bounds for test-time resource allocation. We hope that this work provides insights into the cost-benefit trade-offs of test-time scaling, guiding the development of more resource-efficient inference strategies for large reasoning models.

Recent advancements in Large Language Models (LLMs) have created new opportunities to enhance performance on complex reasoning tasks by leveraging test-time computation. However, conventional approaches such as repeated sampling with majority voting or reward model scoring, often face diminishing returns as test-time compute scales, in addition to requiring costly task-specific reward model training. In this paper, we present Self-Enhanced Test-Time Scaling (SETS), a novel method that leverages the self-verification and self-correction capabilities of recent advanced LLMs to overcome these limitations. SETS integrates sampling, self-verification, and self-correction into a unified framework, enabling efficient and scalable test-time computation for improved capabilities at complex tasks. Through extensive experiments on challenging planning and reasoning benchmarks, compared to the alternatives, we demonstrate that SETS achieves significant performance improvements and more favorable test-time scaling laws.

This paper presents a simple, effective, and cost-efficient strategy to improve LLM performance by scaling test-time compute. Our strategy builds upon the repeated-sampling-then-voting framework, with a novel twist: incorporating multiple models, even weaker ones, to leverage their complementary strengths that potentially arise from diverse training data and paradigms. By using consistency as a signal, our strategy dynamically switches between models. Theoretical analysis highlights the efficiency and performance advantages of our strategy. Extensive experiments on six datasets demonstrate that our strategy not only outperforms self-consistency and state-of-the-art multi-agent debate approaches, but also significantly reduces inference costs. Additionally, ModelSwitch requires only a few comparable LLMs to achieve optimal performance and can be extended with verification methods, demonstrating the potential of leveraging multiple LLMs in the generation-verification paradigm.

Test-time compute has emerged as a powerful paradigm for improving the performance of large language models (LLMs), where generating multiple outputs or refining individual chains can significantly boost answer accuracy. However, existing methods like Best-of-N, majority voting, and self-reflection typically apply reasoning in a uniform way across inputs, overlooking the fact that different problems may require different levels of reasoning depth. In this work, we propose Fractional Reasoning, a training-free and model-agnostic framework that enables continuous control over reasoning intensity at inference time, going beyond the limitations of fixed instructional prompts. Our method operates by extracting the latent steering vector associated with deeper reasoning and reapplying it with a tunable scaling factor, allowing the model to tailor its reasoning process to the complexity of each input. This supports two key modes of test-time scaling: (1) improving output quality in breadth-based strategies (e.g., Best-of-N, majority voting), and (2) enhancing the correctness of individual reasoning chains in depth-based strategies (e.g., self-reflection). Experiments on GSM8K, MATH500, and GPQA demonstrate that Fractional Reasoning consistently improves performance across diverse reasoning tasks and models.

Sampling-based search, a simple paradigm for utilizing test-time compute, involves generating multiple candidate responses and selecting the best one -- typically by verifying each response for correctness. In this paper, we study the scaling trends governing sampling-based search. Among our findings is that simply scaling up a minimalist implementation that uses only random sampling and direct self-verification results in sustained performance improvements that, for example, elevate the Gemini v1.5 Pro model's reasoning capabilities past that of o1-Preview on popular benchmarks. We partially attribute the scalability of sampling-based search to a phenomenon of implicit scaling, where sampling a larger pool of responses in turn improves verification accuracy. We further identify two useful principles for improving self-verification capabilities with test-time compute: (1) comparing across responses provides helpful signals about the locations of errors and hallucinations, and (2) different model output styles are useful for different contexts -- chains of thought are useful for reasoning but harder to verify. We also find that, though accurate verification can be elicited, frontier models demonstrate remarkably weak out-of-box verification capabilities and introduce a benchmark to measure progress on these deficiencies.

Scaling test-time compute has emerged as a key strategy for enhancing the reasoning capabilities of large language models (LLMs), particularly in tasks like mathematical problem-solving. A traditional approach, Self-Consistency (SC), generates multiple solutions to a problem and selects the most common answer via majority voting. Another common method involves scoring each solution with a reward model (verifier) and choosing the best one. Recent advancements in Generative Reward Models (GenRM) reframe verification as a next-token prediction task, enabling inference-time scaling along a new axis. Specifically, GenRM generates multiple verification chains-of-thought to score each solution. Under a limited inference budget, this introduces a fundamental trade-off: should you spend the budget on scaling solutions via SC or generate fewer solutions and allocate compute to verification via GenRM? To address this, we evaluate GenRM against SC under a fixed inference budget. Interestingly, we find that SC is more compute-efficient than GenRM for most practical inference budgets across diverse models and datasets. For instance, GenRM first matches SC after consuming up to 8x the inference compute and requires significantly more compute to outperform it. Furthermore, we derive inference scaling laws for the GenRM paradigm, revealing that compute-optimal inference favors scaling solution generation more aggressively than scaling the number of verifications. Our work provides practical guidance on optimizing test-time scaling by balancing solution generation and verification. The code is available at https://github.com/nishadsinghi/sc-genrm-scaling.

The scaling of inference computation has unlocked the potential of long-context large language models (LLMs) across diverse settings. For knowledge-intensive tasks, the increased compute is often allocated to incorporate more external knowledge. However, without effectively utilizing such knowledge, solely expanding context does not always enhance performance. In this work, we investigate inference scaling for retrieval augmented generation (RAG), exploring strategies beyond simply increasing the quantity of knowledge. We focus on two inference scaling strategies: in-context learning and iterative prompting. These strategies provide additional flexibility to scale test-time computation (e.g., by increasing retrieved documents or generation steps), thereby enhancing LLMs' ability to effectively acquire and utilize contextual information. We address two key questions: (1) How does RAG performance benefit from the scaling of inference computation when optimally configured? (2) Can we predict the optimal test-time compute allocation for a given budget by modeling the relationship between RAG performance and inference parameters? Our observations reveal that increasing inference computation leads to nearly linear gains in RAG performance when optimally allocated, a relationship we describe as the inference scaling laws for RAG. Building on this, we further develop the computation allocation model to estimate RAG performance across different inference configurations. The model predicts optimal inference parameters under various computation constraints, which align closely with the experimental results. By applying these optimal configurations, we demonstrate that scaling inference compute on long-context LLMs achieves up to 58.9% gains on benchmark datasets compared to standard RAG.

Recent studies on large language model (LLM) reasoning capabilities have demonstrated promising improvements in model performance by leveraging a lengthy thinking process and additional computational resources during inference, primarily in tasks involving mathematical reasoning (Muennighoff et al., 2025). However, it remains uncertain if longer reasoning chains inherently enhance factual accuracy, particularly beyond mathematical contexts. In this work, we thoroughly examine LLM reasoning within complex open-domain question-answering (QA) scenarios. We initially distill reasoning traces from advanced, large-scale reasoning models (QwQ-32B and DeepSeek-R1-671B), then fine-tune a variety of models ranging from smaller, instruction-tuned variants to larger architectures based on Qwen2.5. To enrich reasoning traces, we introduce factual information from knowledge graphs in the form of paths into our reasoning traces. Our experimental setup includes four baseline approaches and six different instruction-tuned models evaluated across a benchmark of six datasets, encompassing over 22.6K questions. Overall, we carry out 168 experimental runs and analyze approximately 1.7 million reasoning traces. Our findings indicate that, within a single run, smaller reasoning models achieve noticeable improvements in factual accuracy compared to their original instruction-tuned counterparts. Moreover, our analysis demonstrates that adding test-time compute and token budgets factual accuracy consistently improves by 2-8%, further confirming the effectiveness of test-time scaling for enhancing performance and consequently improving reasoning accuracy in open-domain QA tasks. We release all the experimental artifacts for further research.

We introduce Goedel-Prover-V2, a series of open-source language models that set a new state-of-the-art in automated theorem proving. Built on the standard expert iteration and reinforcement learning pipeline, our approach incorporates three key innovations: (1) Scaffolded data synthesis: We generate synthetic tasks of increasing difficulty to train the model to master increasingly complex theorems; (2) Verifier-guided self-correction: We enable the model to iteratively revise its proofs by leveraging feedback from the Lean compiler; (3) Model averaging: We merge model checkpoints to mitigate the decrease in model output diversity in later stages of training. Our small model, Goedel-Prover-V2-8B, reaches 84.6% pass@32 on MiniF2F and outperforms DeepSeek-Prover-V2-671B under the same metric, despite being 80X smaller. Our flagship model, Goedel-Prover-V2-32B, achieves 88.1% on MiniF2F at pass@32 in standard mode and 90.4% in self-correction mode, outperforming prior SOTA by a large margin. Additionally, our flagship model solves 86 problems on PutnamBench at pass@184, securing the first place among open-source models on the leaderboard, surpassing DeepSeek-Prover-V2-671B's record of solving 47 problems by pass@1024 with a significantly smaller model size and compute budget. At the time of its release (July-August 2025), Goedel-Prover-V2 achieves the strongest overall performance among all open-source theorem provers. It also ranks among the top-performing models--including closed-source systems with publicly reported performance--under a constrained test-time compute budget. Our models, code, and data are released at https://github.com/Goedel-LM/Goedel-Prover-V2.

Vision-language models (VLMs) trained via reinforcement learning with verifiable reward (RLVR) have shown notable progress in scaling test-time compute effectively. In this work, we investigate how synthesized RL data can further improve RLVR. To this end, we propose SynthRL-a scalable and guaranteed pipeline for automatic data scaling in reasoning-oriented RL training. SynthRL comprises three key stages: (1) selecting seed questions with appropriate distribution, (2) augmenting them into more challenging variants while preserving the original answers, and (3) a guaranteed verification stage that ensures near-perfect correctness and difficulty enhancement. Our empirical experiments demonstrate SynthRL's scalability and effectiveness. When applied to the MMK12 dataset, SynthRL synthesizes over 3.3K additional verifiable, challenging questions from approximately 8K seed samples. Models trained with our synthesized data achieve consistent gains across five out-of-domain visual math reasoning benchmarks, with a significant improvement over baseline models trained on seed data alone. Notably, detailed analysis reveals that the gains are more pronounced on the most challenging evaluation samples, highlighting SynthRL's effectiveness in eliciting deeper and more complex reasoning patterns.

The largest experiments in machine learning now require resources far beyond the budget of all but a few institutions. Fortunately, it has recently been shown that the results of these huge experiments can often be extrapolated from the results of a sequence of far smaller, cheaper experiments. In this work, we show that not only can the extrapolation be done based on the size of the model, but on the size of the problem as well. By conducting a sequence of experiments using AlphaZero and Hex, we show that the performance achievable with a fixed amount of compute degrades predictably as the game gets larger and harder. Along with our main result, we further show that the test-time and train-time compute available to an agent can be traded off while maintaining performance.

High-resolution perception of visual details is crucial for daily tasks. Current vision pre-training, however, is still limited to low resolutions (e.g., 378 x 378 pixels) due to the quadratic cost of processing larger images. We introduce PS3 that scales CLIP-style vision pre-training to 4K resolution with a near-constant cost. Instead of contrastive learning on global image representation, PS3 is pre-trained by selectively processing local regions and contrasting them with local detailed captions, enabling high-resolution representation learning with greatly reduced computational overhead. The pre-trained PS3 is able to both encode the global image at low resolution and selectively process local high-resolution regions based on their saliency or relevance to a text prompt. When applying PS3 to multi-modal LLM (MLLM), the resulting model, named VILA-HD, significantly improves high-resolution visual perception compared to baselines without high-resolution vision pre-training such as AnyRes and S^2 while using up to 4.3x fewer tokens. PS3 also unlocks appealing scaling properties of VILA-HD, including scaling up resolution for free and scaling up test-time compute for better performance. Compared to state of the arts, VILA-HD outperforms previous MLLMs such as NVILA and Qwen2-VL across multiple benchmarks and achieves better efficiency than latest token pruning approaches. Finally, we find current benchmarks do not require 4K-resolution perception, which motivates us to propose 4KPro, a new benchmark of image QA at 4K resolution, on which VILA-HD outperforms all previous MLLMs, including a 14.5% improvement over GPT-4o, and a 3.2% improvement and 2.96x speedup over Qwen2-VL.

In this paper, we argue that iterative computation with diffusion models offers a powerful paradigm for not only generation but also visual perception tasks. We unify tasks such as depth estimation, optical flow, and segmentation under image-to-image translation, and show how diffusion models benefit from scaling training and test-time compute for these perception tasks. Through a careful analysis of these scaling behaviors, we present various techniques to efficiently train diffusion models for visual perception tasks. Our models achieve improved or comparable performance to state-of-the-art methods using significantly less data and compute. To use our code and models, see https://scaling-diffusion-perception.github.io .

Scaling test-time compute is crucial for enhancing the reasoning capabilities of large language models (LLMs). Existing approaches typically employ reinforcement learning (RL) to maximize a verifiable reward obtained at the end of reasoning traces. However, such methods optimize only the final performance under a large and fixed token budget, which hinders efficiency in both training and deployment. In this work, we present a novel framework, AnytimeReasoner, to optimize anytime reasoning performance, which aims to improve token efficiency and the flexibility of reasoning under varying token budget constraints. To achieve this, we truncate the complete thinking process to fit within sampled token budgets from a prior distribution, compelling the model to summarize the optimal answer for each truncated thinking for verification. This introduces verifiable dense rewards into the reasoning process, facilitating more effective credit assignment in RL optimization. We then optimize the thinking and summary policies in a decoupled manner to maximize the cumulative reward. Additionally, we introduce a novel variance reduction technique, Budget Relative Policy Optimization (BRPO), to enhance the robustness and efficiency of the learning process when reinforcing the thinking policy. Empirical results in mathematical reasoning tasks demonstrate that our method consistently outperforms GRPO across all thinking budgets under various prior distributions, enhancing both training and token efficiency.

Scaling test-time compute brings substantial performance gains for large language models (LLMs). By sampling multiple answers and heuristically aggregate their answers (e.g., either through majority voting or using verifiers to rank the answers), one can achieve consistent performance gains in math domains. In this paper, we propose a new way to leverage such multiple sample set. We train a compact LLM, called Sample Set Aggregator (SSA), that takes a concatenated sequence of multiple samples and output the final answer, optimizing it for the answer accuracy with reinforcement learning. Experiments on multiple reasoning datasets show that SSA outperforms other test-time scaling methods such as reward model-based re-ranking. Our approach also shows a promising generalization ability, across sample set sizes, base model families and scales, and tasks. By separating LLMs to generate answers and LLMs to analyze and aggregate sampled answers, our approach can work with the outputs from premier black box models easily and efficiently.

Scaling up test-time compute, by generating multiple independent solutions and selecting or aggregating among them, has become a central paradigm for improving large language models (LLMs) on challenging reasoning tasks. While most prior work relies on simple majority voting or reward model ranking to aggregate solutions, these approaches may only yield limited benefits. In this work, we propose to learn aggregation as an explicit reasoning skill: given a set of candidate solutions, we train an aggregator model to review, reconcile, and synthesize a final, correct answer using reinforcement learning from verifiable rewards. A key ingredient is careful balancing of easy and hard training examples, allowing the model to learn both to recover minority-but-correct answers as well as easy majority-correct answers. Empirically, we find our method, AggLM, outperforms both strong rule-based and reward-model baselines, across multiple benchmarks. Furthermore, it generalizes effectively to solutions from differing models, including stronger ones than contained in the training data, all while requiring substantially fewer tokens than majority voting with larger numbers of solutions.

