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MathBode-LinearSolve

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math
reasoning
dynamic-analysis
bode-plot
llm-evaluation
linear-algebra
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family
stringclasses
1 value
question_id
int64
0
2
signal_type
stringclasses
2 values
amplitude_scale
float64
0.5
2.5
frequency_cycles
float64
1
16
phase_deg
float64
0
240
⌀
time_step
int64
0
255
p_value
float64
3.5
4.5
prompt
stringlengths
35
50
ground_truth
float64
3.56
10.3
symbolic_baseline_answer
float64
3.56
10.3
linear_solve
0
sinusoid
0.5
1
0
0
4
Solve for x: 4.0x + 3 = 27 FINAL:
6
6
linear_solve
0
sinusoid
0.5
1
0
1
4.009802
Solve for x: 4.009801714032956x + 3 = 27 FINAL:
5.985333
5.985333
linear_solve
0
sinusoid
0.5
1
0
2
4.019509
Solve for x: 4.019509032201613x + 3 = 27 FINAL:
5.970878
5.970878
linear_solve
0
sinusoid
0.5
1
0
3
4.029028
Solve for x: 4.029028467725446x + 3 = 27 FINAL:
5.956771
5.956771
linear_solve
0
sinusoid
0.5
1
0
4
4.038268
Solve for x: 4.038268343236509x + 3 = 27 FINAL:
5.943141
5.943141
linear_solve
0
sinusoid
0.5
1
0
5
4.04714
Solve for x: 4.0471396736826x + 3 = 27 FINAL:
5.930114
5.930114
linear_solve
0
sinusoid
0.5
1
0
6
4.055557
Solve for x: 4.05555702330196x + 3 = 27 FINAL:
5.917806
5.917806
linear_solve
0
sinusoid
0.5
1
0
7
4.063439
Solve for x: 4.063439328416364x + 3 = 27 FINAL:
5.906327
5.906327
linear_solve
0
sinusoid
0.5
1
0
8
4.070711
Solve for x: 4.070710678118655x + 3 = 27 FINAL:
5.895776
5.895776
linear_solve
0
sinusoid
0.5
1
0
9
4.077301
Solve for x: 4.077301045336274x + 3 = 27 FINAL:
5.886247
5.886247
linear_solve
0
sinusoid
0.5
1
0
10
4.083147
Solve for x: 4.083146961230255x + 3 = 27 FINAL:
5.877819
5.877819
linear_solve
0
sinusoid
0.5
1
0
11
4.088192
Solve for x: 4.088192126434835x + 3 = 27 FINAL:
5.870566
5.870566
linear_solve
0
sinusoid
0.5
1
0
12
4.092388
Solve for x: 4.092387953251128x + 3 = 27 FINAL:
5.864547
5.864547
linear_solve
0
sinusoid
0.5
1
0
13
4.095694
Solve for x: 4.095694033573221x + 3 = 27 FINAL:
5.859813
5.859813
linear_solve
0
sinusoid
0.5
1
0
14
4.098079
Solve for x: 4.098078528040323x + 3 = 27 FINAL:
5.856403
5.856403
linear_solve
0
sinusoid
0.5
1
0
15
4.099518
Solve for x: 4.09951847266722x + 3 = 27 FINAL:
5.854346
5.854346
linear_solve
0
sinusoid
0.5
1
0
16
4.1
Solve for x: 4.1x + 3 = 27 FINAL:
5.853659
5.853659
linear_solve
0
sinusoid
0.5
1
0
17
4.099518
Solve for x: 4.09951847266722x + 3 = 27 FINAL:
5.854346
5.854346
linear_solve
0
sinusoid
0.5
1
0
18
4.098079
Solve for x: 4.098078528040323x + 3 = 27 FINAL:
5.856403
5.856403
linear_solve
0
sinusoid
0.5
1
0
19
4.095694
Solve for x: 4.095694033573221x + 3 = 27 FINAL:
5.859813
5.859813
linear_solve
0
sinusoid
0.5
1
0
20
4.092388
Solve for x: 4.092387953251128x + 3 = 27 FINAL:
5.864547
5.864547
linear_solve
0
sinusoid
0.5
1
0
21
4.088192
Solve for x: 4.088192126434835x + 3 = 27 FINAL:
5.870566
5.870566
linear_solve
0
sinusoid
0.5
1
0
22
4.083147
Solve for x: 4.083146961230255x + 3 = 27 FINAL:
5.877819
5.877819
linear_solve
0
sinusoid
0.5
1
0
23
4.077301
Solve for x: 4.077301045336274x + 3 = 27 FINAL:
5.886247
5.886247
linear_solve
0
sinusoid
0.5
1
0
24
4.070711
Solve for x: 4.070710678118655x + 3 = 27 FINAL:
5.895776
5.895776
linear_solve
0
sinusoid
0.5
1
0
25
4.063439
Solve for x: 4.063439328416364x + 3 = 27 FINAL:
5.906327
5.906327
linear_solve
0
sinusoid
0.5
1
0
26
4.055557
Solve for x: 4.05555702330196x + 3 = 27 FINAL:
5.917806
5.917806
linear_solve
0
sinusoid
0.5
1
0
27
4.04714
Solve for x: 4.0471396736826x + 3 = 27 FINAL:
5.930114
5.930114
linear_solve
0
sinusoid
0.5
1
0
28
4.038268
Solve for x: 4.038268343236509x + 3 = 27 FINAL:
5.943141
5.943141
linear_solve
0
sinusoid
0.5
1
0
29
4.029028
Solve for x: 4.029028467725446x + 3 = 27 FINAL:
5.956771
5.956771
