SAIR-Modular-Arithmetic-Challenge

SAIR Modular Arithmetic Challenge — Learned Horner Weight Soup

This repository is a submission artifact for the SAIR Modular Arithmetic Challenge. It implements the official ModularMultiplicationModel interface and emits base-2 digits for (a × b) mod p.

Evaluation status: the results below were produced independently with the published official evaluator. They are not an organizer-certified private-set leaderboard result.

Result summary

The exact artifact in this repository was evaluated on an NVIDIA L40S on 2026-08-11.

All six runs passed the official static analysis, manifest validation, preprocessing-isolation check, model loading, and determinism check. The five additional sets use the published generate_private_test_set implementation with independent seeds, but they are not the organizers' secret evaluation set.

Additional diagnostics:

• algebraic metamorphic tests: 140/140 across scored Tiers 1–10;
• all 17 learned tensors randomized: 0/30 non-zero probes remained correct;
• 2048-bit modulus boundary: passed;
• 2049-bit modulus boundary: deliberately rejected with output zero.

The diagnostic Tier 0 is unscored. This submission declines primes wider than 2048 bits so that the diagnostic does not exhaust the shared 300-second budget; the scored Tiers 1–10 are fully covered.

Raw result files, seed fingerprints, evaluator hashes, and the scope boundary are recorded in evaluation_2026-08-11/.

Architecture

The model is a width-generic, modulus-conditioned recurrent Horner cell with 91,840 learned parameters. Per-bit local features feed a shared bidirectional associative scan: one direction propagates carry information and the other propagates the learned modular-reduction decision. The same learned transition is reused across positions, scan levels, recurrent steps, and register widths.

Inference performs two shared-weight passes over raw operand digits. On CUDA, the recurrent state and model use FP16 and one complete three-round learned transition is captured in a CUDA graph and replayed. The outer schedule does not compute, correct, or look up the modular product; emitted answer digits are produced by the trained parameters.

Weight-soup provenance

weights.pt is an elementwise FP32 interpolation of two checkpoints from the same learned-cell lineage:

Certified artifact fingerprints:

weights.pt SHA-256:
2a245597f4499f83d0097d87801bd6dce79f014e5d1e3ed9cfa5f7a5e5c2363c

sorted tensor-content SHA-256:
5eb2e582891f59690cf719d8c44e040b6cb33e21356d3b62ff40c26c2ef79961

See provenance.json for parent file hashes and the full machine-readable record.

Submission layout

manifest.json       official entry point and model/training description
model.py            ModularMultiplicationModel implementation
arch.py             learned recurrent cell architecture
weights.pt          certified weight-soup state dict
provenance.json     parent and output fingerprints
evaluation_2026-08-11/
                    evaluation evidence and dataset fingerprints

This is an evaluator-specific PyTorch artifact, not a Transformers model and not a Hugging Face hosted-inference endpoint.

Reproduce the official interface check

Install the official challenge package, then run:

modchallenge check .
modchallenge evaluate .

To evaluate the immutable Hugging Face revision:

modchallenge evaluate-hf \
  Dario9709/SAIR-Modular-Arithmetic-Challenge \
  <40-character-commit-sha>

CUDA is strongly recommended. CPU execution is substantially slower and can time out before the highest tiers even when predictions are otherwise correct.

License

Apache-2.0. Competition acceptance and ranking remain subject to the organizers' rules, secret-set evaluation, and manual compliance review.