| # bitserial-modmul-v7 (tier 9, L=1024) |
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| Submission for the SAIR Modular Arithmetic Challenge. One shared, p-conditioned recurrent cell |
| in a fixed bit-serial Horner loop computes (a * b) mod p; the cell learns the per-step transition |
| s' = (2*s + d*x) mod p and the loop only sequences bits. entry_class model.BitSerialReducer, |
| output_base 2, ~471K params, L=1024 (warm-started from the L=512 cell). |
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| ## Local evaluation (official open-source scorer, run locally; not the organizers' leaderboard) |
| - modchallenge evaluate (full 1100, public/default seed, A100-class hardware): tiers 1-9 = 1.00, |
| highest tier 9, overall 0.902, wall-clock 139s (inside the 300s budget on this hardware; the |
| organizers' sandbox may be slower). |
| - Randomising the weights collapses every solved tier to 0.00 (capability is in the trained parameters). |
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| ## Limitation (honest) |
| Not exact. The per-step map is exact on random states and exhaustively on primes < 64, but a sparse |
| set of structured-trajectory inputs (powers-of-two-times-random) still fails at large primes, |
| reproducing the Neural GPU limitation (Price, Zaremba, Sutskever 2016). The benchmark tiers reflect |
| average-case accuracy on the official scorer's random-operand distribution, not worst-case exactness. |
| Not organizer-verified; compliance ruling on the loop scaffold pending. |
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