Datasets:
metadata
license: apache-2.0
tags:
- math
- reasoning
- dynamic-analysis
- bode-plot
- llm-evaluation
- scientific-question-answering
pretty_name: MathBode
size_categories:
- 10K<n<100K
configs:
- config_name: linear_solve
data_files: linear_solve.parquet
- config_name: ratio_saturation
data_files: ratio_saturation.parquet
- config_name: exponential_interest
data_files: exponential_interest.parquet
- config_name: linear_system
data_files: linear_system.parquet
- config_name: similar_triangles
data_files: similar_triangles.parquet
MathBode: A Dynamic Benchmark for Mathematical Reasoning
MathBode is a benchmark designed to evaluate the dynamic reasoning capabilities of large language models (LLMs) by treating parametric math problems as dynamic systems. Instead of testing static accuracy on fixed problems, MathBode treats parametric math problems as dynamic systems. It sinusoidally varies a parameter and measures the model's response in terms of gain (amplitude tracking) and phase (reasoning lag), analogous to a Bode plot in control theory.
This dataset contains the complete set of prompts and ground truth values for the benchmark.
Dataset Structure
The dataset is provided in a single Parquet file and contains the following columns:
| Column | Description |
|---|---|
family |
The mathematical problem family (e.g., linear_solve, ratio_saturation). |
question_id |
An index (0-2) for the specific question variant within a family. |
signal_type |
The type of parameter variation: sinusoid or chirp. |
amplitude_scale |
The scaling factor for the input signal's amplitude (0.5, 1.0, or 2.5). Used for non-linearity testing. |
frequency_cycles |
The frequency of the sinusoidal input in cycles per sweep. For chirp signals, this is the instantaneous frequency. |
phase_deg |
The starting phase of the sinusoidal signal in degrees (0, 120, 240). null for chirp signals. |
time_step |
The step index within a sweep (0-63 for sinusoids, 0-255 for chirps). |
p_value |
The precise value of the dynamic parameter p for this time step. |
prompt |
The full prompt text to be sent to the model. |
ground_truth |
The correct numerical answer for the given prompt. |
symbolic_baseline_answer |
The answer from a perfect symbolic solver (identical to ground_truth). |
Usage
You can load the dataset easily using the datasets library:
from datasets import load_dataset
# Load the dataset
dataset = load_dataset("cognitive-metrology-lab/MathBode")
# Access the data
print(dataset['train'][0])
Citing
If you use this dataset, please cite our work.
@misc{wang2025mathbode,
title = {MathBode: Understanding LLM Reasoning with Dynamical Systems},
author = {Charles L. Wang},
year = {2025},
eprint = {2509.23143},
archivePrefix= {arXiv},
primaryClass = {cs.AI},
url = {https://arxiv.org/abs/2509.23143}
}