Recent research enhances language model reasoning by scaling test-time compute via longer chain-of-thought traces. This often improves accuracy but also introduces redundancy and high computational cost, especially for small language models distilled with supervised fine-tuning (SFT). In this work, we propose new algorithms to improve token-efficient reasoning with small-scale models by effectively trading off accuracy and computation. We first show that the post-SFT model fails to determine the optimal stopping point of the reasoning process, resulting in verbose and repetitive outputs. Verbosity also significantly varies across wrong vs correct responses. To address these issues, we propose two solutions: (1) Temperature scaling (TS) to control the stopping point for the thinking phase and thereby trace length, and (2) TLDR: a length-regularized reinforcement learning method based on GRPO that facilitates multi-level trace length control (e.g. short, medium, long reasoning). Experiments on four reasoning benchmarks, MATH500, AMC, AIME24 and OlympiadBench, demonstrate that TS is highly effective compared to s1's budget forcing approach and TLDR significantly improves token efficiency by about 50% with minimal to no accuracy loss over the SFT baseline. Moreover, TLDR also facilitates flexible control over the response length, offering a practical and effective solution for token-efficient reasoning in small models. Ultimately, our work reveals the importance of stopping time control, highlights shortcomings of pure SFT, and provides effective algorithmic recipes.

Reasoning large language models (LLMs) heavily rely on scaling test-time compute to perform complex reasoning tasks by generating extensive "thinking" chains. While demonstrating impressive results, this approach incurs significant computational costs and inference time. In this work, we challenge the assumption that long thinking chains results in better reasoning capabilities. We first demonstrate that shorter reasoning chains within individual questions are significantly more likely to yield correct answers - up to 34.5% more accurate than the longest chain sampled for the same question. Based on these results, we suggest short-m@k, a novel reasoning LLM inference method. Our method executes k independent generations in parallel and halts computation once the first m thinking processes are done. The final answer is chosen using majority voting among these m chains. Basic short-1@k demonstrates similar or even superior performance over standard majority voting in low-compute settings - using up to 40% fewer thinking tokens. short-3@k, while slightly less efficient than short-1@k, consistently surpasses majority voting across all compute budgets, while still being substantially faster (up to 33% wall time reduction). Inspired by our results, we finetune an LLM using short, long, and randomly selected reasoning chains. We then observe that training on the shorter ones leads to better performance. Our findings suggest rethinking current methods of test-time compute in reasoning LLMs, emphasizing that longer "thinking" does not necessarily translate to improved performance and can, counter-intuitively, lead to degraded results.

Recent thinking models solve complex reasoning tasks by scaling test-time compute, but this scaling must be allocated in line with task difficulty. On one hand, short reasoning (underthinking) leads to errors on harder problems that require extended reasoning steps; but, excessively long reasoning (overthinking) can be token-inefficient, generating unnecessary steps even after reaching a correct intermediate solution. We refer to this as under-adaptivity, where the model fails to modulate its response length appropriately given problems of varying difficulty. To address under-adaptivity and strike a balance between under- and overthinking, we propose TRAAC (Think Right with Adaptive, Attentive Compression), an online post-training RL method that leverages the model's self-attention over a long reasoning trajectory to identify important steps and prune redundant ones. TRAAC also estimates difficulty and incorporates it into training rewards, thereby learning to allocate reasoning budget commensurate with example difficulty. Our approach improves accuracy, reduces reasoning steps, and enables adaptive thinking compared to base models and other RL baselines. Across a variety of tasks (AIME, AMC, GPQA-D, BBEH), TRAAC (Qwen3-4B) achieves an average absolute accuracy gain of 8.4% with a relative reduction in reasoning length of 36.8% compared to the base model, and a 7.9% accuracy gain paired with a 29.4% length drop compared to the best RL baseline. TRAAC also shows strong generalization: although our models are trained on math datasets, they show accuracy and efficiency gains on out-of-distribution non-math datasets like GPQA-D, BBEH, and OptimalThinkingBench. Our analysis further verifies that TRAAC provides fine-grained adjustments to thinking budget based on difficulty and that a combination of task-difficulty calibration and attention-based compression yields gains across diverse tasks.

Large language models (LLMs) benefit from increased test-time compute, a phenomenon known as test-time scaling. However, reasoning-optimized models often overthink even simple problems, producing excessively verbose outputs and leading to low token efficiency. By comparing these models with equally sized instruct models, we identify two key causes of this verbosity: (1) reinforcement learning reduces the information density of forward reasoning, and (2) backward chain-of thought training encourages redundant and often unnecessary verification steps. Since LLMs cannot assess the difficulty of a given problem, they tend to apply the same cautious reasoning strategy across all tasks, resulting in inefficient overthinking. To address this, we propose CoThink, an embarrassingly simple pipeline: an instruct model first drafts a high-level solution outline; a reasoning model then works out the solution. We observe that CoThink enables dynamic adjustment of reasoning depth based on input difficulty. Evaluated with three reasoning models DAPO, DeepSeek-R1, and QwQ on three datasets GSM8K, MATH500, and AIME24, CoThink reduces total token generation by 22.3% while maintaining pass@1 accuracy within a 0.42% margin on average. With reference to the instruct model, we formally define reasoning efficiency and observe a potential reasoning efficiency scaling law in LLMs.

Recent advances in large language models (LLMs) demonstrate their effectiveness in scaling test-time compute for software engineering tasks. However, these approaches often focus on high-level solutions, with limited attention to optimizing low-level CUDA kernel implementations. Additionally, existing kernel generation benchmarks suffer from exploitable loopholes and insufficient diversity in testing conditions, hindering true generalization assessment. To address these limitations, we introduce robust-kbench, a new benchmark for rigorous evaluation of kernel performance and correctness across varied scenarios. Furthermore, we present a comprehensive agentic framework that automates CUDA kernel discovery, verification, and optimization. This pipeline enables frontier LLMs to translate torch code to CUDA kernels and iteratively improve their runtime within our robust evaluation setting. Our sequential workflow first translates PyTorch code into equivalent CUDA kernels. It then optimizes their runtime using a novel evolutionary meta-generation procedure tailored to the CUDA ecosystem, guided by LLM-based verifiers for correctness and efficient filtering. Evaluated on robust-kbench, our approach produces CUDA kernels outperforming torch implementations for practical applications, including forward and backward passes. It can fuse operations and deploy various runtime optimization strategies. The verifier workflow accurately classifies incorrect kernels, enhancing hardware verification efficiency.

Recent advancements in large language models have significantly improved their reasoning abilities, particularly through techniques involving search and backtracking. Backtracking naturally scales test-time compute by enabling sequential, linearized exploration via long chain-of-thought (CoT) generation. However, this is not the only strategy for scaling test-time compute: parallel sampling with best-of-n selection provides an alternative that generates diverse solutions simultaneously. Despite the growing adoption of sequential search, its advantages over parallel sampling--especially under a fixed compute budget remain poorly understood. In this paper, we systematically compare these two approaches on two challenging reasoning tasks: CountDown and Sudoku. Surprisingly, we find that sequential search underperforms parallel sampling on CountDown but outperforms it on Sudoku, suggesting that backtracking is not universally beneficial. We identify two factors that can cause backtracking to degrade performance: (1) training on fixed search traces can lock models into suboptimal strategies, and (2) explicit CoT supervision can discourage "implicit" (non-verbalized) reasoning. Extending our analysis to reinforcement learning (RL), we show that models with backtracking capabilities benefit significantly from RL fine-tuning, while models without backtracking see limited, mixed gains. Together, these findings challenge the assumption that backtracking universally enhances LLM reasoning, instead revealing a complex interaction between task structure, training data, model scale, and learning paradigm.

Large language models (LLMs) such as OpenAI's o1 have demonstrated remarkable abilities in complex reasoning tasks by scaling test-time compute and exhibiting human-like deep thinking. However, we identify a phenomenon we term underthinking, where o1-like LLMs frequently switch between different reasoning thoughts without sufficiently exploring promising paths to reach a correct solution. This behavior leads to inadequate depth of reasoning and decreased performance, particularly on challenging mathematical problems. To systematically analyze this issue, we conduct experiments on three challenging test sets and two representative open-source o1-like models, revealing that frequent thought switching correlates with incorrect responses. We introduce a novel metric to quantify underthinking by measuring token efficiency in incorrect answers. To address underthinking, we propose a decoding strategy with thought switching penalty TIP that discourages premature transitions between thoughts, encouraging deeper exploration of each reasoning path. Experimental results demonstrate that our approach improves accuracy across challenging datasets without requiring model fine-tuning. Our findings contribute to understanding reasoning inefficiencies in o1-like LLMs and offer a practical solution to enhance their problem-solving capabilities.

We present AMO-Bench, an Advanced Mathematical reasoning benchmark with Olympiad level or even higher difficulty, comprising 50 human-crafted problems. Existing benchmarks have widely leveraged high school math competitions for evaluating mathematical reasoning capabilities of large language models (LLMs). However, many existing math competitions are becoming less effective for assessing top-tier LLMs due to performance saturation (e.g., AIME24/25). To address this, AMO-Bench introduces more rigorous challenges by ensuring all 50 problems are (1) cross-validated by experts to meet at least the International Mathematical Olympiad (IMO) difficulty standards, and (2) entirely original problems to prevent potential performance leakages from data memorization. Moreover, each problem in AMO-Bench requires only a final answer rather than a proof, enabling automatic and robust grading for evaluation. Experimental results across 26 LLMs on AMO-Bench show that even the best-performing model achieves only 52.4% accuracy on AMO-Bench, with most LLMs scoring below 40%. Beyond these poor performances, our further analysis reveals a promising scaling trend with increasing test-time compute on AMO-Bench. These results highlight the significant room for improving the mathematical reasoning in current LLMs. We release AMO-Bench to facilitate further research into advancing the reasoning abilities of language models. https://amo-bench.github.io/

The sequential structure of videos poses a challenge to the ability of multimodal large language models (MLLMs) to locate multi-frame evidence and conduct multimodal reasoning. However, existing video benchmarks mainly focus on understanding tasks, which only require models to match frames mentioned in the question (hereafter referred to as "question frame") and perceive a few adjacent frames. To address this gap, we propose MMR-V: A Benchmark for Multimodal Deep Reasoning in Videos. The benchmark is characterized by the following features. (1) Long-range, multi-frame reasoning: Models are required to infer and analyze evidence frames that may be far from the question frame. (2) Beyond perception: Questions cannot be answered through direct perception alone but require reasoning over hidden information. (3) Reliability: All tasks are manually annotated, referencing extensive real-world user understanding to align with common perceptions. (4) Confusability: Carefully designed distractor annotation strategies to reduce model shortcuts. MMR-V consists of 317 videos and 1,257 tasks. Our experiments reveal that current models still struggle with multi-modal reasoning; even the best-performing model, o4-mini, achieves only 52.5% accuracy. Additionally, current reasoning enhancement strategies (Chain-of-Thought and scaling test-time compute) bring limited gains. Further analysis indicates that the CoT demanded for multi-modal reasoning differs from it in textual reasoning, which partly explains the limited performance gains. We hope that MMR-V can inspire further research into enhancing multi-modal reasoning capabilities.

Large Reasoning Models(LRMs) such as OpenAI o1 and DeepSeek-R1 have shown remarkable reasoning capabilities by scaling test-time compute and generating long Chain-of-Thought(CoT). Distillation--post-training on LRMs-generated data--is a straightforward yet effective method to enhance the reasoning abilities of smaller models, but faces a critical bottleneck: we found that distilled long CoT data poses learning difficulty for small models and leads to the inheritance of biases (i.e. over-thinking) when using Supervised Fine-tuning(SFT) and Reinforcement Learning(RL) methods. To alleviate this bottleneck, we propose constructing tree-based CoT data from scratch via Monte Carlo Tree Search(MCTS). We then exploit a set of CoT-aware approaches, including Thoughts Length Balance, Fine-grained DPO, and Joint Post-training Objective, to enhance SFT and RL on the construted data.

This work presents a framework for assessing whether large language models (LLMs) encode more factual knowledge in their parameters than what they express in their outputs. While a few studies hint at this possibility, none has clearly defined or demonstrated this phenomenon. We first propose a formal definition of knowledge, quantifying it for a given question as the fraction of correct-incorrect answer pairs where the correct one is ranked higher. This gives rise to external and internal knowledge, depending on the information used to score individual answer candidates: either the model's observable token-level probabilities or its intermediate computations. Hidden knowledge arises when internal knowledge exceeds external knowledge. We then present a case study, applying this framework to three popular open-weights LLMs in a closed-book QA setup. Our results indicate that: (1) LLMs consistently encode more factual knowledge internally than what they express externally, with an average gap of 40%. (2) Surprisingly, some knowledge is so deeply hidden that a model can internally know an answer perfectly, yet fail to generate it even once, despite large-scale repeated sampling of 1,000 answers. This reveals fundamental limitations in the generation capabilities of LLMs, which (3) puts a practical constraint on scaling test-time compute via repeated answer sampling in closed-book QA: significant performance improvements remain inaccessible because some answers are practically never sampled, yet if they were, we would be guaranteed to rank them first.

Does continued scaling of large language models (LLMs) yield diminishing returns? Real-world value often stems from the length of task an agent can complete. We start this work by observing the simple but counterintuitive fact that marginal gains in single-step accuracy can compound into exponential improvements in the length of a task a model can successfully complete. Then, we argue that failures of LLMs when simple tasks are made longer arise from mistakes in execution, rather than an inability to reason. We propose isolating execution capability, by explicitly providing the knowledge and plan needed to solve a long-horizon task. We find that larger models can correctly execute significantly more turns even when small models have 100\% single-turn accuracy. We observe that the per-step accuracy of models degrades as the number of steps increases. This is not just due to long-context limitations -- curiously, we observe a self-conditioning effect -- models become more likely to make mistakes when the context contains their errors from prior turns. Self-conditioning does not reduce by just scaling the model size. In contrast, recent thinking models do not self-condition, and can also execute much longer tasks in a single turn. We conclude by benchmarking frontier thinking models on the length of task they can execute in a single turn. Overall, by focusing on the ability to execute, we hope to reconcile debates on how LLMs can solve complex reasoning problems yet fail at simple tasks when made longer, and highlight the massive benefits of scaling model size and sequential test-time compute for long-horizon tasks.

Test-time scaling (TTS) has proven effective in enhancing the reasoning capabilities of large language models (LLMs). Verification plays a key role in TTS, simultaneously influencing (1) reasoning performance and (2) compute efficiency, due to the quality and computational cost of verification. In this work, we challenge the conventional paradigms of verification, and make the first attempt toward systematically investigating the impact of verification granularity-that is, how frequently the verifier is invoked during generation, beyond verifying only the final output or individual generation steps. To this end, we introduce Variable Granularity Search (VG-Search), a unified algorithm that generalizes beam search and Best-of-N sampling via a tunable granularity parameter g. Extensive experiments with VG-Search under varying compute budgets, generator-verifier configurations, and task attributes reveal that dynamically selecting g can improve the compute efficiency and scaling behavior. Building on these findings, we propose adaptive VG-Search strategies that achieve accuracy gains of up to 3.1\% over Beam Search and 3.6\% over Best-of-N, while reducing FLOPs by over 52\%. We will open-source the code to support future research.