linear_solve
0
sinusoid
0.5
1
0
30
4.019509
Solve for x: 4.019509032201613x + 3 = 27 FINAL:
5.970878
5.970878
linear_solve
0
sinusoid
0.5
1
0
31
4.009802
Solve for x: 4.009801714032956x + 3 = 27 FINAL:
5.985333
5.985333
linear_solve
0
sinusoid
0.5
1
0
32
4
Solve for x: 4.0x + 3 = 27 FINAL:
6
6
linear_solve
0
sinusoid
0.5
1
0
33
3.990198
Solve for x: 3.9901982859670437x + 3 = 27 FINAL:
6.014739
6.014739
linear_solve
0
sinusoid
0.5
1
0
34
3.980491
Solve for x: 3.9804909677983873x + 3 = 27 FINAL:
6.029407
6.029407
linear_solve
0
sinusoid
0.5
1
0
35
3.970972
Solve for x: 3.970971532274554x + 3 = 27 FINAL:
6.043861
6.043861
linear_solve
0
sinusoid
0.5
1
0
36
3.961732
Solve for x: 3.961731656763491x + 3 = 27 FINAL:
6.057957
6.057957
linear_solve
0
sinusoid
0.5
1
0
37
3.95286
Solve for x: 3.9528603263174x + 3 = 27 FINAL:
6.071553
6.071553
linear_solve
0
sinusoid
0.5
1
0
38
3.944443
Solve for x: 3.94444297669804x + 3 = 27 FINAL:
6.084509
6.084509
linear_solve
0
sinusoid
0.5
1
0
39
3.936561
Solve for x: 3.9365606715836354x + 3 = 27 FINAL:
6.096693
6.096693
linear_solve
0
sinusoid
0.5
1
0
40
3.929289
Solve for x: 3.9292893218813454x + 3 = 27 FINAL:
6.107975
6.107975
linear_solve
0
sinusoid
0.5
1
0
41
3.922699
Solve for x: 3.9226989546637263x + 3 = 27 FINAL:
6.118237
6.118237
linear_solve
0
sinusoid
0.5
1
0
42
3.916853
Solve for x: 3.9168530387697453x + 3 = 27 FINAL:
6.127368
6.127368
linear_solve
0
sinusoid
0.5
1
0
43
3.911808
Solve for x: 3.9118078735651647x + 3 = 27 FINAL:
6.135271
6.135271
linear_solve
0
sinusoid
0.5
1
0
44
3.907612
Solve for x: 3.9076120467488713x + 3 = 27 FINAL:
6.141858
6.141858
linear_solve
0
sinusoid
0.5
1
0
45
3.904306
Solve for x: 3.904305966426779x + 3 = 27 FINAL:
6.147059
6.147059
linear_solve
0
sinusoid
0.5
1
0
46
3.901921
Solve for x: 3.901921471959677x + 3 = 27 FINAL:
6.150816
6.150816
linear_solve
0
sinusoid
0.5
1
0
47
3.900482
Solve for x: 3.90048152733278x + 3 = 27 FINAL:
6.153086
6.153086
linear_solve
0
sinusoid
0.5
1
0
48
3.9
Solve for x: 3.9x + 3 = 27 FINAL:
6.153846
6.153846
linear_solve
0
sinusoid
0.5
1
0
49
3.900482
Solve for x: 3.90048152733278x + 3 = 27 FINAL:
6.153086
6.153086
linear_solve
0
sinusoid
0.5
1
0
50
3.901921
Solve for x: 3.901921471959677x + 3 = 27 FINAL:
6.150816
6.150816
linear_solve
0
sinusoid
0.5
1
0
51
3.904306
Solve for x: 3.904305966426779x + 3 = 27 FINAL:
6.147059
6.147059
linear_solve
0
sinusoid
0.5
1
0
52
3.907612
Solve for x: 3.9076120467488713x + 3 = 27 FINAL:
6.141858
6.141858
linear_solve
0
sinusoid
0.5
1
0
53
3.911808
Solve for x: 3.9118078735651647x + 3 = 27 FINAL:
6.135271
6.135271
linear_solve
0
sinusoid
0.5
1
0
54
3.916853
Solve for x: 3.9168530387697453x + 3 = 27 FINAL:
6.127368
6.127368
linear_solve
0
sinusoid
0.5
1
0
55
3.922699
Solve for x: 3.9226989546637263x + 3 = 27 FINAL:
6.118237
6.118237
linear_solve
0
sinusoid
0.5
1
0
56
3.929289
Solve for x: 3.9292893218813454x + 3 = 27 FINAL:
6.107975
6.107975
linear_solve
0
sinusoid
0.5
1
0
57
3.936561
Solve for x: 3.9365606715836354x + 3 = 27 FINAL:
6.096693
6.096693
linear_solve
0
sinusoid
0.5
1
0
58
3.944443
Solve for x: 3.94444297669804x + 3 = 27 FINAL:
6.084509
6.084509
linear_solve
0
sinusoid
0.5
1
0
59
3.95286
Solve for x: 3.9528603263174x + 3 = 27 FINAL:
6.071553
6.071553
linear_solve
0
sinusoid
0.5
1
0
60
3.961732
Solve for x: 3.961731656763491x + 3 = 27 FINAL:
6.057957
6.057957
linear_solve
0
sinusoid
0.5
1
0
61
3.970972
Solve for x: 3.970971532274554x + 3 = 27 FINAL:
6.043861
6.043861
linear_solve
0
sinusoid
0.5
1
0
62
3.980491
Solve for x: 3.9804909677983873x + 3 = 27 FINAL:
6.029407
6.029407
linear_solve
0
sinusoid
0.5
1
0
63
3.990198
Solve for x: 3.9901982859670437x + 3 = 27 FINAL:
6.014739
6.014739
linear_solve
0
sinusoid
0.5
2
0
0
4
Solve for x: 4.0x + 3 = 27 FINAL:
6
6
linear_solve
0
sinusoid
0.5
2
0
1
