| { | |
| "entry_class": "model.ResidueRouterV1", | |
| "output_base": 256, | |
| "framework": "pytorch", | |
| "model_description": "Router over per-tier residue specialists, selected by the size of p; inputs outside the trained regime return [0]. The shipped specialist covers every prime p <= 251 (tiers 1-2). Operands are reduced mod p inside predict_digits, the same two-argument normalization both reference models use. The specialist (~2.9M parameters) embeds each operand residue through a shared per-(prime, residue) table, combines the two vectors by addition (a discrete-log inductive bias: logs add under multiplication), transforms the sum with a residual MLP trunk, and scores logits against a per-(prime, class) output table masked to the p classes of the current prime. The answer is a single base-256 digit, below p by construction.", | |
| "training_description": "Trained from random initialization on the complete synthetic input space for primes <= 251: all 995,777 triples (x, y, p) with x, y in [0, p) and label (x * y) mod p, with edge rows (x or y in {0, 1}) oversampled 8x. Cross-entropy on the p-way classification, AdamW (lr 1e-3, cosine schedule, no weight decay), batch 8192, seed 0, 15 epochs to 0 errors on the full space (verified on CPU from the saved checkpoint). Because the training set is the entire reachable input space for these tiers, accuracy is interpolation over trained points; no claim of cross-prime generalization is made. Training code, logs, and seeds are archived and available on request." | |
| } | |