Test-Time Scaling (TTS) is an important method for improving the performance of Large Language Models (LLMs) by using additional computation during the inference phase. However, current studies do not systematically analyze how policy models, Process Reward Models (PRMs), and problem difficulty influence TTS. This lack of analysis limits the understanding and practical use of TTS methods. In this paper, we focus on two core questions: (1) What is the optimal approach to scale test-time computation across different policy models, PRMs, and problem difficulty levels? (2) To what extent can extended computation improve the performance of LLMs on complex tasks, and can smaller language models outperform larger ones through this approach? Through comprehensive experiments on MATH-500 and challenging AIME24 tasks, we have the following observations: (1) The compute-optimal TTS strategy is highly dependent on the choice of policy model, PRM, and problem difficulty. (2) With our compute-optimal TTS strategy, extremely small policy models can outperform larger models. For example, a 1B LLM can exceed a 405B LLM on MATH-500. Moreover, on both MATH-500 and AIME24, a 0.5B LLM outperforms GPT-4o, a 3B LLM surpasses a 405B LLM, and a 7B LLM beats o1 and DeepSeek-R1, while with higher inference efficiency. These findings show the significance of adapting TTS strategies to the specific characteristics of each task and model and indicate that TTS is a promising approach for enhancing the reasoning abilities of LLMs.

Test-time scaling improves large language model performance by adding extra compute during decoding. Best-of-N (BoN) sampling serves as a common scaling technique, broadening the search space for finding better solutions from the model distribution. However, traditional BoN requires N full generations, leading to high GPU memory overhead and time latency. Moreover, some methods depend on reward models, adding computational cost and limiting domain generalization. In this paper, we propose Self-Truncation Best-of-N (ST-BoN), a novel decoding method that avoids fully generating all samplings and eliminates the need for reward models. ST-BoN introduces early sampling consistency to estimate the most promising sample, truncating suboptimal ones to free memory and accelerate inference. This pushes the sampling-efficient test-time scaling. Compared to traditional BoN, ST-BoN can reduce dynamic GPU memory overhead by over 90% and time latency by 50%, while achieving comparable or even better performance across reasoning and open-ended domains.

Parallel test-time scaling (TTS) is a pivotal approach for enhancing large language models (LLMs), typically by sampling multiple token-based chains-of-thought in parallel and aggregating outcomes through voting or search. Recent advances in latent reasoning, where intermediate reasoning unfolds in continuous vector spaces, offer a more efficient alternative to explicit Chain-of-Thought, yet whether such latent models can similarly benefit from parallel TTS remains open, mainly due to the absence of sampling mechanisms in continuous space, and the lack of probabilistic signals for advanced trajectory aggregation. \ This work enables parallel TTS for latent reasoning models by addressing the above issues. For sampling, we introduce two uncertainty-inspired stochastic strategies: Monte Carlo Dropout and Additive Gaussian Noise. For aggregation, we design a Latent Reward Model (LatentRM) trained with step-wise contrastive objective to score and guide latent reasoning. Extensive experiments and visualization analyses show that both sampling strategies scale effectively with compute and exhibit distinct exploration dynamics, while LatentRM enables effective trajectory selection. Together, our explorations open a new direction for scalable inference in continuous spaces. Code released at https://github.com/YRYangang/LatentTTS.

Test-Time Scaling (TTS) improves the reasoning performance of Large Language Models (LLMs) by allocating additional compute during inference. We conduct a structured survey of TTS methods and categorize them into sampling-based, search-based, and trajectory optimization strategies. We observe that reasoning-optimized models often produce less diverse outputs, which limits TTS effectiveness. To address this, we propose ADAPT (A Diversity Aware Prefix fine-Tuning), a lightweight method that applies prefix tuning with a diversity-focused data strategy. Experiments on mathematical reasoning tasks show that ADAPT reaches 80% accuracy using eight times less compute than strong baselines. Our findings highlight the essential role of generative diversity in maximizing TTS effectiveness.

Scaling pre-training compute has proven effective for achieving mulitlinguality, but does the same hold for test-time scaling? In this work, we introduce MCLM, a multilingual math benchmark featuring competition-level problems in 55 languages. We test three test-time scaling methods-Outcome Reward Modeling (ORM), Process Reward Modeling (ORM), and Budget Forcing (BF)-on both Qwen2.5-1.5B Math and MR1-1.5B, a multilingual LLM we trained for extended reasoning. Our experiments show that using Qwen2.5-1.5B Math with ORM achieves a score of 35.8 on MCLM, while BF on MR1-1.5B attains 35.2. Although "thinking LLMs" have recently garnered significant attention, we find that their performance is comparable to traditional scaling methods like best-of-N once constrained to similar levels of inference FLOPs. Moreover, while BF yields a 20-point improvement on English AIME, it provides only a 1.94-point average gain across other languages-a pattern consistent across the other test-time scaling methods we studied-higlighting that test-time scaling may not generalize as effectively to multilingual tasks. To foster further research, we release MCLM, MR1-1.5B, and evaluation results.

Test-time scaling has emerged as an effective approach for improving language model performance by utilizing additional compute at inference time. Recent studies have shown that overriding end-of-thinking tokens (e.g., replacing "</think>" with "Wait") can extend reasoning steps and improve accuracy. In this work, we explore whether a dedicated continue-thinking token can be learned to trigger extended reasoning. We augment a distilled version of DeepSeek-R1 with a single learned "<|continue-thinking|>" token, training only its embedding via reinforcement learning while keeping the model weights frozen. Our experiments show that this learned token achieves improved accuracy on standard math benchmarks compared to both the baseline model and a test-time scaling approach that uses a fixed token (e.g., "Wait") for budget forcing. In particular, we observe that in cases where the fixed-token approach enhances the base model's accuracy, our method achieves a markedly greater improvement. For example, on the GSM8K benchmark, the fixed-token approach yields a 1.3% absolute improvement in accuracy, whereas our learned-token method achieves a 4.2% improvement over the base model that does not use budget forcing.

Test-time scaling is a powerful strategy for boosting the performance of large language models on complex reasoning tasks. While state-of-the-art approaches often employ generative verifiers to select the best solution from a pool of candidates, this method incurs prohibitive computational costs, limiting its practicality. In this work, we shift the focus to a more budget-aware paradigm: discriminative verification. We conduct a thorough empirical analysis and demonstrate that while discriminative verifiers may underperform in isolation, combining them with self-consistency in a hybrid approach creates a powerful and efficient test-time scaling mechanism. Notably, under a fixed compute budget, this hybrid approach surpasses state-of-the-art generative verification by a significant margin: achieving up to 15.3\% higher accuracy on AIME2025. Our findings establish that for practical, real-world applications, budget-aware scaling with discriminative verifiers is not only a "free" upgrade over self-consistency, but also a more effective and efficient alternative to costly generative techniques. Code is available at https://github.com/wang-research-lab/verification.

Test-time scaling (TTS), which involves dynamic allocation of compute during inference, offers a promising way to improve reasoning in large language models. While existing TTS methods work well, they often rely on long decoding paths or require a large number of samples to be generated, increasing the token usage and inference latency. We observe the surprising fact that for reasoning tasks, shorter traces are much more likely to be correct than longer ones. Motivated by this, we introduce First Finish Search (FFS), a training-free parallel decoding strategy that launches n independent samples and returns as soon as any one completes. We evaluate FFS alongside simple decoding, beam search, majority voting, and budget forcing on four reasoning models (DeepSeek-R1, R1-Distill-Qwen-32B, QwQ-32B and Phi-4-Reasoning-Plus) and across four datasets (AIME24, AIME25-I, AIME25-II and GPQA Diamond). With DeepSeek-R1, FFS achieves 82.23% accuracy on the AIME datasets, a 15% improvement over DeepSeek-R1's standalone accuracy, nearly matching OpenAI's o4-mini performance. Our theoretical analysis explains why stopping at the shortest trace is likely to yield a correct answer and identifies the conditions under which early stopping may be suboptimal. The elegance and simplicity of FFS demonstrate that straightforward TTS strategies can perform remarkably well, revealing the untapped potential of simple approaches at inference time.

World foundation models, which simulate the physical world by predicting future states from current observations and inputs, have become central to many applications in physical intelligence, including autonomous driving and robotics. However, these models require substantial computational resources for pretraining and are further constrained by available data during post-training. As such, scaling computation at test time emerges as both a critical and practical alternative to traditional model enlargement or re-training. In this work, we introduce SWIFT, a test-time scaling framework tailored for WFMs. SWIFT integrates our extensible WFM evaluation toolkit with process-level inference strategies, including fast tokenization, probability-based Top-K pruning, and efficient beam search. Empirical results on the COSMOS model demonstrate that test-time scaling exists even in a compute-optimal way. Our findings reveal that test-time scaling laws hold for WFMs and that SWIFT provides a scalable and effective pathway for improving WFM inference without retraining or increasing model size. The code is available at https://github.com/Mia-Cong/SWIFT.git.

An AI system can create and maintain knowledge only to the extent that it can verify that knowledge itself. Recent work on long Chain-of-Thought reasoning has demonstrated great potential of LLMs on solving competitive problems, but their verification ability remains to be weak and not sufficiently investigated. In this paper, we propose Heimdall, the long CoT verification LLM that can accurately judge the correctness of solutions. With pure reinforcement learning, we boost the verification accuracy from 62.5% to 94.5% on competitive math problems. By scaling with repeated sampling, the accuracy further increases to 97.5%. Through human evaluation, Heimdall demonstrates impressive generalization capabilities, successfully detecting most issues in challenging math proofs, the type of which is not included during training. Furthermore, we propose Pessimistic Verification to extend the functionality of Heimdall to scaling up the problem solving. It calls Heimdall to judge the solutions from a solver model and based on the pessimistic principle, selects the most likely correct solution with the least uncertainty. Taking DeepSeek-R1-Distill-Qwen-32B as the solver model, Pessimistic Verification improves the solution accuracy on AIME2025 from 54.2% to 70.0% with 16x compute budget and to 83.3% with more compute budget. With the stronger solver Gemini 2.5 Pro, the score reaches 93.0%. Finally, we prototype an automatic knowledge discovery system, a ternary system where one poses questions, another provides solutions, and the third verifies the solutions. Using the data synthesis work NuminaMath for the first two components, Heimdall effectively identifies problematic records within the dataset and reveals that nearly half of the data is flawed, which interestingly aligns with the recent ablation studies from NuminaMath.

One common strategy for improving the performance of Large Language Models (LLMs) on downstream tasks involves using a verifier model to either select the best answer from a pool of candidates or to steer the auto-regressive generation process towards better outputs. This class of methods typically results in improved accuracy at the cost of increased computation at test-time, a paradigm known as test-time scaling. However, most existing approaches increase computation uniformly across all samples and generation steps, without considering the complexity of individual instances, leading to inefficient resource use. We address this limitation by proposing an approach, called Locally Adaptive Test-Time Scaling (LATTS), that allocates variable compute across generation steps. Specifically, at each generation step, LATTS employs a verifier-based acceptance criterion to decide whether to resample, backtrack, restart, or stop the generation process. This criterion effectively adjusts the per-step computational effort based on a precise notion of local difficulty derived from the verifier model. Empirical results show that LATTS achieves significantly superior accuracy--compute tradeoffs compared to standard verifier-based methods.

Large language models (LLMs) have achieved impressive results on multi-step mathematical reasoning, yet at the cost of high computational overhead. This challenge is particularly acute for test-time scaling methods such as parallel decoding, which increase answer diversity but scale poorly in efficiency. To address this efficiency-accuracy trade-off, we propose SSR (Speculative Parallel Scaling Reasoning), a training-free framework that leverages a key insight: by introducing speculative decoding at the step level, we can accelerate reasoning without sacrificing correctness. SSR integrates two components: a Selective Parallel Module (SPM) that identifies a small set of promising reasoning strategies via model-internal scoring, and Step-level Speculative Decoding (SSD), which enables efficient draft-target collaboration for fine-grained reasoning acceleration. Experiments on three mathematical benchmarks-AIME 2024, MATH-500, and LiveMathBench - demonstrate that SSR achieves strong gains over baselines. For instance, on LiveMathBench, SSR improves pass@1 accuracy by 13.84% while reducing computation to 80.5% of the baseline FLOPs. On MATH-500, SSR reduces compute to only 30% with no loss in accuracy.

Reasoning capabilities of large language models are primarily studied for English, even when pretrained models are multilingual. In this work, we investigate to what extent English reasoning finetuning with long chain-of-thoughts (CoTs) can generalize across languages. First, we find that scaling up inference compute for English-centric reasoning language models (RLMs) improves multilingual mathematical reasoning across many languages including low-resource languages, to an extent where they outperform models twice their size. Second, we reveal that while English-centric RLM's CoTs are naturally predominantly English, they consistently follow a quote-and-think pattern to reason about quoted non-English inputs. Third, we discover an effective strategy to control the language of long CoT reasoning, and we observe that models reason better and more efficiently in high-resource languages. Finally, we observe poor out-of-domain reasoning generalization, in particular from STEM to cultural commonsense knowledge, even for English. Overall, we demonstrate the potentials, study the mechanisms and outline the limitations of crosslingual generalization of English reasoning test-time scaling. We conclude that practitioners should let English-centric RLMs reason in high-resource languages, while further work is needed to improve reasoning in low-resource languages and out-of-domain contexts.

Test-Time Scaling (TTS) has proven effective in improving the performance of Large Language Models (LLMs) during inference. However, existing research has overlooked the efficiency of TTS from a latency-sensitive perspective. Through a latency-aware evaluation of representative TTS methods, we demonstrate that a compute-optimal TTS does not always result in the lowest latency in scenarios where latency is critical. To address this gap and achieve latency-optimal TTS, we propose two key approaches by optimizing the concurrency configurations: (1) branch-wise parallelism, which leverages multiple concurrent inference branches, and (2) sequence-wise parallelism, enabled by speculative decoding. By integrating these two approaches and allocating computational resources properly to each, our latency-optimal TTS enables a 32B model to reach 82.3% accuracy on MATH-500 within 1 minute and a smaller 3B model to achieve 72.4% within 10 seconds. Our work emphasizes the importance of latency-aware TTS and demonstrates its ability to deliver both speed and accuracy in latency-sensitive scenarios.

The current paradigm of test-time scaling relies on generating long reasoning traces ("thinking" more) before producing a response. In agent problems that require interaction, this can be done by generating thinking traces before acting in the world. However, this process does not allow agents to acquire new information from the environment or adapt their behavior over time. In this work, we propose to scale test-time interaction, an untapped dimension of test-time scaling that increases the agent's interaction horizon to enable running rich behaviors such as exploration, backtracking, and dynamic re-planning within a single rollout. To demonstrate the promise of this scaling dimension, we study the domain of web agents. We first show that even prompting-based interaction scaling without any training can improve task success on web benchmarks non-trivially. Building on this, we introduce TTI (Test-Time Interaction), a curriculum-based online reinforcement learning (RL) approach that trains agents by adaptively adjusting their rollout lengths. Using a Gemma 3 12B model, TTI produces state-of-the-art open-source, open-data web agents on WebVoyager and WebArena benchmarks. We further show that TTI enables agents to balance exploration and exploitation adaptively. Our results establish interaction scaling as a powerful, complementary axis to scaling per-step compute, offering new avenues for training adaptive agents.