4.019509
Solve for x: 4.019509032201613x + 3 = 27 FINAL:
5.970878
5.970878
linear_solve
0
sinusoid
0.5
2
0
2
4.038268
Solve for x: 4.038268343236509x + 3 = 27 FINAL:
5.943141
5.943141
linear_solve
0
sinusoid
0.5
2
0
3
4.055557
Solve for x: 4.05555702330196x + 3 = 27 FINAL:
5.917806
5.917806
linear_solve
0
sinusoid
0.5
2
0
4
4.070711
Solve for x: 4.070710678118655x + 3 = 27 FINAL:
5.895776
5.895776
linear_solve
0
sinusoid
0.5
2
0
5
4.083147
Solve for x: 4.083146961230255x + 3 = 27 FINAL:
5.877819
5.877819
linear_solve
0
sinusoid
0.5
2
0
6
4.092388
Solve for x: 4.092387953251128x + 3 = 27 FINAL:
5.864547
5.864547
linear_solve
0
sinusoid
0.5
2
0
7
4.098079
Solve for x: 4.098078528040323x + 3 = 27 FINAL:
5.856403
5.856403
linear_solve
0
sinusoid
0.5
2
0
8
4.1
Solve for x: 4.1x + 3 = 27 FINAL:
5.853659
5.853659
linear_solve
0
sinusoid
0.5
2
0
9
4.098079
Solve for x: 4.098078528040323x + 3 = 27 FINAL:
5.856403
5.856403
linear_solve
0
sinusoid
0.5
2
0
10
4.092388
Solve for x: 4.092387953251128x + 3 = 27 FINAL:
5.864547
5.864547
linear_solve
0
sinusoid
0.5
2
0
11
4.083147
Solve for x: 4.083146961230255x + 3 = 27 FINAL:
5.877819
5.877819
linear_solve
0
sinusoid
0.5
2
0
12
4.070711
Solve for x: 4.070710678118655x + 3 = 27 FINAL:
5.895776
5.895776
linear_solve
0
sinusoid
0.5
2
0
13
4.055557
Solve for x: 4.05555702330196x + 3 = 27 FINAL:
5.917806
5.917806
linear_solve
0
sinusoid
0.5
2
0
14
4.038268
Solve for x: 4.038268343236509x + 3 = 27 FINAL:
5.943141
5.943141
linear_solve
0
sinusoid
0.5
2
0
15
4.019509
Solve for x: 4.019509032201613x + 3 = 27 FINAL:
5.970878
5.970878
linear_solve
0
sinusoid
0.5
2
0
16
4
Solve for x: 4.0x + 3 = 27 FINAL:
6
6
linear_solve
0
sinusoid
0.5
2
0
17
3.980491
Solve for x: 3.9804909677983873x + 3 = 27 FINAL:
6.029407
6.029407
linear_solve
0
sinusoid
0.5
2
0
18
3.961732
Solve for x: 3.961731656763491x + 3 = 27 FINAL:
6.057957
6.057957
linear_solve
0
sinusoid
0.5
2
0
19
3.944443
Solve for x: 3.94444297669804x + 3 = 27 FINAL:
6.084509
6.084509
linear_solve
0
sinusoid
0.5
2
0
20
3.929289
Solve for x: 3.9292893218813454x + 3 = 27 FINAL:
6.107975
6.107975
linear_solve
0
sinusoid
0.5
2
0
21
3.916853
Solve for x: 3.9168530387697453x + 3 = 27 FINAL:
6.127368
6.127368
linear_solve
0
sinusoid
0.5
2
0
22
3.907612
Solve for x: 3.9076120467488713x + 3 = 27 FINAL:
6.141858
6.141858
linear_solve
0
sinusoid
0.5
2
0
23
3.901921
Solve for x: 3.901921471959677x + 3 = 27 FINAL:
6.150816
6.150816
linear_solve
0
sinusoid
0.5
2
0
24
3.9
Solve for x: 3.9x + 3 = 27 FINAL:
6.153846
6.153846
linear_solve
0
sinusoid
0.5
2
0
25
3.901921
Solve for x: 3.901921471959677x + 3 = 27 FINAL:
6.150816
6.150816
linear_solve
0
sinusoid
0.5
2
0
26
3.907612
Solve for x: 3.9076120467488713x + 3 = 27 FINAL:
6.141858
6.141858
linear_solve
0
sinusoid
0.5
2
0
27
3.916853
Solve for x: 3.9168530387697453x + 3 = 27 FINAL:
6.127368
6.127368
linear_solve
0
sinusoid
0.5
2
0
28
3.929289
Solve for x: 3.9292893218813454x + 3 = 27 FINAL:
6.107975
6.107975
linear_solve
0
sinusoid
0.5
2
0
29
3.944443
Solve for x: 3.94444297669804x + 3 = 27 FINAL:
6.084509
6.084509
linear_solve
0
sinusoid
0.5
2
0
30
3.961732
Solve for x: 3.961731656763491x + 3 = 27 FINAL:
6.057957
6.057957
linear_solve
0
sinusoid
0.5
2
0
31
3.980491
Solve for x: 3.9804909677983873x + 3 = 27 FINAL:
6.029407
6.029407
linear_solve
0
sinusoid
0.5
2
0
32
4
Solve for x: 4.0x + 3 = 27 FINAL:
6
6
linear_solve
0
sinusoid
0.5
2
0
33
4.019509
Solve for x: 4.019509032201613x + 3 = 27 FINAL:
5.970878
5.970878
linear_solve
0
sinusoid
0.5
2
0
34
4.038268
Solve for x: 4.038268343236509x + 3 = 27 FINAL:
5.943141
5.943141
linear_solve
0
sinusoid
0.5
2
0
35
4.055557
Solve for x: 4.05555702330196x + 3 = 27 FINAL:
5.917806
5.917806
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MathBode-LinearSolve: Linear Algebra Domain

