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: Frequency-Domain Fingerprints of LLM Mathematical Reasoning},
  author       = {Charles L. Wang},
  year         = {2025},
  eprint       = {2509.23143},
  archivePrefix= {arXiv},
  primaryClass = {cs.AI},
  url          = {https://arxiv.org/abs/2509.23143}
}