A promising approach for improving reasoning in large language models is to use process reward models (PRMs). PRMs provide feedback at each step of a multi-step reasoning trace, potentially improving credit assignment over outcome reward models (ORMs) that only provide feedback at the final step. However, collecting dense, per-step human labels is not scalable, and training PRMs from automatically-labeled data has thus far led to limited gains. To improve a base policy by running search against a PRM or using it as dense rewards for reinforcement learning (RL), we ask: "How should we design process rewards?". Our key insight is that, to be effective, the process reward for a step should measure progress: a change in the likelihood of producing a correct response in the future, before and after taking the step, corresponding to the notion of step-level advantages in RL. Crucially, this progress should be measured under a prover policy distinct from the base policy. We theoretically characterize the set of good provers and our results show that optimizing process rewards from such provers improves exploration during test-time search and online RL. In fact, our characterization shows that weak prover policies can substantially improve a stronger base policy, which we also observe empirically. We validate our claims by training process advantage verifiers (PAVs) to predict progress under such provers, and show that compared to ORMs, test-time search against PAVs is >8% more accurate, and 1.5-5times more compute-efficient. Online RL with dense rewards from PAVs enables one of the first results with 5-6times gain in sample efficiency, and >6% gain in accuracy, over ORMs.

Large language models are usually fine-tuned to align with human preferences. However, fine-tuning a large language model can be challenging. In this work, we introduce weak-to-strong search, framing the alignment of a large language model as a test-time greedy search to maximize the log-likelihood difference between small tuned and untuned models while sampling from the frozen large model. This method serves both as (i) a compute-efficient model up-scaling strategy that avoids directly tuning the large model and as (ii) an instance of weak-to-strong generalization that enhances a strong model with weak test-time guidance. Empirically, we demonstrate the flexibility of weak-to-strong search across different tasks. In controlled-sentiment generation and summarization, we use tuned and untuned gpt2s to effectively improve the alignment of large models without additional training. Crucially, in a more difficult instruction-following benchmark, AlpacaEval 2.0, we show that reusing off-the-shelf small model pairs (e.g., zephyr-7b-beta and its untuned version) can significantly improve the length-controlled win rates of both white-box and black-box large models against gpt-4-turbo (e.g., 34.4 rightarrow 37.9 for Llama-3-70B-Instruct and 16.0 rightarrow 20.1 for gpt-3.5-turbo-instruct), despite the small models' low win rates approx 10.0.

Large language models (LLMs) have shown remarkable progress in complex reasoning tasks, largely enabled by test-time scaling (TTS) paradigms that allocate additional compute during inference. Among these, external TTS (particularly the Best-of-N selection paradigm) yields scalable performance improvements by selecting from multiple independently generated reasoning trajectories. However, this approach faces key limitations: (i) the high computational overhead of deploying process reward models, (ii) the underutilization of the LLM's intrinsic latent representations. We introduce TrajSelector, an efficient and effective Best-of-N framework that exploit the hidden states in the sampler LLM for process-level scoring. A lightweight verifier (with only 0.6B parameters) evaluates the quality of step-wise trajectory, and then aggregates these scores to identify the optimal reasoning trajectory. Our framework employs a fully data-driven, end-to-end training recipe that eliminates reliance on massive step-level annotations. Experiential results across five benchmarks demonstrate that TrajSelector delivers consistent performance gains. In Best-of-32 settings, it surpasses majority voting by 4.61% accuracy and outperforms existing process reward models by 4.31% to 12.21%, all while maintaining lower inference costs.

Theory-of-Mind (ToM) tasks pose a unique challenge for small language models (SLMs) with limited scale, which often lack the capacity to perform deep social reasoning. In this work, we propose DEL-ToM, a framework that improves ToM reasoning through inference-time scaling rather than architectural changes. Our approach decomposes ToM tasks into a sequence of belief updates grounded in Dynamic Epistemic Logic (DEL), enabling structured and transparent reasoning. We train a verifier, called the Process Belief Model (PBM), to score each belief update step using labels generated automatically via a DEL simulator. During inference, candidate belief traces generated by a language model are evaluated by the PBM, and the highest-scoring trace is selected. This allows SLMs to emulate more deliberate reasoning by allocating additional compute at test time. Experiments across multiple model scales and benchmarks show that DEL-ToM consistently improves performance, demonstrating that verifiable belief supervision can significantly enhance ToM abilities of SLMs without retraining.

Scaling laws for large language models (LLMs) predict model performance based on parameters like size and training data. However, differences in training configurations and data processing across model families lead to significant variations in benchmark performance, making it difficult for a single scaling law to generalize across all LLMs. On the other hand, training family-specific scaling laws requires training models of varying sizes for every family. In this work, we propose Skills Scaling Laws (SSLaws, pronounced as Sloth), a novel scaling law that leverages publicly available benchmark data and assumes LLM performance is driven by low-dimensional latent skills, such as reasoning and instruction following. These latent skills are influenced by computational resources like model size and training tokens but with varying efficiencies across model families. Sloth exploits correlations across benchmarks to provide more accurate and interpretable predictions while alleviating the need to train multiple LLMs per family. We present both theoretical results on parameter identification and empirical evaluations on 12 prominent benchmarks, from Open LLM Leaderboard v1/v2, demonstrating that Sloth predicts LLM performance efficiently and offers insights into scaling behaviors for complex downstream tasks and increased test-time compute.

Improving open-source models on real-world SWE tasks (solving GITHUB issues) faces two key challenges: 1) scalable curation of execution environments to train these models, and, 2) optimal scaling of test-time compute. We introduce AgentGym, the largest procedurally-curated executable gym environment for training real-world SWE-agents, consisting of more than 8.7K tasks. AgentGym is powered by two main contributions: 1) SYNGEN: a synthetic data curation recipe that enables scalable curation of executable environments using test-generation and back-translation directly from commits, thereby reducing reliance on human-written issues or unit tests. We show that this enables more scalable training leading to pass@1 performance of 34.4% on SWE-Bench Verified benchmark with our 32B model. 2) Hybrid Test-time Scaling: we provide an in-depth analysis of two test-time scaling axes; execution-based and execution-free verifiers, demonstrating that they exhibit complementary strengths and limitations. Test-based verifiers suffer from low distinguishability, while execution-free verifiers are biased and often rely on stylistic features. Surprisingly, we find that while each approach individually saturates around 42-43%, significantly higher gains can be obtained by leveraging their complementary strengths. Overall, our approach achieves 51% on the SWE-Bench Verified benchmark, reflecting a new state-of-the-art for open-weight SWE-agents and for the first time showing competitive performance with proprietary models such as o1, o1-preview and sonnet-3.5-v2 (with tools). We will open-source our environments, models, and agent trajectories.

Large language models (LLMs) can perform reasoning computations both internally within their latent space and externally by generating explicit token sequences like chains of thought. Significant progress in enhancing reasoning abilities has been made by scaling test-time compute. However, understanding and quantifying model-internal reasoning abilities - the inferential "leaps" models make between individual token predictions - remains crucial. This study introduces a benchmark (n = 4,000 items) designed to quantify model-internal reasoning in different domains. We achieve this by having LLMs indicate the correct solution to reasoning problems not through descriptive text, but by selecting a specific language of their initial response token that is different from English, the benchmark language. This not only requires models to reason beyond their context window, but also to overrise their default tendency to respond in the same language as the prompt, thereby posing an additional cognitive strain. We evaluate a set of 18 LLMs, showing significant performance variations, with GPT-4.5 achieving the highest accuracy (74.7%), outperforming models like Grok-2 (67.2%), and Llama 3.1 405B (65.6%). Control experiments and difficulty scaling analyses suggest that while LLMs engage in internal reasoning, we cannot rule out heuristic exploitations under certain conditions, marking an area for future investigation. Our experiments demonstrate that LLMs can "think" via latent-space computations, revealing model-internal inference strategies that need further understanding, especially regarding safety-related concerns such as covert planning, goal-seeking, or deception emerging without explicit token traces.

Recent research has shown that LLM performance on reasoning tasks can be enhanced by scaling test-time compute. One promising approach, particularly with decomposable problems, involves arranging intermediate solutions as a graph on which transformations are performed to explore the solution space. However, prior works rely on pre-determined, task-specific transformation schedules which are subject to a set of searched hyperparameters. In this work, we view thought graph transformations as actions in a Markov decision process, and implement policy agents to drive effective action policies for the underlying reasoning LLM agent. In particular, we investigate the ability for another LLM to act as a policy agent on thought graph environments and introduce ARIES, a multi-agent architecture for reasoning with LLMs. In ARIES, reasoning LLM agents solve decomposed subproblems, while policy LLM agents maintain visibility of the thought graph states, and dynamically adapt the problem-solving strategy. Through extensive experiments, we observe that using off-the-shelf LLMs as policy agents with no supervised fine-tuning (SFT) can yield up to 29% higher accuracy on HumanEval relative to static transformation schedules, as well as reducing inference costs by 35% and avoid any search requirements. We also conduct a thorough analysis of observed failure modes, highlighting that limitations on LLM sizes and the depth of problem decomposition can be seen as challenges to scaling LLM-guided reasoning.

Scientific discovery relies on scientists generating novel hypotheses that undergo rigorous experimental validation. To augment this process, we introduce an AI co-scientist, a multi-agent system built on Gemini 2.0. The AI co-scientist is intended to help uncover new, original knowledge and to formulate demonstrably novel research hypotheses and proposals, building upon prior evidence and aligned to scientist-provided research objectives and guidance. The system's design incorporates a generate, debate, and evolve approach to hypothesis generation, inspired by the scientific method and accelerated by scaling test-time compute. Key contributions include: (1) a multi-agent architecture with an asynchronous task execution framework for flexible compute scaling; (2) a tournament evolution process for self-improving hypotheses generation. Automated evaluations show continued benefits of test-time compute, improving hypothesis quality. While general purpose, we focus development and validation in three biomedical areas: drug repurposing, novel target discovery, and explaining mechanisms of bacterial evolution and anti-microbial resistance. For drug repurposing, the system proposes candidates with promising validation findings, including candidates for acute myeloid leukemia that show tumor inhibition in vitro at clinically applicable concentrations. For novel target discovery, the AI co-scientist proposed new epigenetic targets for liver fibrosis, validated by anti-fibrotic activity and liver cell regeneration in human hepatic organoids. Finally, the AI co-scientist recapitulated unpublished experimental results via a parallel in silico discovery of a novel gene transfer mechanism in bacterial evolution. These results, detailed in separate, co-timed reports, demonstrate the potential to augment biomedical and scientific discovery and usher an era of AI empowered scientists.

Inducing reasoning in multimodal large language models (MLLMs) is critical for achieving human-level perception and understanding. Existing methods mainly leverage LLM reasoning to analyze parsed visuals, often limited by static perception stages. This paper introduces Visual Test-Time Scaling (VTTS), a novel approach to enhance MLLMs' reasoning via iterative perception during inference. VTTS mimics humans' hierarchical attention by progressively refining focus on high-confidence spatio-temporal regions, guided by updated textual predictions. Specifically, VTTS employs an Iterative Perception (ITP) mechanism, incorporating reinforcement learning with spatio-temporal supervision to optimize reasoning. To support this paradigm, we also present VTTS-80K, a dataset tailored for iterative perception. These designs allows a MLLM to enhance its performance by increasing its perceptual compute. Extensive experiments validate VTTS's effectiveness and generalization across diverse tasks and benchmarks. Our newly introduced Videochat-R1.5 model has achieved remarkable improvements, with an average increase of over 5\%, compared to robust baselines such as Qwen2.5VL-3B and -7B, across more than 15 benchmarks that encompass video conversation, video reasoning, and spatio-temporal perception.

As enthusiasm for scaling computation (data and parameters) in the pretraining era gradually diminished, test-time scaling (TTS), also referred to as ``test-time computing'' has emerged as a prominent research focus. Recent studies demonstrate that TTS can further elicit the problem-solving capabilities of large language models (LLMs), enabling significant breakthroughs not only in specialized reasoning tasks, such as mathematics and coding, but also in general tasks like open-ended Q&A. However, despite the explosion of recent efforts in this area, there remains an urgent need for a comprehensive survey offering a systemic understanding. To fill this gap, we propose a unified, multidimensional framework structured along four core dimensions of TTS research: what to scale, how to scale, where to scale, and how well to scale. Building upon this taxonomy, we conduct an extensive review of methods, application scenarios, and assessment aspects, and present an organized decomposition that highlights the unique functional roles of individual techniques within the broader TTS landscape. From this analysis, we distill the major developmental trajectories of TTS to date and offer hands-on guidelines for practical deployment. Furthermore, we identify several open challenges and offer insights into promising future directions, including further scaling, clarifying the functional essence of techniques, generalizing to more tasks, and more attributions.

The remarkable performance of the o1 model in complex reasoning demonstrates that test-time computing scaling can further unlock the model's potential, enabling powerful System-2 thinking. However, there is still a lack of comprehensive surveys for test-time computing scaling. We trace the concept of test-time computing back to System-1 models. In System-1 models, test-time computing addresses distribution shifts and improves robustness and generalization through parameter updating, input modification, representation editing, and output calibration. In System-2 models, it enhances the model's reasoning ability to solve complex problems through repeated sampling, self-correction, and tree search. We organize this survey according to the trend of System-1 to System-2 thinking, highlighting the key role of test-time computing in the transition from System-1 models to weak System-2 models, and then to strong System-2 models. We also point out a few possible future directions.

Test-time scaling has emerged as a transformative paradigm for enhancing the performance of large reasoning models, enabling dynamic allocation of computational resources during inference. However, as the landscape of reasoning models rapidly expands, a critical question remains: how can we systematically compare and evaluate the test-time scaling capabilities across different models? In this paper, we introduce ARISE (Adaptive Resolution-aware Scaling Evaluation), a novel metric specifically designed to assess the test-time scaling effectiveness of large reasoning models. Unlike existing evaluation approaches, ARISE incorporates two key innovations: (1) sample-level awareness that effectively penalizes negative scaling behaviors where increased computation leads to performance degradation, and (2) a dynamic sampling mechanism that mitigates the impact of accuracy fluctuations and token count instability on the final assessment. We conduct comprehensive experiments evaluating state-of-the-art reasoning models across diverse domains including mathematical reasoning, code generation, and agentic tasks. Our results demonstrate that ARISE provides a reliable and fine-grained measurement of test-time scaling capabilities, revealing significant variations in scaling efficiency across models. Notably, our evaluation identifies Claude Opus as exhibiting superior scaling characteristics compared to other contemporary reasoning models.

Large language models (LLMs) benefit from test-time scaling but are often hampered by high inference latency. Speculative decoding is a natural way to accelerate the scaling process; however, scaling along both the parallel and sequential dimensions poses significant challenges, including substantial memory-bound execution and synchronization overhead. We introduce ATTS (Asynchronous Test-Time Scaling), a statistically guaranteed adaptive scaling framework that follows the hypothesis testing process to address these challenges. By revisiting arithmetic intensity, ATTS identifies synchronization as the primary bottleneck. It enables asynchronous inference through online calibration and proposes an ordinal classification algorithm that supports a three-stage rejection sampling pipeline, scaling along both the sequential and parallel axes. Across experiments on the MATH, AMC23, AIME24, and AIME25 datasets and across multiple draft-target model families, we show that ATTS delivers up to 56.7x speedup in test-time scaling and a 4.14x throughput improvement, while maintaining accurate control of the rejection rate, reducing latency and memory overhead, and incurring no accuracy loss. By scaling both in parallel and sequential dimensions, we enable the 1.5B/70B draft/target model combination to achieve the performance of the state-of-the-art reasoning model o3-mini (high) on the AIME dataset. We have released the code at https://github.com/menik1126/asynchronous-test-time-scaling.

