| --- |
| license: apache-2.0 |
| tags: |
| - math |
| - reasoning |
| - dynamic-analysis |
| - bode-plot |
| - llm-evaluation |
| - systems-of-linear-equations |
| pretty_name: "MathBode-LinearSystem" |
| size_categories: |
| - "1K<n<10K" |
| --- |
| |
| # MathBode-LinearSystem: Systems of Linear Equations Domain |
|
|
| Linear system 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 |
|
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| This dataset contains **Systems of Linear Equations** 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_system` 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 |
|
|
| ```python |
| from datasets import load_dataset |
| |
| # Load this specific domain |
| dataset = load_dataset("cognitive-metrology-lab/MathBode-LinearSystem") |
| |
| # Access the data |
| print(dataset['train'][0]) |
| ``` |
|
|
| ## Related Datasets |
|
|
| - [MathBode](https://huggingface.co/datasets/cognitive-metrology-lab/MathBode) - Complete benchmark with all families |
| - [MathBode-LinearSolve](https://huggingface.co/datasets/cognitive-metrology-lab/MathBode-LinearSolve) |
| - [MathBode-RatioSaturation](https://huggingface.co/datasets/cognitive-metrology-lab/MathBode-RatioSaturation) |
| - [MathBode-ExponentialInterest](https://huggingface.co/datasets/cognitive-metrology-lab/MathBode-ExponentialInterest) |
| - [MathBode-LinearSystem](https://huggingface.co/datasets/cognitive-metrology-lab/MathBode-LinearSystem) |
| - [MathBode-SimilarTriangles](https://huggingface.co/datasets/cognitive-metrology-lab/MathBode-SimilarTriangles) |
|
|
| ## Citation |
|
|
| If you use this dataset, please cite our work (citation to be added). |
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|