Linear equation solving problems from the MathBode benchmark.

This dataset is part of the MathBode benchmark, which evaluates 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 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.

About This Domain

This dataset contains Linear Algebra problems specifically, with approximately 9,408 prompts covering:

  • 3 question variants with different constants
  • Sinusoidal parameter sweeps at 5 frequencies (1, 2, 4, 8, 16 cycles)
  • 3 phase offsets (0°, 120°, 240°) for statistical robustness
  • 3 amplitude scales (0.5x, 1.0x, 2.5x) for non-linearity testing
  • Chirp signal validation with continuous frequency sweeps

Dataset Structure

Column Description
family Problem family name (always linear_solve for this dataset)
question_id Question variant ID (0, 1, or 2)
signal_type Type of parameter variation (sinusoid or chirp)
amplitude_scale Scaling factor for parameter variation amplitude
frequency_cycles Frequency of parameter variation in cycles per sweep
phase_deg Starting phase of sinusoidal signal in degrees
time_step Step index within the sweep
p_value The dynamic parameter value for this time step
prompt The complete prompt text for the model
ground_truth The correct numerical answer
symbolic_baseline_answer Answer from perfect symbolic solver

Usage 

from datasets import load_dataset

# Load this specific domain
dataset = load_dataset("cognitive-metrology-lab/MathBode-LinearSolve")

# Access the data
print(dataset['train'][0])

Related Datasets

Citation

If you use this dataset, please cite our work (citation to be added).

Downloads last month
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Size of downloaded dataset files:
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Size of the auto-converted Parquet files:
106 kB
Number of rows:
9,408