Test-Time Scaling (TTS) is a promising approach to progressively elicit the model's intelligence during inference. Recently, training-based TTS methods, such as continued reinforcement learning (RL), have further surged in popularity, while training-free TTS methods are gradually fading from prominence. However, the additional computation overhead of training amplifies the burden on test-time scaling. In this paper, we focus on training-free TTS methods for reasoning. We first design Conditional Step-level Self-refinement, a fine-grained sequential scaling method guided by process verification. On top of its effectiveness, we further combine it with other classical parallel scaling methods at the step level, to introduce a novel inference paradigm called Hybrid Test-Time Scaling. Extensive experiments on five instruction-tuned LLMs across different scales (3B-14B) and families demonstrate that hybrid strategy incorporating various training-free TTS methods at a fine granularity has considerable potential for expanding the reasoning performance boundaries of LLMs.

The advent of test-time scaling in large language models (LLMs), exemplified by OpenAI's o1 series, has advanced reasoning capabilities by scaling computational resource allocation during inference. While successors like QwQ, Deepseek-R1 (R1) and LIMO replicate these advancements, whether these models truly possess test-time scaling capabilities remains underexplored. This study found that longer CoTs of these o1-like models do not consistently enhance accuracy; in fact, correct solutions are often shorter than incorrect ones for the same questions. Further investigation shows this phenomenon is closely related to models' self-revision capabilities - longer CoTs contain more self-revisions, which often lead to performance degradation. We then compare sequential and parallel scaling strategies on QwQ, R1 and LIMO, finding that parallel scaling achieves better coverage and scalability. Based on these insights, we propose Shortest Majority Vote, a method that combines parallel scaling strategies with CoT length characteristics, significantly improving models' test-time scalability compared to conventional majority voting approaches.

Training models to effectively use test-time compute is crucial for improving the reasoning performance of LLMs. Current methods mostly do so via fine-tuning on search traces or running RL with 0/1 outcome reward, but do these approaches efficiently utilize test-time compute? Would these approaches continue to scale as the budget improves? In this paper, we try to answer these questions. We formalize the problem of optimizing test-time compute as a meta-reinforcement learning (RL) problem, which provides a principled perspective on spending test-time compute. This perspective enables us to view the long output stream from the LLM as consisting of several episodes run at test time and leads us to use a notion of cumulative regret over output tokens as a way to measure the efficacy of test-time compute. Akin to how RL algorithms can best tradeoff exploration and exploitation over training, minimizing cumulative regret would also provide the best balance between exploration and exploitation in the token stream. While we show that state-of-the-art models do not minimize regret, one can do so by maximizing a dense reward bonus in conjunction with the outcome 0/1 reward RL. This bonus is the ''progress'' made by each subsequent block in the output stream, quantified by the change in the likelihood of eventual success. Using these insights, we develop Meta Reinforcement Fine-Tuning, or MRT, a new class of fine-tuning methods for optimizing test-time compute. MRT leads to a 2-3x relative gain in performance and roughly a 1.5x gain in token efficiency for math reasoning compared to outcome-reward RL.

Test-time scaling seeks to improve the reasoning performance of large language models (LLMs) by adding computational resources. A prevalent approach within the field is sampling-based test-time scaling methods, which enhance reasoning by generating multiple reasoning paths for a given input during inference. However, despite its practical success, the theoretical foundations remain underexplored. In this paper, we provide the first theoretical framework for analyzing sampling-based test-time scaling methods, grounded in the perspective of confidence estimation. Based on the framework, we analyze two dominant paradigms: self-consistency and perplexity, and reveal key limitations: self-consistency suffers from high estimation error while perplexity exhibits substantial modeling error and possible degradation of the estimation error convergence. To address these limitations, we introduce RPC, a hybrid method that leverages our theoretical insights through two key components: Perplexity Consistency and Reasoning Pruning. Perplexity Consistency combines the strengths of self-consistency and perplexity, boosting the convergence rate of estimation error from linear to exponential while preserving model error. Reasoning Pruning prevents degradation by eliminating low-probability reasoning paths. Both theoretical analysis and empirical results across seven benchmark datasets demonstrate that RPC has a strong potential for reducing reasoning error. Notably, RPC achieves reasoning performance comparable to self-consistency while not only enhancing confidence reliability but also reducing sampling costs by 50%. The code and resources are available at https://wnjxyk.github.io/RPC.

Allocating more computation during inference time (test-time scaling) improves language model performance, especially for reasoning tasks. However, popular methods like Best-of-N sampling often show diminishing returns as N increases. To address this inefficiency, we introduce a general test-time calibration framework that adaptively modifies the model toward high-reward reasoning paths, with theoretical guarantees of improving the lower bound of expected reward under finite sampling, all without large language model (LLM) retraining. Within this framework, we propose CarBoN (Calibrated Best-of-N), a two-phase method that first explores the solution space and then learns a calibration of the logits via an input-specific temperature T and additive shift vector delta, guiding generation toward more reliable reasoning. Experiments on MATH-500 and AIME-2024 show that CarBoN improves efficiency, with up to 4times fewer rollouts to reach the same accuracy, while often achieving higher accuracy under fixed budgets. We also analyze the complementary roles of T and delta in balancing output diversity and correctness, and demonstrate that the framework also generalizes to step-level sampling strategies such as beam search. For more information, please refer to our project page at huggingface.co/spaces/TrustSafeAI/Test-Time-Calibration.

Test-time scaling has emerged as a prominent research direction in machine learning, enabling models to enhance their expressive capabilities during inference.Transformers, renowned for striking a delicate balance between efficiency and expressiveness, have benefited from test-time scaling techniques that leverage an expanding key-value (KV) cache to significantly improve performance.In this paper, we introduce a novel state-based approach to test-time scaling, which we term state tuning, tailored to the RNN-based RWKV-7 model.By exploiting the unique strengths of RWKV-7, our method achieves state-of-the-art performance on the target task without altering the model's pre-trained weights. Our approach centers on three key innovations. First, we develop an observer framework that allows a smaller model to replicate and learn the state dynamics of the RWKV-7 model. Second, we employ a kernel method to dynamically upscale the state size, enhancing the model's capacity to capture intricate patterns. Third, we integrate Decorrelated Backpropagation (DBP) to optimize the upscaled state matrix, thereby improving convergence and expressivity. By tuning only the state matrix, we demonstrate that a smaller model can outperform larger models on the given task. This method preserves the efficiency of the original RWKV-7 architecture while harnessing the power of test-time scaling to deliver superior results. Our findings underscore the potential of state tuning as an effective strategy for advancing model performance in resource-constrained settings. Our code is https://github.com/TorchRWKV/flash-linear-attention.

Edge intelligence paradigm is increasingly demanded by the emerging autonomous systems, such as robotics. Beyond ensuring privacy-preserving operation and resilience in connectivity-limited environments, edge deployment offers significant energy and cost advantages over cloud-based solutions. However, deploying large language models (LLMs) for reasoning tasks on edge GPUs faces critical challenges from strict latency constraints and limited computational resources. To navigate these constraints, developers must balance multiple design factors - choosing reasoning versus non-reasoning architectures, selecting appropriate model sizes, allocating token budgets, and applying test-time scaling strategies - to meet target latency and optimize accuracy. Yet guidance on optimal combinations of these variables remains scarce. In this work, we present EdgeReasoning, a comprehensive study characterizing the deployment of reasoning LLMs on edge GPUs. We systematically quantify latency-accuracy tradeoffs across various LLM architectures and model sizes. We systematically evaluate prompt-based and model-tuning-based techniques for reducing reasoning token length while maintaining performance quality. We further profile test-time scaling methods with varying degrees of parallelism to maximize accuracy under strict latency budgets. Through these analyses, EdgeReasoning maps the Pareto frontier of achievable accuracy-latency configurations, offering systematic guidance for optimal edge deployment of reasoning LLMs.

Scale has become a main ingredient in obtaining strong machine learning models. As a result, understanding a model's scaling properties is key to effectively designing both the right training setup as well as future generations of architectures. In this work, we argue that scale and training research has been needlessly complex due to reliance on the cosine schedule, which prevents training across different lengths for the same model size. We investigate the training behavior of a direct alternative - constant learning rate and cooldowns - and find that it scales predictably and reliably similar to cosine. Additionally, we show that stochastic weight averaging yields improved performance along the training trajectory, without additional training costs, across different scales. Importantly, with these findings we demonstrate that scaling experiments can be performed with significantly reduced compute and GPU hours by utilizing fewer but reusable training runs.

In this work we analyze strategies for convolutional neural network scaling; that is, the process of scaling a base convolutional network to endow it with greater computational complexity and consequently representational power. Example scaling strategies may include increasing model width, depth, resolution, etc. While various scaling strategies exist, their tradeoffs are not fully understood. Existing analysis typically focuses on the interplay of accuracy and flops (floating point operations). Yet, as we demonstrate, various scaling strategies affect model parameters, activations, and consequently actual runtime quite differently. In our experiments we show the surprising result that numerous scaling strategies yield networks with similar accuracy but with widely varying properties. This leads us to propose a simple fast compound scaling strategy that encourages primarily scaling model width, while scaling depth and resolution to a lesser extent. Unlike currently popular scaling strategies, which result in about O(s) increase in model activation w.r.t. scaling flops by a factor of s, the proposed fast compound scaling results in close to O(s) increase in activations, while achieving excellent accuracy. This leads to comparable speedups on modern memory-limited hardware (e.g., GPU, TPU). More generally, we hope this work provides a framework for analyzing and selecting scaling strategies under various computational constraints.

LLM test-time compute (or LLM inference) via search has emerged as a promising research area with rapid developments. However, current frameworks often adopt distinct perspectives on three key aspects (task definition, LLM profiling, and search procedures), making direct comparisons challenging. Moreover, the search algorithms employed often diverge from standard implementations, and their specific characteristics are not thoroughly specified. In this survey, we provide a comprehensive technical review that unifies task definitions and provides modular definitions of LLM profiling and search procedures. The definitions enable precise comparisons of various LLM inference frameworks while highlighting their departures from conventional search algorithms. We also discuss the applicability, performance, and efficiency of these methods. For further details and ongoing updates, please refer to our GitHub repository: https://github.com/xinzhel/LLM-Agent-Survey/blob/main/search.md

The remarkable performance of models like the OpenAI o1 can be attributed to their ability to emulate human-like long-time thinking during inference. These models employ extended chain-of-thought (CoT) processes, exploring multiple strategies to enhance problem-solving capabilities. However, a critical question remains: How to intelligently and efficiently scale computational resources during testing. This paper presents the first comprehensive study on the prevalent issue of overthinking in these models, where excessive computational resources are allocated for simple problems with minimal benefit. We introduce novel efficiency metrics from both outcome and process perspectives to evaluate the rational use of computational resources by o1-like models. Using a self-training paradigm, we propose strategies to mitigate overthinking, streamlining reasoning processes without compromising accuracy. Experimental results show that our approach successfully reduces computational overhead while preserving model performance across a range of testsets with varying difficulty levels, such as GSM8K, MATH500, GPQA, and AIME.

Test-time scaling increases inference-time computation by allowing models to generate long reasoning chains, and has shown strong performance across many domains. However, in this work, we show that this approach is not yet effective for knowledge-intensive tasks, where high factual accuracy and low hallucination rates are essential. We conduct a comprehensive evaluation of test-time scaling using 12 reasoning models on two knowledge-intensive benchmarks. Our results reveal that increasing test-time computation does not consistently improve accuracy and, in many cases, it even leads to more hallucinations. We then analyze how extended reasoning affects hallucination behavior. We find that reduced hallucinations often result from the model choosing to abstain after thinking more, rather than from improved factual recall. Conversely, for some models, longer reasoning encourages attempts on previously unanswered questions, many of which result in hallucinations. Case studies show that extended reasoning can induce confirmation bias, leading to overconfident hallucinations. Despite these limitations, we observe that compared to non-thinking, enabling thinking remains beneficial. Code and data are available at https://github.com/XuZhao0/tts-knowledge

Large Language Models (LLMs) have achieved impressive performance on reasoning-intensive tasks, yet optimizing their reasoning efficiency remains an open challenge. While Test-Time Scaling (TTS) improves reasoning quality, it often leads to overthinking, wasting tokens on redundant computations. This work investigates how to efficiently and adaptively guide LLM test-time scaling without additional training. Inspired by the concept of momentum in physics, we propose Momentum Uncertainty-guided Reasoning (MUR), which dynamically allocates thinking budgets to critical reasoning steps by tracking and aggregating stepwise uncertainty over time. To support flexible inference-time control, we introduce gamma-control, a simple mechanism that tunes the reasoning budget via a single hyperparameter. We provide in-depth theoretical proof to support the superiority of MUR in terms of stability and biases. MUR is comprehensively evaluated against various TTS methods across four challenging benchmarks (MATH-500, AIME24, AIME25, and GPQA-diamond) using different sizes of recent Qwen3 models (1.7B, 4B, and 8B). Results demonstrate that MUR reduces computation by over 50% on average while improving accuracy by 0.62-3.37%.

It is commonly believed that scaling language models should commit a significant space or time cost, by increasing the parameters (parameter scaling) or output tokens (inference-time scaling). We introduce the third and more inference-efficient scaling paradigm: increasing the model's parallel computation during both training and inference time. We apply P diverse and learnable transformations to the input, execute forward passes of the model in parallel, and dynamically aggregate the P outputs. This method, namely parallel scaling (ParScale), scales parallel computation by reusing existing parameters and can be applied to any model structure, optimization procedure, data, or task. We theoretically propose a new scaling law and validate it through large-scale pre-training, which shows that a model with P parallel streams is similar to scaling the parameters by O(log P) while showing superior inference efficiency. For example, ParScale can use up to 22times less memory increase and 6times less latency increase compared to parameter scaling that achieves the same performance improvement. It can also recycle an off-the-shelf pre-trained model into a parallelly scaled one by post-training on a small amount of tokens, further reducing the training budget. The new scaling law we discovered potentially facilitates the deployment of more powerful models in low-resource scenarios, and provides an alternative perspective for the role of computation in machine learning.

We investigate large language model performance across five orders of magnitude of compute scaling in eleven recent model architectures. We show that average benchmark performance, aggregating over many individual tasks and evaluations as in the commonly-used BIG-Bench dataset, is decently predictable as a function of training compute scale. Specifically, when extrapolating BIG-Bench Hard performance across one order of magnitude in compute, we observe average absolute errors of 6 percentage points (pp). By contrast, extrapolation for individual BIG-Bench tasks across an order of magnitude in compute yields higher average errors of 18pp. Nonetheless, individual task performance remains significantly more predictable than chance. Overall, our work suggests compute scaling provides a promising basis to forecast AI capabilities in diverse benchmarks, though predicting performance in specific tasks poses challenges.

This paper presents a detailed analysis of the scalability and parallelization of local search algorithms for the Satisfiability problem. We propose a framework to estimate the parallel performance of a given algorithm by analyzing the runtime behavior of its sequential version. Indeed, by approximating the runtime distribution of the sequential process with statistical methods, the runtime behavior of the parallel process can be predicted by a model based on order statistics. We apply this approach to study the parallel performance of two SAT local search solvers, namely Sparrow and CCASAT, and compare the predicted performances to the results of an actual experimentation on parallel hardware up to 384 cores. We show that the model is accurate and predicts performance close to the empirical data. Moreover, as we study different types of instances (random and crafted), we observe that the local search solvers exhibit different behaviors and that their runtime distributions can be approximated by two types of distributions: exponential (shifted and non-shifted) and lognormal.

