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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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- systems-of-linear-equations |
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pretty_name: "MathBode-LinearSystem" |
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size_categories: |
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- "1K<n<10K" |
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--- |
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# MathBode-LinearSystem: Systems of Linear Equations Domain |
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Linear system solving problems from the MathBode benchmark. |
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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. |
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## About This Domain |
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This dataset contains **Systems of Linear Equations** problems specifically, with approximately 9,408 prompts covering: |
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- **3 question variants** with different constants |
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- **Sinusoidal parameter sweeps** at 5 frequencies (1, 2, 4, 8, 16 cycles) |
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- **3 phase offsets** (0°, 120°, 240°) for statistical robustness |
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- **3 amplitude scales** (0.5x, 1.0x, 2.5x) for non-linearity testing |
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- **Chirp signal validation** with continuous frequency sweeps |
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## Dataset Structure |
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| Column | Description | |
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|--------|-------------| |
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| `family` | Problem family name (always `linear_system` for this dataset) | |
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| `question_id` | Question variant ID (0, 1, or 2) | |
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| `signal_type` | Type of parameter variation (`sinusoid` or `chirp`) | |
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| `amplitude_scale` | Scaling factor for parameter variation amplitude | |
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| `frequency_cycles` | Frequency of parameter variation in cycles per sweep | |
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| `phase_deg` | Starting phase of sinusoidal signal in degrees | |
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| `time_step` | Step index within the sweep | |
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| `p_value` | The dynamic parameter value for this time step | |
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| `prompt` | The complete prompt text for the model | |
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| `ground_truth` | The correct numerical answer | |
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| `symbolic_baseline_answer` | Answer from perfect symbolic solver | |
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## Usage |
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```python |
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from datasets import load_dataset |
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# Load this specific domain |
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dataset = load_dataset("cognitive-metrology-lab/MathBode-LinearSystem") |
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# Access the data |
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print(dataset['train'][0]) |
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``` |
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## Related Datasets |
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- [MathBode](https://huggingface.co/datasets/cognitive-metrology-lab/MathBode) - Complete benchmark with all families |
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- [MathBode-LinearSolve](https://huggingface.co/datasets/cognitive-metrology-lab/MathBode-LinearSolve) |
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- [MathBode-RatioSaturation](https://huggingface.co/datasets/cognitive-metrology-lab/MathBode-RatioSaturation) |
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- [MathBode-ExponentialInterest](https://huggingface.co/datasets/cognitive-metrology-lab/MathBode-ExponentialInterest) |
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- [MathBode-LinearSystem](https://huggingface.co/datasets/cognitive-metrology-lab/MathBode-LinearSystem) |
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- [MathBode-SimilarTriangles](https://huggingface.co/datasets/cognitive-metrology-lab/MathBode-SimilarTriangles) |
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## Citation |
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If you use this dataset, please cite our work (citation to be added). |
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