| --- |
| license: mit |
| library_name: pytorch |
| tags: |
| - modular-arithmetic |
| - neural-algorithm |
| - mechanistic-verification |
| - sair |
| --- |
| |
| # Uniform-Transition Learned Modular Arithmetic |
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| Primary submission artifact for the SAIR Modular Arithmetic Challenge. |
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| This 68,406-parameter scan-register machine processes every raw operand bit |
| with the same fixed learned transition and emits `(a * b) mod p` as base-32 |
| digits. Preprocessing performs independent representation conversion only; it |
| does not reduce the operands. |
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| The transition is composed from learned finite-domain carry, comparison, and |
| borrow monoids plus learned digit resolvers. At inference time, the shipped |
| weights materialize the complete primitive tables. All 15,387 possible learned |
| primitive cells match their specifications, and randomizing the weights |
| collapses accuracy. |
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| Local evaluation with the official pipeline: 1,000/1,000 scored problems, |
| 100% through Tier 10, deterministic, 83.9 seconds inference on Apple MPS. |
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| The included `train.py` reproduces an exact checkpoint from random |
| initialization using complete local primitive domains and no end-to-end modular |
| answers. |
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| Source, audit scripts, paper, and Lean development: |
| [github.com/alerad/modarith-model](https://github.com/alerad/modarith-model) |
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