Scaling laws are a critical component of the LLM development pipeline, most famously as a way to forecast training decisions such as 'compute-optimally' trading-off parameter count and dataset size, alongside a more recent growing list of other crucial decisions. In this work, we ask whether compute-optimal scaling behaviour can be skill-dependent. In particular, we examine knowledge and reasoning-based skills such as knowledge-based QA and code generation, and we answer this question in the affirmative: scaling laws are skill-dependent. Next, to understand whether skill-dependent scaling is an artefact of the pretraining datamix, we conduct an extensive ablation of different datamixes and find that, also when correcting for datamix differences, knowledge and code exhibit fundamental differences in scaling behaviour. We conclude with an analysis of how our findings relate to standard compute-optimal scaling using a validation set, and find that a misspecified validation set can impact compute-optimal parameter count by nearly 50%, depending on its skill composition.

Reinforcement learning (RL) has become central to training large language models (LLMs), yet the field lacks predictive scaling methodologies comparable to those established for pre-training. Despite rapidly rising compute budgets, there is no principled understanding of how to evaluate algorithmic improvements for scaling RL compute. We present the first large-scale systematic study, amounting to more than 400,000 GPU-hours, that defines a principled framework for analyzing and predicting RL scaling in LLMs. We fit sigmoidal compute-performance curves for RL training and ablate a wide range of common design choices to analyze their effects on asymptotic performance and compute efficiency. We observe: (1) Not all recipes yield similar asymptotic performance, (2) Details such as loss aggregation, normalization, curriculum, and off-policy algorithm primarily modulate compute efficiency without materially shifting the asymptote, and (3) Stable, scalable recipes follow predictable scaling trajectories, enabling extrapolation from smaller-scale runs. Combining these insights, we propose a best-practice recipe, ScaleRL, and demonstrate its effectiveness by successfully scaling and predicting validation performance on a single RL run scaled up to 100,000 GPU-hours. Our work provides both a scientific framework for analyzing scaling in RL and a practical recipe that brings RL training closer to the predictability long achieved in pre-training.

Recently, Test-Time Scaling (TTS) has gained increasing attention for improving LLM reasoning performance at test time without retraining the model. A notable TTS technique is Self-Consistency (SC), which generates multiple reasoning chains in parallel and selects the final answer via majority voting. While effective, the order-of-magnitude computational overhead limits its broad deployment. Prior attempts to accelerate SC mainly rely on model-based confidence scores or heuristics with limited empirical support. For the first time, we theoretically and empirically analyze the inefficiencies of SC and reveal actionable opportunities for improvement. Building on these insights, we propose Slim-SC, a step-wise pruning strategy that identifies and removes redundant chains using inter-chain similarity at the thought level. Experiments on three STEM reasoning datasets and two recent LLM architectures show that Slim-SC reduces inference latency and KVC usage by up to 45% and 26%, respectively, with R1-Distill, while maintaining or improving accuracy, thus offering a simple yet efficient TTS alternative for SC.

While 4-bit quantization has emerged as a memory-optimal choice for non-reasoning models and zero-shot tasks across scales, we show that this universal prescription fails for reasoning models, where the KV cache rather than model size can dominate memory. Through systematic experiments across 1,700 inference scenarios on AIME25 and GPQA-Diamond, we find a scale-dependent trade-off: models with an effective size below 8-bit 4B parameters achieve better accuracy by allocating memory to more weights rather than longer generation, while larger models achieve better accuracy by allocating memory to longer generations. This scale threshold also determines when parallel scaling becomes memory-efficient and whether KV cache eviction outperforms KV quantization. Our findings show that memory optimization for LLMs cannot be scale-agnostic, while providing principled guidelines: for small reasoning models, prioritize model capacity over test-time compute, while for larger ones, maximize test-time compute. Our results suggest that optimizing reasoning models for deployment requires fundamentally different strategies from those established for non-reasoning models.

Test-Time Adaptation (TTA) has recently emerged as a promising approach for tackling the robustness challenge under distribution shifts. However, the lack of consistent settings and systematic studies in prior literature hinders thorough assessments of existing methods. To address this issue, we present TTAB, a test-time adaptation benchmark that encompasses ten state-of-the-art algorithms, a diverse array of distribution shifts, and two evaluation protocols. Through extensive experiments, our benchmark reveals three common pitfalls in prior efforts. First, selecting appropriate hyper-parameters, especially for model selection, is exceedingly difficult due to online batch dependency. Second, the effectiveness of TTA varies greatly depending on the quality and properties of the model being adapted. Third, even under optimal algorithmic conditions, none of the existing methods are capable of addressing all common types of distribution shifts. Our findings underscore the need for future research in the field to conduct rigorous evaluations on a broader set of models and shifts, and to re-examine the assumptions behind the empirical success of TTA. Our code is available at https://github.com/lins-lab/ttab.

Scaling data and compute is critical to the success of machine learning. However, scaling demands predictability: we want methods to not only perform well with more compute or data, but also have their performance be predictable from small-scale runs, without running the large-scale experiment. In this paper, we show that value-based off-policy RL methods are predictable despite community lore regarding their pathological behavior. First, we show that data and compute requirements to attain a given performance level lie on a Pareto frontier, controlled by the updates-to-data (UTD) ratio. By estimating this frontier, we can predict this data requirement when given more compute, and this compute requirement when given more data. Second, we determine the optimal allocation of a total resource budget across data and compute for a given performance and use it to determine hyperparameters that maximize performance for a given budget. Third, this scaling behavior is enabled by first estimating predictable relationships between hyperparameters, which is used to manage effects of overfitting and plasticity loss unique to RL. We validate our approach using three algorithms: SAC, BRO, and PQL on DeepMind Control, OpenAI gym, and IsaacGym, when extrapolating to higher levels of data, compute, budget, or performance.

Scaling the amount of compute used to train language models has dramatically improved their capabilities. However, when it comes to inference, we often limit the amount of compute to only one attempt per problem. Here, we explore inference compute as another axis for scaling by increasing the number of generated samples. Across multiple tasks and models, we observe that coverage - the fraction of problems solved by any attempt - scales with the number of samples over four orders of magnitude. In domains like coding and formal proofs, where all answers can be automatically verified, these increases in coverage directly translate into improved performance. When we apply repeated sampling to SWE-bench Lite, the fraction of issues solved with DeepSeek-V2-Coder-Instruct increases from 15.9% with one sample to 56% with 250 samples, outperforming the single-attempt state-of-the-art of 43% which uses more capable frontier models. Moreover, using current API pricing, amplifying the cheaper DeepSeek model with five samples is more cost-effective and solves more issues than paying a premium for one sample from GPT-4o or Claude 3.5 Sonnet. Interestingly, the relationship between coverage and the number of samples is often log-linear and can be modelled with an exponentiated power law, suggesting the existence of inference-time scaling laws. Finally, we find that identifying correct samples out of many generations remains an important direction for future research in domains without automatic verifiers. When solving math word problems from GSM8K and MATH, coverage with Llama-3 models grows to over 95% with 10,000 samples. However, common methods to pick correct solutions from a sample collection, such as majority voting or reward models, plateau beyond several hundred samples and fail to fully scale with the sample budget.

Language models (LMs) perform well on standardized coding benchmarks but struggle with real-world software engineering tasks such as resolving GitHub issues in SWE-Bench, especially when model parameters are less than 100B. While smaller models are preferable in practice due to their lower computational cost, improving their performance remains challenging. Existing approaches primarily rely on supervised fine-tuning (SFT) with high-quality data, which is expensive to curate at scale. An alternative is test-time scaling: generating multiple outputs, scoring them using a verifier, and selecting the best one. Although effective, this strategy often requires excessive sampling and costly scoring, limiting its practical application. We propose Evolutionary Test-Time Scaling (EvoScale), a sample-efficient method that treats generation as an evolutionary process. By iteratively refining outputs via selection and mutation, EvoScale shifts the output distribution toward higher-scoring regions, reducing the number of samples needed to find correct solutions. To reduce the overhead from repeatedly sampling and selection, we train the model to self-evolve using reinforcement learning (RL). Rather than relying on external verifiers at inference time, the model learns to self-improve the scores of its own generations across iterations. Evaluated on SWE-Bench-Verified, EvoScale enables our 32B model, Satori-SWE-32B, to match or exceed the performance of models with over 100B parameters while using a few samples. Code, data, and models will be fully open-sourced.

Pre-training is notoriously compute-intensive and academic researchers are notoriously under-resourced. It is, therefore, commonly assumed that academics can't pre-train models. In this paper, we seek to clarify this assumption. We first survey academic researchers to learn about their available compute and then empirically measure the time to replicate models on such resources. We introduce a benchmark to measure the time to pre-train models on given GPUs and also identify ideal settings for maximizing training speed. We run our benchmark on a range of models and academic GPUs, spending 2,000 GPU-hours on our experiments. Our results reveal a brighter picture for academic pre-training: for example, although Pythia-1B was originally trained on 64 GPUs for 3 days, we find it is also possible to replicate this model (with the same hyper-parameters) in 3x fewer GPU-days: i.e. on 4 GPUs in 18 days. We conclude with a cost-benefit analysis to help clarify the trade-offs between price and pre-training time. We believe our benchmark will help academic researchers conduct experiments that require training larger models on more data. We fully release our codebase at: https://github.com/apoorvkh/academic-pretraining.

Hoffmann et al. (2022) propose three methods for estimating a compute-optimal scaling law. We attempt to replicate their third estimation procedure, which involves fitting a parametric loss function to a reconstruction of data from their plots. We find that the reported estimates are inconsistent with their first two estimation methods, fail at fitting the extracted data, and report implausibly narrow confidence intervals--intervals this narrow would require over 600,000 experiments, while they likely only ran fewer than 500. In contrast, our rederivation of the scaling law using the third approach yields results that are compatible with the findings from the first two estimation procedures described by Hoffmann et al.

We introduce TimeSeriesGym, a scalable benchmarking framework for evaluating Artificial Intelligence (AI) agents on time series machine learning engineering challenges. Existing benchmarks lack scalability, focus narrowly on model building in well-defined settings, and evaluate only a limited set of research artifacts (e.g., CSV submission files). To make AI agent benchmarking more relevant to the practice of machine learning engineering, our framework scales along two critical dimensions. First, recognizing that effective ML engineering requires a range of diverse skills, TimeSeriesGym incorporates challenges from diverse sources spanning multiple domains and tasks. We design challenges to evaluate both isolated capabilities (including data handling, understanding research repositories, and code translation) and their combinations, and rather than addressing each challenge independently, we develop tools that support designing multiple challenges at scale. Second, we implement evaluation mechanisms for multiple research artifacts, including submission files, code, and models, using both precise numeric measures and more flexible LLM-based evaluation approaches. This dual strategy balances objective assessment with contextual judgment. Although our initial focus is on time series applications, our framework can be readily extended to other data modalities, broadly enhancing the comprehensiveness and practical utility of agentic AI evaluation. We open-source our benchmarking framework to facilitate future research on the ML engineering capabilities of AI agents.

While inference-time scaling enables LLMs to carry out increasingly long and capable reasoning traces, the patterns and insights uncovered during these traces are immediately discarded once the context window is reset for a new query. External memory is a natural way to persist these discoveries, and recent work has shown clear benefits for reasoning-intensive tasks. We see an opportunity to make such memories more broadly reusable and scalable by moving beyond instance-based memory entries (e.g. exact query/response pairs, or summaries tightly coupled with the original problem context) toward concept-level memory: reusable, modular abstractions distilled from solution traces and stored in natural language. For future queries, relevant concepts are selectively retrieved and integrated into the prompt, enabling test-time continual learning without weight updates. Our design introduces new strategies for abstracting takeaways from rollouts and retrieving entries for new queries, promoting reuse and allowing memory to expand with additional experiences. We evaluate on ARC-AGI, a benchmark that stresses compositional generalization and abstract reasoning, making it a natural fit for concept memory. Our method yields a 7.5% relative gain over a strong no-memory baseline with performance continuing to scale with inference compute. We find abstract concepts to be the most consistent memory design, outscoring the baseline at all tested inference compute scales. Moreover, dynamically updating memory during test-time outperforms fixed settings, supporting the hypothesis that accumulating and abstracting patterns enables further solutions in a form of self-improvement. Code is available at https://github.com/matt-seb-ho/arc_memo.

Recently, test-time adaptation (TTA) has been proposed as a promising solution for addressing distribution shifts. It allows a base model to adapt to an unforeseen distribution during inference by leveraging the information from the batch of (unlabeled) test data. However, we uncover a novel security vulnerability of TTA based on the insight that predictions on benign samples can be impacted by malicious samples in the same batch. To exploit this vulnerability, we propose Distribution Invading Attack (DIA), which injects a small fraction of malicious data into the test batch. DIA causes models using TTA to misclassify benign and unperturbed test data, providing an entirely new capability for adversaries that is infeasible in canonical machine learning pipelines. Through comprehensive evaluations, we demonstrate the high effectiveness of our attack on multiple benchmarks across six TTA methods. In response, we investigate two countermeasures to robustify the existing insecure TTA implementations, following the principle of "security by design". Together, we hope our findings can make the community aware of the utility-security tradeoffs in deploying TTA and provide valuable insights for developing robust TTA approaches.

Solving the inverse problem is the key step in evaluating the capacity of a physical model to describe real phenomena. In medical image computing, it aligns with the classical theme of image-based model personalization. Traditionally, a solution to the problem is obtained by performing either sampling or variational inference based methods. Both approaches aim to identify a set of free physical model parameters that results in a simulation best matching an empirical observation. When applied to brain tumor modeling, one of the instances of image-based model personalization in medical image computing, the overarching drawback of the methods is the time complexity for finding such a set. In a clinical setting with limited time between imaging and diagnosis or even intervention, this time complexity may prove critical. As the history of quantitative science is the history of compression, we align in this paper with the historical tendency and propose a method compressing complex traditional strategies for solving an inverse problem into a simple database query task. We evaluated different ways of performing the database query task assessing the trade-off between accuracy and execution time. On the exemplary task of brain tumor growth modeling, we prove that the proposed method achieves one order speed-up compared to existing approaches for solving the inverse problem. The resulting compute time offers critical means for relying on more complex and, hence, realistic models, for integrating image preprocessing and inverse modeling even deeper, or for implementing the current model into a clinical workflow.

On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is the compute-optimal scaling law, which reports the performance as a function of units of compute when choosing model sizes optimally. We analyze a random feature model trained with gradient descent as a solvable model of network training and generalization. This reproduces many observations about neural scaling laws. First, our model makes a prediction about why the scaling of performance with training time and with model size have different power law exponents. Consequently, the theory predicts an asymmetric compute-optimal scaling rule where the number of training steps are increased faster than model parameters, consistent with recent empirical observations. Second, it has been observed that early in training, networks converge to their infinite-width dynamics at a rate 1/width but at late time exhibit a rate width^{-c}, where c depends on the structure of the architecture and task. We show that our model exhibits this behavior. Lastly, our theory shows how the gap between training and test loss can gradually build up over time due to repeated reuse of data.

This paper presents our approach to accelerate computer architecture simulation by leveraging machine learning techniques. Traditional computer architecture simulations are time-consuming, making it challenging to explore different design choices efficiently. Our proposed model utilizes a combination of application features and micro-architectural features to predict the performance of an application. These features are derived from simulations of a small portion of the application. We demonstrate the effectiveness of our approach by building and evaluating a machine learning model that offers significant speedup in architectural exploration. This model demonstrates the ability to predict IPC values for the testing data with a root mean square error of less than 0.1.

