T9_bigru_raw_b_two_pass_s91001

T9 BiGRU raw-b two-pass frontier candidate

This is a deterministic Modular Arithmetic Challenge submission candidate. It routes 513-1,024-bit primes to a learned bit-axis bidirectional-GRU transition cell and preserves the previously validated T1-T8 experts byte-for-byte.

Status: local T9 promotion candidate. This records frozen local scientific and submission-router evidence; it is not an unseen Playground result.

Fixed inference schedule

T9 preprocessing makes fixed 2,048-bit representations of both raw operands and a fixed 1,024-bit representation of the raw prime. Before the first learned call, all 4,096 external tokens are fixed:

1. 2,048 raw_a bits update a learned residue with multiplier one.
2. 2,048 raw_b bits update the product state using that learned fixed-width residue tensor as the multiplier.

The radix is 2 and every transition is hard-thresholded back to an explicit binary residue. No prediction becomes a later digit token or controls token order, indices, masks, branches, loop bounds, padding, trimming, or length. Preprocessing does not deterministically compute either operand modulo p.

Transition cell and training

Each bit position receives state, multiplier, and prime features, projected from 3 to 96 dimensions plus a binary digit embedding. A two-layer bidirectional GRU uses hidden size 128 per direction and a Linear 256-to-1 head. The 470,849 parameters are shared across the bit axis.

The T9 expert was warm-started from the frozen externally confirmed T8 checkpoint and trained for exactly 10,000 one-step AdamW updates on adjacent T9/T10 widths: batch 128, BF16, learning rate 0.001, weight decay 0.01, 250-step warmup, cosine decay, gradient clipping 1.0, seed 55002, on one local RTX 4070. No DAgger, STE, auxiliary loss, architecture change, or unrolled BPTT was used. No Pod or remote GPU was used.

Frozen local scientific evidence

• 1,000,000/1,000,000 fresh one-step transitions exact;
• 9,995/10,000 fresh T9 raw-input rollouts exact (99.95%);
• 4,092/4,094 in the 1,017-1,024-bit prime tail (99.9511%);
• five independent 100-case/five-prime panels all 100%;
• edge panel 256/256 and operand-width panel 900/900;
• bitwise-identical logits, histories, and final states on repeat execution;
• randomized weights collapsed to 0/100;
• normal and randomized weights produced the same precomputed token plan.

Public-router accuracy, runtime, static, preprocess-isolation, and cross-process determinism are recorded separately by the router audit and are local public-benchmark evidence, not a secret-seed score.

Checkpoint integrity

T9 checkpoint SHA-256:

4a4ccf809400e1f782676b78d8a92b4b31f775ac0d40540d80c067aafa83ae41

Frozen T8 warm-start checkpoint SHA-256:

e8eac9c8994bef3b744f3841b0c8108fb868643a4af4839bf76ec11759161bcc

The builder verifies the exact inherited T8 package inventory, byte identity of all T5-T9 checkpoints, and records SHA-256 for every packaged artifact.

Prior work and acknowledgments

This project benefited from public technical discussion in the SAIR Foundation #Modular Arithmetic Challenge channel, including discussion by Robby Sneiderman, Hongyue Lei, Marcos Costa Santos Carreira, and YZ about learned recurrent arithmetic, fixed Horner schedules, rollout drift, width robustness, and raw-input rules. Robby Sneiderman's NeuralHorner was a methodological reference.

The inherited T4 temporal-convolution path was informed by the public XllentAI/modular_arithmetic model card. The T5-T9 BiGRU code, fixed raw_b_two_pass schedule, data, and weights were independently designed or generated; no code, weights, checkpoints, replay buffers, or generated artifacts from those references were copied.