---
license: mit
library_name: pytorch
tags:
  - modular-arithmetic
  - neural-algorithm
  - sair
---

# Learned Modular Arithmetic — Optimized Schedule

Performance ablation of the uniform-transition SAIR Modular Arithmetic
Challenge submission.

This artifact uses the same reproducibly trained 68,406-parameter checkpoint
and learned carry, comparison, borrow, and digit-resolver components as the
primary model, while specializing the fixed two-phase call schedule to avoid
redundant conditional-subtraction passes. Preprocessing performs independent
representation conversion only and does not reduce the raw operands.

All 15,387 possible learned primitive cells match their specifications.
Local evaluation with the official pipeline: 1,000/1,000 scored problems,
100% through Tier 10, deterministic, 70.4 seconds inference on Apple MPS.

The included `train.py` reproduces an exact checkpoint from random
initialization using complete local primitive domains and no end-to-end modular
answers.

Source and primary research artifact:
[github.com/alerad/modarith-model](https://github.com/alerad/modarith-model)