MathBode-RatioSaturation: Rational Functions Domain

Ratio and saturation function 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 Rational Functions 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 ratio_saturation 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-RatioSaturation")

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

Related Datasets

• MathBode - Complete benchmark with all families
• MathBode-LinearSolve
• MathBode-RatioSaturation
• MathBode-ExponentialInterest
• MathBode-LinearSystem
• MathBode-SimilarTriangles

Citation

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