{
  "entry_class": "model.ModMulRouter",
  "output_base": 10,
  "framework": "pytorch",
  "model_description": "Prime-magnitude router over four from-random-init ByteGPT members (entmax15+ALiBi, BCE+reg). Tiers 1-4 members generate SRT-style signed-digit long-division chains of thought (signed quotient digits in {-9..9} from a learned leading-limbs lookup, 10's-complement remainders with emitted carry/borrow chain bits, final correction step) after a schoolbook multiply stage; a multiplication-only member covers larger p whose products fit 20-digit operands (tier-0 style inputs; oversized operands emit the honest [0]). Routing keys on the size of p only; all answers are generated digit sequences from trained weights.",
  "training_description": "All members trained from random init with BCE(+reg) LM loss plus per-block BP-install probe losses on intermediate variables (carries, borrows, quotient digits). Synthetic data from the official tier geometry with held-out seeds; magnitude-balanced prime sampling; example-aligned batch rows. SRT members additionally train on alternate-valid-digit (dithered) traces so generation is robust to either choice in the redundant digit windows. The digit-selection tables, products, and complement arithmetic are all generated by trained weights; randomising weights collapses accuracy. Training code: github.com/area9innovation/modmul-challenge (available to organizers/reviewers on request)."
}