Inference-time scaling trades efficiency for increased reasoning accuracy by generating longer or more parallel sequences. However, in Transformer LLMs, generation cost is bottlenecked by the size of the key-value (KV) cache, rather than the number of generated tokens. Hence, we explore inference-time hyper-scaling: by compressing the KV cache, we can generate more tokens within the same compute budget and further improve the accuracy of scaled inference. The success of this approach, however, hinges on the ability of compression methods to preserve accuracy even at high compression ratios. To make hyper-scaling practical, we introduce Dynamic Memory Sparsification (DMS), a novel method for sparsifying KV caches that only requires 1K training steps to achieve 8times compression, while maintaining better accuracy than training-free sparse attention. Instead of prematurely discarding cached tokens, DMS delays token eviction, implicitly merging representations and preserving critical information. We demonstrate the effectiveness of inference-time hyper-scaling with DMS on multiple families of LLMs, showing that it boosts accuracy for comparable inference runtime and memory load. For instance, we enhance Qwen-R1 32B by an average of 9.1 points on AIME 24, 7.6 on GPQA, and 9.6 on LiveCodeBench across compute budgets.

We consider the solvable neural scaling model with three parameters: data complexity, target complexity, and model-parameter-count. We use this neural scaling model to derive new predictions about the compute-limited, infinite-data scaling law regime. To train the neural scaling model, we run one-pass stochastic gradient descent on a mean-squared loss. We derive a representation of the loss curves which holds over all iteration counts and improves in accuracy as the model parameter count grows. We then analyze the compute-optimal model-parameter-count, and identify 4 phases (+3 subphases) in the data-complexity/target-complexity phase-plane. The phase boundaries are determined by the relative importance of model capacity, optimizer noise, and embedding of the features. We furthermore derive, with mathematical proof and extensive numerical evidence, the scaling-law exponents in all of these phases, in particular computing the optimal model-parameter-count as a function of floating point operation budget.

The Languini Kitchen serves as both a research collective and codebase designed to empower researchers with limited computational resources to contribute meaningfully to the field of language modelling. We introduce an experimental protocol that enables model comparisons based on equivalent compute, measured in accelerator hours. The number of tokens on which a model is trained is defined by the model's throughput and the chosen compute class. Notably, this approach avoids constraints on critical hyperparameters which affect total parameters or floating-point operations. For evaluation, we pre-process an existing large, diverse, and high-quality dataset of books that surpasses existing academic benchmarks in quality, diversity, and document length. On it, we compare methods based on their empirical scaling trends which are estimated through experiments at various levels of compute. This work also provides two baseline models: a feed-forward model derived from the GPT-2 architecture and a recurrent model in the form of a novel LSTM with ten-fold throughput. While the GPT baseline achieves better perplexity throughout all our levels of compute, our LSTM baseline exhibits a predictable and more favourable scaling law. This is due to the improved throughput and the need for fewer training tokens to achieve the same decrease in test perplexity. Extrapolating the scaling laws leads of both models results in an intersection at roughly 50,000 accelerator hours. We hope this work can serve as the foundation for meaningful and reproducible language modelling research.

Standardized benchmarks drive progress in machine learning. However, with repeated testing, the risk of overfitting grows as algorithms over-exploit benchmark idiosyncrasies. In our work, we seek to mitigate this challenge by compiling ever-expanding large-scale benchmarks called Lifelong Benchmarks. As exemplars of our approach, we create Lifelong-CIFAR10 and Lifelong-ImageNet, containing (for now) 1.69M and 1.98M test samples, respectively. While reducing overfitting, lifelong benchmarks introduce a key challenge: the high cost of evaluating a growing number of models across an ever-expanding sample set. To address this challenge, we also introduce an efficient evaluation framework: Sort \& Search (S&S), which reuses previously evaluated models by leveraging dynamic programming algorithms to selectively rank and sub-select test samples, enabling cost-effective lifelong benchmarking. Extensive empirical evaluations across 31,000 models demonstrate that S&S achieves highly-efficient approximate accuracy measurement, reducing compute cost from 180 GPU days to 5 GPU hours (1000x reduction) on a single A100 GPU, with low approximation error. As such, lifelong benchmarks offer a robust, practical solution to the "benchmark exhaustion" problem.

The increasing versatility of language models LMs has given rise to a new class of benchmarks that comprehensively assess a broad range of capabilities. Such benchmarks are associated with massive computational costs reaching thousands of GPU hours per model. However the efficiency aspect of these evaluation efforts had raised little discussion in the literature. In this work we present the problem of Efficient Benchmarking namely intelligently reducing the computation costs of LM evaluation without compromising reliability. Using the HELM benchmark as a test case we investigate how different benchmark design choices affect the computation-reliability tradeoff. We propose to evaluate the reliability of such decisions by using a new measure Decision Impact on Reliability DIoR for short. We find for example that the current leader on HELM may change by merely removing a low-ranked model from the benchmark and observe that a handful of examples suffice to obtain the correct benchmark ranking. Conversely a slightly different choice of HELM scenarios varies ranking widely. Based on our findings we outline a set of concrete recommendations for more efficient benchmark design and utilization practices leading to dramatic cost savings with minimal loss of benchmark reliability often reducing computation by x100 or more.

We examine the reasoning and planning capabilities of large language models (LLMs) in solving complex tasks. Recent advances in inference-time techniques demonstrate the potential to enhance LLM reasoning without additional training by exploring intermediate steps during inference. Notably, OpenAI's o1 model shows promising performance through its novel use of multi-step reasoning and verification. Here, we explore how scaling inference-time techniques can improve reasoning and planning, focusing on understanding the tradeoff between computational cost and performance. To this end, we construct a comprehensive benchmark, known as Sys2Bench, and perform extensive experiments evaluating existing inference-time techniques on eleven diverse tasks across five categories, including arithmetic reasoning, logical reasoning, common sense reasoning, algorithmic reasoning, and planning. Our findings indicate that simply scaling inference-time computation has limitations, as no single inference-time technique consistently performs well across all reasoning and planning tasks.

The challenge of mapping AI architectures to GPU hardware is creating a critical bottleneck in AI progress. Despite substantial efforts, hand-written custom kernels fail to meet their theoretical performance thresholds, even on well-established operations like linear attention. The diverse hardware capabilities of GPUs might suggest that we need a wide variety of techniques to achieve high performance. However, our work explores whether a small number of key abstractions can drastically simplify the process. We present ThunderKittens (TK), a framework for writing performant AI kernels while remaining easy to use and maintain. Our abstractions map to the three levels of the GPU hierarchy: (1) at the warp-level, we provide 16x16 matrix tiles as basic data structures and PyTorch-like parallel compute operations over tiles, (2) at the thread-block level, we provide a template for overlapping asynchronous operations across parallel warps, and (3) at the grid-level, we provide support to help hide the block launch and tear-down, and memory costs. We show the value of TK by providing kernels that match or outperform prior kernels for a range of AI operations. We match CuBLAS and FlashAttention-3 on GEMM and attention inference performance and outperform the strongest baselines by 10-40% on attention backwards, 8times on state space models, and 14times on linear attention.

Community GPU platforms are emerging as a cost-effective and democratized alternative to centralized GPU clusters for AI workloads, aggregating idle consumer GPUs from globally distributed and heterogeneous environments. However, their extreme hardware/software diversity, volatile availability, and variable network conditions render traditional schedulers ineffective, leading to suboptimal task completion. In this work, we present REACH (Reinforcement Learning for Efficient Allocation in Community and Heterogeneous Networks), a Transformer-based reinforcement learning framework that redefines task scheduling as a sequence scoring problem to balance performance, reliability, cost, and network efficiency. By modeling both global GPU states and task requirements, REACH learns to adaptively co-locate computation with data, prioritize critical jobs, and mitigate the impact of unreliable resources. Extensive simulation results show that REACH improves task completion rates by up to 17%, more than doubles the success rate for high-priority tasks, and reduces bandwidth penalties by over 80% compared to state-of-the-art baselines. Stress tests further demonstrate its robustness to GPU churn and network congestion, while scalability experiments confirm its effectiveness in large-scale, high-contention scenarios.

Cloud platforms are increasingly relied upon to host diverse, resource-intensive workloads due to their scalability, flexibility, and cost-efficiency. In multi-tenant cloud environments, virtual machines are consolidated on shared physical servers to improve resource utilization. While virtualization guarantees resource partitioning for CPU, memory, and storage, it cannot ensure performance isolation. Competition for shared resources such as last-level cache, memory bandwidth, and network interfaces often leads to severe performance degradation. Existing management techniques, including VM scheduling and resource provisioning, require accurate performance prediction to mitigate interference. However, this remains challenging in public clouds due to the black-box nature of VMs and the highly dynamic nature of workloads. To address these limitations, we propose CloudFormer, a dual-branch Transformer-based model designed to predict VM performance degradation in black-box environments. CloudFormer jointly models temporal dynamics and system-level interactions, leveraging 206 system metrics at one-second resolution across both static and dynamic scenarios. This design enables the model to capture transient interference effects and adapt to varying workload conditions without scenario-specific tuning. Complementing the methodology, we provide a fine-grained dataset that significantly expands the temporal resolution and metric diversity compared to existing benchmarks. Experimental results demonstrate that CloudFormer consistently outperforms state-of-the-art baselines across multiple evaluation metrics, achieving robust generalization across diverse and previously unseen workloads. Notably, CloudFormer attains a mean absolute error (MAE) of just 7.8%, representing a substantial improvement in predictive accuracy and outperforming existing methods at least by 28%.

Traditionally, data selection has been studied in settings where all samples from prospective sources are fully revealed to a machine learning developer. However, in practical data exchange scenarios, data providers often reveal only a limited subset of samples before an acquisition decision is made. Recently, there have been efforts to fit scaling laws that predict model performance at any size and data source composition using the limited available samples. However, these scaling functions are black-box, computationally expensive to fit, highly susceptible to overfitting, or/and difficult to optimize for data selection. This paper proposes a framework called <projektor>, which predicts model performance and supports data selection decisions based on partial samples of prospective data sources. Our approach distinguishes itself from existing work by introducing a novel *two-stage* performance inference process. In the first stage, we leverage the Optimal Transport distance to predict the model's performance for any data mixture ratio within the range of disclosed data sizes. In the second stage, we extrapolate the performance to larger undisclosed data sizes based on a novel parameter-free mapping technique inspired by neural scaling laws. We further derive an efficient gradient-based method to select data sources based on the projected model performance. Evaluation over a diverse range of applications demonstrates that <projektor> significantly improves existing performance scaling approaches in terms of both the accuracy of performance inference and the computation costs associated with constructing the performance predictor. Also, <projektor> outperforms by a wide margin in data selection effectiveness compared to a range of other off-the-shelf solutions.

The recent shift in Generative AI (GenAI) applications from cloud-only environments to end-user devices introduces new challenges in resource management, system efficiency, and user experience. This paper presents ConsumerBench, a comprehensive benchmarking framework designed to evaluate the system efficiency and response time of GenAI models running on end-user devices. Unlike existing benchmarks that assume exclusive model access on dedicated GPUs, ConsumerBench simulates realistic multi-application scenarios executing concurrently on constrained hardware. Furthermore, ConsumerBench supports customizable workflows that simulate complex tasks requiring coordination among multiple applications. ConsumerBench captures both application-level metrics, including latency and Service Level Objective (SLO) attainment, and system-level metrics like CPU/GPU utilization and memory bandwidth. Through extensive experiments, ConsumerBench reveals inefficiencies in resource sharing, unfair scheduling under greedy allocation, and performance pitfalls of static model server configurations. The paper also provides practical insights for model developers and system designers, highlighting the benefits of custom kernels tailored to consumer-grade GPU architectures and the value of implementing SLO-aware scheduling strategies.

Deep learning thrives with large neural networks and large datasets. However, larger networks and larger datasets result in longer training times that impede research and development progress. Distributed synchronous SGD offers a potential solution to this problem by dividing SGD minibatches over a pool of parallel workers. Yet to make this scheme efficient, the per-worker workload must be large, which implies nontrivial growth in the SGD minibatch size. In this paper, we empirically show that on the ImageNet dataset large minibatches cause optimization difficulties, but when these are addressed the trained networks exhibit good generalization. Specifically, we show no loss of accuracy when training with large minibatch sizes up to 8192 images. To achieve this result, we adopt a hyper-parameter-free linear scaling rule for adjusting learning rates as a function of minibatch size and develop a new warmup scheme that overcomes optimization challenges early in training. With these simple techniques, our Caffe2-based system trains ResNet-50 with a minibatch size of 8192 on 256 GPUs in one hour, while matching small minibatch accuracy. Using commodity hardware, our implementation achieves ~90% scaling efficiency when moving from 8 to 256 GPUs. Our findings enable training visual recognition models on internet-scale data with high efficiency.

Exponential increases in scientific experimental data are outstripping the rate of progress in silicon technology. As a result, heterogeneous combinations of architectures and process or device technologies are increasingly important to meet the computing demands of future scientific experiments. However, the complexity of heterogeneous computing systems requires systematic modeling to understand performance. We present a model which addresses this need by framing key aspects of data collection pipelines and constraints, and combines them with the important vectors of technology that shape alternatives, computing metrics that allow complex alternatives to be compared. For instance, a data collection pipeline may be characterized by parameters such as sensor sampling rates, amount of data collected, and the overall relevancy of retrieved samples. Alternatives to this pipeline are enabled by hardware development vectors including advancing CMOS, GPUs, neuromorphic computing, and edge computing. By calculating metrics for each alternative such as overall F1 score, power, hardware cost, and energy expended per relevant sample, this model allows alternate data collection systems to be rigorously compared. To demonstrate this model's capability, we apply it to the CMS experiment (and planned HL-LHC upgrade) to evaluate and compare the application of novel technologies in the data acquisition system (DAQ). We demonstrate that improvements to early stages in the DAQ are highly beneficial, greatly reducing the resources required at later stages of processing (such as a 60% power reduction) and increasing the amount of relevant data retrieved from the experiment per unit power (improving from 0.065 to 0.31 samples/kJ) However, we predict further advances will be required in order to meet overall power and cost constraints for the DAQ.

It is a common belief that large language models (LLMs) are better than smaller-sized ones. However, larger models also require significantly more time and compute during inference. This begs the question: what happens when both models operate under the same budget? (e.g., compute, run-time). To address this question, we analyze code generation LLMs of various sizes and make comparisons such as running a 70B model once vs. generating five outputs from a 13B model. We consider a standard unit-test setup, which can be used to select the correct output from the smaller model. Our findings reveal that the repeated use of smaller models can yield consistent improvements, with gains of up to 15% across five tasks. On the other hand, in scenarios where unit-tests are unavailable, a ranking-based selection of candidates from the smaller model falls short of the performance of a single output from larger ones. Our results highlight the potential of using smaller models instead of larger ones, and the importance of studying approaches for ranking LLM outputs.

We introduce our first reflective generative model MetaStone-S1, which obtains OpenAI o3's performance via the self-supervised process reward model (SPRM). Through sharing the backbone network and using task-specific heads for next token prediction and process scoring respectively, SPRM successfully integrates the policy model and process reward model(PRM) into a unified interface without extra process annotation, reducing over 99% PRM parameters for efficient reasoning. Equipped with SPRM, MetaStone-S1 is naturally suitable for test time scaling (TTS), and we provide three reasoning effort modes (low, medium, and high), based on the controllable thinking length. Moreover, we empirically establish a scaling law that reveals the relationship between total thinking computation and TTS performance. Experiments demonstrate that our MetaStone-S1 achieves comparable performance to OpenAI-o3-mini's series with only 32B parameter size. To support the research community, we have open-sourced MetaStone-S1 at https://github.com/MetaStone-AI/MetaStone-S1.

