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.
| Evaluation set | H90 | Overall accuracy | Scored cases | Inference time |
|---|---|---|---|---|
| Published benchmark | 10 | 1.0000 | 1000/1000 | 248.4 s |
| Independent generator seed 1 | 10 | 1.0000 | 1000/1000 | 249.9 s |
| Independent generator seed 2 | 10 | 1.0000 | 1000/1000 | 248.9 s |
| Independent generator seed 3 | 10 | 1.0000 | 1000/1000 | 249.2 s |
| Independent generator seed 4 | 10 | 1.0000 | 1000/1000 | 246.0 s |
| Independent generator seed 5 | 10 | 1.0000 | 1000/1000 | 247.2 s |
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:
| Parent | Git revision | Mixture weight |
|---|---|---|
| 814,335-step harvest checkpoint | c00027c6db90076e58bac25ce6c4c23a46ccfd40 |
0.75 |
r15 champion (17b8eb341153) |
4a6cbbead597cdbafd618b28666a730313857dd1 |
0.25 |
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.