| { | |
| "entry_class": "model.BitSerialReducer", | |
| "output_base": 2, | |
| "framework": "pytorch", | |
| "model_description": "One shared, p-conditioned recurrent transition cell (~471K parameters: a bidirectional 2-layer GRU over three bit-channels, a control-bit embedding, a per-bit output head) applied in a fixed bit-serial Horner loop, at 256-bit state width. Each operand is tokenised per-argument into its MSB-first bit list; the modulus is fed as its 256-bit binary form (extracted via 32-bit limbs so values above 2^63 do not overflow). The cell maps (state_bits, multiplicand_bits, modulus_bits, control_bit) to the next state bits and is used with shared weights to reduce a mod p, reduce b mod p (multiplicand 1), and multiply the two residues (multiplicand a mod p, control bits scanning b mod p). Answers are emitted as base-2 digits and reconstructed by the harness decoder. State is carried as bits between steps; no integer reconstruction or modular product happens in Python. A single cell handles tiers 1-7 (primes below 2^256, operands up to 1024 bits); outside that regime it abstains and emits a single zero. Same architecture as bit-serial-v1/v2/v3, widened to 256 bits.", | |
| "training_description": "Trained from random initialisation on one-step transitions s' = (2*s + d*x) mod p sampled over moduli covering tiers 1-7 (modulus bit-length stratified across 1-256 bits, wrap-boundary transitions oversampled). Objective is per-output-bit binary cross-entropy; optimiser AdamW (peak lr 1.5e-3, weight decay 0.01, gradient clipping) with lr warmup and cosine decay, on an NVIDIA H100; the reported weights are the best-by-validation checkpoint. No precomputed tables, no hand-coded reduction or multiplication: the per-step modular transition (including the conditional wrap, at most two subtractions of p since 2*s + d*x < 3*p) is what is learned; the loop only sequences the bits. The capability lives in the weights, so randomising them collapses exact-match accuracy to chance. Evaluation primes are unseen during training (secret seed)." | |
| } | |