mikelou/mod-arithmetic

NeuralHorner v8 compact inference experiment

This local derivative tests storage and inference optimizations against the published MIT-licensed TrickyRex/bitserial-modmul-v8 checkpoint. It is not a newly trained model. Original model and weights by Robert Sneiderman: https://huggingface.co/TrickyRex/bitserial-modmul-v8.

Changes:

• checkpoint tensors stored as bfloat16;
• direct logit > 0 decisions instead of sigmoid(logit) > 0.5;
• one operand is reduced and the other is streamed directly through the learned multiplication transition, removing one modulus-width pass;
• static multiplicand/modulus feature channels are allocated once per scan instead of rebuilt at every recurrent step.

The last change is mathematically equivalent for an exact transition, but the learned cell is not proven exact. Benchmark equivalence therefore must be measured before this is treated as an accuracy-preserving release.

Local validation

Hardware: Apple GPU through PyTorch MPS. Dataset: the official 100-case public benchmark for each tier.

• Tiers 1-7: 700/700 exact.
• Tier 6 runtime: 19.07 seconds versus 27.02 seconds for the published wrapper (29.4% lower wall-clock in this comparison). The earlier short-schedule version took 20.45-21.31 seconds before static-channel reuse.
• Tier 6 outputs: 100/100 byte-for-byte identical to the published wrapper.
• The bfloat16 checkpoint with the original three-pass schedule also produced 100/100 outputs identical to the fp32 checkpoint on Tier 6.
• Official static analysis: clean.

The checkpoint is 948,196 bytes versus 1,887,610 bytes (49.8% smaller). The shorter schedule removes exactly one Leff recurrent pass: 20% of recurrent step calls on public Tiers 3 and 5-10, 14.3% on Tier 4, 25% on Tier 2, and 33.3% on Tier 1.

Release gate

Do not claim unchanged Tier 1-10 accuracy yet. The current machine is too slow for a practical full-width Tier 8-10 MPS run. Before release, run the official 1,100-case scorer on CUDA for the three published seeds and require 100% on every scored tier, then repeat the held-out 768-case adversarial battery.