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--- |
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license: apache-2.0 |
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tags: |
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- math |
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- reasoning |
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- dynamic-analysis |
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- bode-plot |
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- llm-evaluation |
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- scientific-question-answering |
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pretty_name: "MathBode" |
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size_categories: |
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- "10K<n<100K" |
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configs: |
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- config_name: linear_solve |
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data_files: linear_solve.parquet |
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- config_name: ratio_saturation |
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data_files: ratio_saturation.parquet |
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- config_name: exponential_interest |
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data_files: exponential_interest.parquet |
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- config_name: linear_system |
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data_files: linear_system.parquet |
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- config_name: similar_triangles |
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data_files: similar_triangles.parquet |
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--- |
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# MathBode: A Dynamic Benchmark for Mathematical Reasoning |
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<!-- Updated: 2025-09-22 --> |
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**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. |
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This dataset contains the complete set of prompts and ground truth values for the benchmark. |
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## Dataset Structure |
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The dataset is provided in a single Parquet file and contains the following columns: |
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| Column | Description | |
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|---|---| |
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| `family` | The mathematical problem family (e.g., `linear_solve`, `ratio_saturation`). | |
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| `question_id` | An index (0-2) for the specific question variant within a family. | |
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| `signal_type` | The type of parameter variation: `sinusoid` or `chirp`. | |
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| `amplitude_scale` | The scaling factor for the input signal's amplitude (0.5, 1.0, or 2.5). Used for non-linearity testing. | |
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| `frequency_cycles` | The frequency of the sinusoidal input in cycles per sweep. For chirp signals, this is the instantaneous frequency. | |
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| `phase_deg` | The starting phase of the sinusoidal signal in degrees (0, 120, 240). `null` for chirp signals. | |
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| `time_step` | The step index within a sweep (0-63 for sinusoids, 0-255 for chirps). | |
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| `p_value` | The precise value of the dynamic parameter `p` for this time step. | |
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| `prompt` | The full prompt text to be sent to the model. | |
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| `ground_truth` | The correct numerical answer for the given prompt. | |
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| `symbolic_baseline_answer` | The answer from a perfect symbolic solver (identical to `ground_truth`). | |
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## Usage |
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You can load the dataset easily using the `datasets` library: |
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```python |
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from datasets import load_dataset |
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# Load the dataset |
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dataset = load_dataset("cognitive-metrology-lab/MathBode") |
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# Access the data |
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print(dataset['train'][0]) |
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``` |
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## Citing |
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If you use this dataset, please cite our work. |
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``` |
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@misc{wang2025mathbode, |
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title = {MathBode: Measuring the Stability of LLM Reasoning using Frequency Response}, |
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author = {Charles L. Wang}, |
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year = {2025}, |
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eprint = {2509.23143}, |
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archivePrefix= {arXiv}, |
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primaryClass = {cs.AI}, |
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url = {https://arxiv.org/abs/2509.23143} |
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} |
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``` |
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