| # rob-rbyte-v2 |
|
|
| Residue router for the SAIR Modular Arithmetic Challenge. Entry class |
| `model.ResidueRouterV1`, output base 256. Covers tiers 1-3. |
|
|
| Routing is by the size of `p`. Operands are reduced mod p inside |
| `predict_digits` (the two-argument normalization both reference models use: |
| a with p, then b with p, never all three). |
|
|
| - **Tiers 1-2 (p <= 251):** the v1 residue specialist. Each operand residue is |
| embedded through a shared per-(prime, residue) table; the two vectors are |
| added (a discrete-log inductive bias: logs add under multiplication); a |
| residual MLP trunk transforms the sum; logits score against a per-(prime, |
| class) output table masked to the p classes of the current prime. The answer |
| is one base-256 digit. ~2.9M parameters. |
|
|
| - **Tier 3 (251 < p < 65536):** two trained shared local-rule step nets |
| composed through fixed wiring. After reduction the operands x, y are 16-bit |
| residues. A MULTIPLY step learns the shared carry rule over the carry-save |
| column sums and, composed closed-loop through a fixed parity readout, emits |
| the exact 32-bit product t = x*y. A REDUCTION step learns the shared |
| per-nibble borrow/compare rule and, composed through fixed restoring-division |
| wiring, emits r = t mod p in [0, p). The answer r is emitted as base-256 |
| digits MSB-first (two digits cover a 16-bit residue). Both step nets are |
| plain GELU MLPs, width 96, depth 3, ~20k parameters each (~40k total). |
| |
| - **Tiers 4-10 (p >= 65536):** outside the trained regime; returns [0]. |
| |
| ## Provenance |
| |
| The carry-save column sums, parity readout, bit shifts, restoring-division |
| topology, and ge-from-final-borrow decision are fixed scaffold. The two |
| nontrivial decisions, the carry rule and the borrow/compare rule, reside in the |
| trained MLP parameters. Randomizing either step net collapses tier-3 exactness: |
| |
| - random-weight pipeline (both step nets re-initialized): exact = 0.000000 |
| - trained multiply + random reduction: exact = 0.002196 (chance) |
| |
| so neither step net is scaffolding. The full collapse receipt is in |
| `t3_collapse_receipt.json`. The two MULTIPLY/REDUCTION step nets are trained |
| teacher-forced on the local-rule transitions of reference traces; the MULTIPLY |
| step is saturated over its realizable 272-case domain (100 realizable cases) |
| and never sees p, the REDUCTION step covers all 512 cases from traces over |
| TRAIN primes only. Five primes near the 16-bit ceiling (33343, 45137, 54497, |
| 55061, 62071) are held out by identity and appear in no training trace; the |
| composed pipeline is exact (1.0) on all five on uniform residue pairs and the |
| four edge cases. |
| |
| ## Public benchmark (1100 problems, fixed seed) |
| |
| - overall_accuracy = 0.314 |
| - highest_tier_above_90 = 3 |
| - deterministic = True (two full runs bit-identical) |
| - tier 1 = 1.000, tier 2 = 1.000, tier 3 = 1.000 |
| - inference wall-clock < 0.1s for 1100 problems (300s budget) |
| |
| Static check: clean. No sympy / gmpy2 / eval / exec / subprocess on any path. |
| See `EVALS.log` and `eval_6d6f6463_1100.json` for the full per-tier breakdown, |
| and `manifest.json` for the model and training descriptions. |
| |
| ## Files |
| |
| `model.py` (architectures + routing + fixed wiring), `weights.safetensors` |
| (tier-1/2 specialist), `t3_mul.safetensors` / `t3_red.safetensors` (tier-3 |
| step nets), `config.json` (per-specialist hyperparameters), `manifest.json`, |
| `t3_collapse_receipt.json`, `EVALS.log`, `eval_6d6f6463_1100.json`. |
| |