Parallel LLM inference scaling involves sampling a set of N>1 responses for a single input prompt. However, these N parallel responses tend to be generated independently from each other, partitioning compute resources and leaving potentially useful information in one generation untapped by others. This is in contrast to response length scaling where past computation is used in all future steps. For higher quality responses and response sets, we propose Bridge to generate interdependent responses in parallel by rethinking batched LLM hidden states as holistic tensors rather than independent slices. With only a small amount (2.8%-5.1%) of new parameters, Bridge improves the relative mean accuracy gains from reinforcement learning with verifiable rewards by up to 50% and boosts consistency of correct responses. Trained once, Bridge scales to any generation width, all with greater performance than independent generations, unlocking a more general mode of parallel scaling that effectively leverages information between sequences, compatible with any post-generation aggregation technique.

Efficient GPU kernels are crucial for building performant machine learning architectures, but writing them is a time-consuming challenge that requires significant expertise; therefore, we explore using language models (LMs) to automate kernel generation. We introduce KernelBench, an open-source framework for evaluating LMs' ability to write fast and correct kernels on a suite of 250 carefully selected PyTorch ML workloads. KernelBench represents a real-world engineering environment and making progress on the introduced benchmark directly translates to faster practical kernels. We introduce a new evaluation metric fast_p, which measures the percentage of generated kernels that are functionally correct and offer a speedup greater than an adjustable threshold p over baseline. Our experiments across various state-of-the-art models and test-time methods show that frontier reasoning models perform the best out of the box but still fall short overall, matching the PyTorch baseline in less than 20% of the cases. While we show that results can improve by leveraging execution and profiling feedback during iterative refinement, KernelBench remains a challenging benchmark, with its difficulty increasing as we raise speedup threshold p.

Large language models (LLMs) have demonstrated remarkable success as foundational models, benefiting various downstream applications through fine-tuning. Recent studies on loss scaling have demonstrated the superior performance of larger LLMs compared to their smaller counterparts. Nevertheless, training LLMs with billions of parameters poses significant challenges and requires considerable computational resources. For example, training a one trillion parameter GPT-style model on 20 trillion tokens requires a staggering 120 million exaflops of computation. This research explores efficient distributed training strategies to extract this computation from Frontier, the world's first exascale supercomputer dedicated to open science. We enable and investigate various model and data parallel training techniques, such as tensor parallelism, pipeline parallelism, and sharded data parallelism, to facilitate training a trillion-parameter model on Frontier. We empirically assess these techniques and their associated parameters to determine their impact on memory footprint, communication latency, and GPU's computational efficiency. We analyze the complex interplay among these techniques and find a strategy to combine them to achieve high throughput through hyperparameter tuning. We have identified efficient strategies for training large LLMs of varying sizes through empirical analysis and hyperparameter tuning. For 22 Billion, 175 Billion, and 1 Trillion parameters, we achieved GPU throughputs of 38.38%, 36.14%, and 31.96%, respectively. For the training of the 175 Billion parameter model and the 1 Trillion parameter model, we achieved 100% weak scaling efficiency on 1024 and 3072 MI250X GPUs, respectively. We also achieved strong scaling efficiencies of 89% and 87% for these two models.

In August 2025, OpenAI released GPT-OSS models, its first open weight large language models since GPT-2 in 2019, comprising two mixture of experts architectures with 120B and 20B parameters. We evaluated both variants against six contemporary open source large language models ranging from 14.7B to 235B parameters, representing both dense and sparse designs, across ten benchmarks covering general knowledge, mathematical reasoning, code generation, multilingual understanding, and conversational ability. All models were tested in unquantised form under standardised inference settings, with statistical validation using McNemars test and effect size analysis. Results show that gpt-oss-20B consistently outperforms gpt-oss-120B on several benchmarks, such as HumanEval and MMLU, despite requiring substantially less memory and energy per response. Both models demonstrate mid-tier overall performance within the current open source landscape, with relative strength in code generation and notable weaknesses in multilingual tasks. These findings provide empirical evidence that scaling in sparse architectures may not yield proportional performance gains, underscoring the need for further investigation into optimisation strategies and informing more efficient model selection for future open source deployments.

AI agents are emerging as a dominant workload in a wide range of applications, promising to be the vehicle that delivers the promised benefits of AI to enterprises and consumers. Unlike conventional software or static inference, agentic workloads are dynamic and structurally complex. Often these agents are directed graphs of compute and IO operations that span multi-modal data input and conversion), data processing and context gathering (e.g vector DB lookups), multiple LLM inferences, tool calls, etc. To scale AI agent usage, we need efficient and scalable deployment and agent-serving infrastructure. To tackle this challenge, in this paper, we present a system design for dynamic orchestration of AI agent workloads on heterogeneous compute infrastructure spanning CPUs and accelerators, both from different vendors and across different performance tiers within a single vendor. The system delivers several building blocks: a framework for planning and optimizing agentic AI execution graphs using cost models that account for compute, memory, and bandwidth constraints of different HW; a MLIR based representation and compilation system that can decompose AI agent execution graphs into granular operators and generate code for different HW options; and a dynamic orchestration system that can place the granular components across a heterogeneous compute infrastructure and stitch them together while meeting an end-to-end SLA. Our design performs a systems level TCO optimization and preliminary results show that leveraging a heterogeneous infrastructure can deliver significant TCO benefits. A preliminary surprising finding is that for some workloads a heterogeneous combination of older generation GPUs with newer accelerators can deliver similar TCO as the latest generation homogenous GPU infrastructure design, potentially extending the life of deployed infrastructure.

In the last three years, the largest dense deep learning models have grown over 1000x to reach hundreds of billions of parameters, while the GPU memory has only grown by 5x (16 GB to 80 GB). Therefore, the growth in model scale has been supported primarily though system innovations that allow large models to fit in the aggregate GPU memory of multiple GPUs. However, we are getting close to the GPU memory wall. It requires 800 NVIDIA V100 GPUs just to fit a trillion parameter model for training, and such clusters are simply out of reach for most data scientists. In addition, training models at that scale requires complex combinations of parallelism techniques that puts a big burden on the data scientists to refactor their model. In this paper we present ZeRO-Infinity, a novel heterogeneous system technology that leverages GPU, CPU, and NVMe memory to allow for unprecedented model scale on limited resources without requiring model code refactoring. At the same time it achieves excellent training throughput and scalability, unencumbered by the limited CPU or NVMe bandwidth. ZeRO-Infinity can fit models with tens and even hundreds of trillions of parameters for training on current generation GPU clusters. It can be used to fine-tune trillion parameter models on a single NVIDIA DGX-2 node, making large models more accessible. In terms of training throughput and scalability, it sustains over 25 petaflops on 512 NVIDIA V100 GPUs(40% of peak), while also demonstrating super linear scalability. An open source implementation of ZeRO-Infinity is available through DeepSpeed, a deep learning optimization library that makes distributed training easy, efficient, and effective.

Training algorithms, broadly construed, are an essential part of every deep learning pipeline. Training algorithm improvements that speed up training across a wide variety of workloads (e.g., better update rules, tuning protocols, learning rate schedules, or data selection schemes) could save time, save computational resources, and lead to better, more accurate, models. Unfortunately, as a community, we are currently unable to reliably identify training algorithm improvements, or even determine the state-of-the-art training algorithm. In this work, using concrete experiments, we argue that real progress in speeding up training requires new benchmarks that resolve three basic challenges faced by empirical comparisons of training algorithms: (1) how to decide when training is complete and precisely measure training time, (2) how to handle the sensitivity of measurements to exact workload details, and (3) how to fairly compare algorithms that require hyperparameter tuning. In order to address these challenges, we introduce a new, competitive, time-to-result benchmark using multiple workloads running on fixed hardware, the AlgoPerf: Training Algorithms benchmark. Our benchmark includes a set of workload variants that make it possible to detect benchmark submissions that are more robust to workload changes than current widely-used methods. Finally, we evaluate baseline submissions constructed using various optimizers that represent current practice, as well as other optimizers that have recently received attention in the literature. These baseline results collectively demonstrate the feasibility of our benchmark, show that non-trivial gaps between methods exist, and set a provisional state-of-the-art for future benchmark submissions to try and surpass.

We conduct experiments on the impact of increasing inference-time compute in reasoning models (specifically OpenAI o1-preview and o1-mini) on their robustness to adversarial attacks. We find that across a variety of attacks, increased inference-time compute leads to improved robustness. In many cases (with important exceptions), the fraction of model samples where the attack succeeds tends to zero as the amount of test-time compute grows. We perform no adversarial training for the tasks we study, and we increase inference-time compute by simply allowing the models to spend more compute on reasoning, independently of the form of attack. Our results suggest that inference-time compute has the potential to improve adversarial robustness for Large Language Models. We also explore new attacks directed at reasoning models, as well as settings where inference-time compute does not improve reliability, and speculate on the reasons for these as well as ways to address them.

Long-sequence state-space models (SSMs) such as Hyena and Mamba replace the quadratic complexity of self-attention with more efficient FFT and scan operations. However, modern accelerators like GPUs are poorly suited to these non-GEMM workloads due to rigid execution models and specialization for dense matrix operations. This paper proposes architectural extensions to a baseline Reconfigurable Dataflow Unit (RDU) that efficiently support FFT-based and scan-based SSMs. By introducing lightweight interconnect enhancements within compute tiles, the extended RDU enables spatial mapping of FFT and scan dataflows with less than 1% area and power overhead. The resulting architecture achieves a 5.95X speedup over the GPU and a 1.95X speedup over the baseline RDU for Hyena, and a 2.12X and 1.75X speedup over the GPU and baseline RDU, respectively, for Mamba.

Inference-time techniques are emerging as highly effective tools to enhance large language model (LLM) capabilities. However, best practices for developing systems that combine these techniques remain underdeveloped due to our limited understanding of the utility of individual inference-time techniques and the interactions between them. Additionally, efficiently and automatically searching the space of model choices, inference-time techniques, and their compositions is challenging due to the large design space. To address these challenges, we introduce Archon, a modular framework for selecting, combining, and stacking layers of inference-time techniques to construct optimized LLM systems for target benchmarks. Rather than relying on a single LLM called once, we leverage a diverse set of LLMs and inference-time techniques, creating LLM systems greater than the sum of their parts. Archon defines an extensible design space, encompassing techniques such as generation ensembling, repeated sampling, ranking, fusion, critiquing, verification, and unit testing. It transforms the problem of building LLM systems into a hyperparameter optimization objective. Given the available LLMs, inference-time techniques, and compute budget, Archon utilizes hyperparameter search techniques to discover optimized architectures for target benchmark(s). We evaluate Archon architectures across a range of instruction-following, reasoning, and coding benchmarks, including MT-Bench, Arena-Hard-Auto, AlpacaEval 2.0, MixEval, MixEval Hard, MATH, and CodeContests. Archon architectures outperform frontier models, such as GPT-4o and Claude 3.5 Sonnet, on these benchmarks, achieving an average accuracy increase of 15.1 percentage points by using all available LLMs. We make our code and datasets available publicly on Github: https://github.com/ScalingIntelligence/Archon.

LLMs have seen rapid adoption in all domains. They need to be trained on high-end high-performance computing (HPC) infrastructures and ingest massive amounts of input data. Unsurprisingly, at such a large scale, unexpected events (e.g., failures of components, instability of the software, undesirable learning patterns, etc.), are frequent and typically impact the training in a negative fashion. Thus, LLMs need to be checkpointed frequently so that they can be rolled back to a stable state and subsequently fine-tuned. However, given the large sizes of LLMs, a straightforward checkpointing solution that directly writes the model parameters and optimizer state to persistent storage (e.g., a parallel file system), incurs significant I/O overheads. To address this challenge, in this paper we study how to reduce the I/O overheads for enabling fast and scalable checkpointing for LLMs that can be applied at high frequency (up to the granularity of individual iterations) without significant impact on the training process. Specifically, we introduce a lazy asynchronous multi-level approach that takes advantage of the fact that the tensors making up the model and optimizer state shards remain immutable for extended periods of time, which makes it possible to copy their content in the background with minimal interference during the training process. We evaluate our approach at scales of up to 180 GPUs using different model sizes, parallelism settings, and checkpointing frequencies. The results show up to 48times faster checkpointing and 2.2times faster end-to-end training runtime compared with the state-of-art checkpointing approaches.

The increasing computational demands of foundation models have spurred research into low-precision training, with 4-bit floating-point (FP4) formats emerging as a frontier for maximizing hardware throughput. While numerous techniques have been proposed to stabilize FP4 training, they often present isolated solutions with varying, and not always clear, computational overheads. This paper aims to provide a unified view of the design space of FP4 training. We introduce a comprehensive, quantisation gradient-based framework for microscaling quantization that allows for a theoretical analysis of the computational costs associated with different stabilization methods on both the forward and backward passes. Using a simulator built on this framework, we conduct an extensive empirical study across a wide range of machine learning tasks, including regression, image classification, diffusion models, and language models. By systematically evaluating thousands of combinations of techniques, such as novel gradient approximations, rounding strategies, and scaling methods, we identify which configurations offer the most favourable performance-to-overhead trade-off. We find that the techniques enabling the best trade-off involve carefully combining Hadamard transformations, tensor scaling and stochastic rounding. We further find that using UE5M3 as a scaling factor potentially offers a good compromise between range and precision with manageable computational overhead.

Web applications are increasingly becoming the primary platform for AI service delivery, making in-browser deep learning (DL) inference more prominent. However, current in-browser inference systems fail to effectively utilize advanced web programming techniques and customize kernels for various client devices, leading to suboptimal performance. To address the issues, this paper presents the first in-browser inference system, nn-JIT.web, which enables just-in-time (JIT) auto-generation of optimized kernels for both CPUs and GPUs during inference. The system achieves this by using two novel web programming techniques that can significantly reduce kernel generation time, compared to other tensor compilers such as TVM, while maintaining or even improving performance. The first technique, Tensor-Web Compiling Co-Design, lowers compiling costs by unifying tensor and web compiling and eliminating redundant and ineffective compiling passes. The second technique, Web-Specific Lite Kernel Optimization Space Design, reduces kernel tuning costs by focusing on web programming requirements and efficient hardware resource utilization, limiting the optimization space to only dozens. nn-JIT.web is evaluated for modern transformer models on a range of client devices, including the mainstream CPUs and GPUs from ARM, Intel, AMD and Nvidia. Results show that nn-JIT.web can achieve up to 8.2x faster within 30 seconds compared to the baselines across various models.

Analytical framework for predicting General Matrix Multiplication (GEMM) performance on modern GPUs, focusing on runtime, power consumption, and energy efficiency. Our study employs two approaches: a custom-implemented tiled matrix multiplication kernel for fundamental analysis, and NVIDIA's CUTLASS library for comprehensive performance data collection across advanced configurations. Using the NVIDIA RTX 4070 as our experimental platform, we developed a Random Forest-based prediction model with multi-output regression capability. Through analysis of both naive tiled matrix multiplication with varying tile sizes (1 to 32) and 16,128 CUTLASS GEMM operations across diverse configurations, we identified critical performance patterns related to matrix dimensions, thread block configurations, and memory access patterns. Our framework achieved exceptional accuracy with an R^2 score of 0.98 for runtime prediction (mean error 15.57%) and 0.78 for power prediction (median error 5.42%). The system successfully predicts performance across matrix sizes, demonstrating robust scaling behavior. Our results show that optimal tile size selection can improve performance by up to 3.2x while reducing power consumption by 22% compared to baseline configurations. Analysis of shared memory utilization and SM occupancy reveals that tile sizes of 16x16 achieve the best balance between parallelism and resource usage. The implementation of our framework, including prediction models and analysis tools, is available as an open-source project at GPPerf [https://github.com/pavlyhalim/GPPerf].