The lowcomm-training programme asks which of sync interval H and gradient compression set the final loss of DiLoCo-style local training. Its three-constant rule fitted a 413k-parameter character GPT to under 1% held-out error. At a 915k-parameter model it missed by 2.54%, almost all of it on one cell (H = 64, keep 1/16) that was held out by 0.174 nats. The log blamed seed noise: that cell had two seeds, 0.027 nats apart.
So we predicted that four more seeds would cut the error, and ran eight more training runs (the two H = 64 cells, seeds 2 to 5, about 17 minutes each). The prediction failed. The cell mean moved by 0.0001 nats (1.6456, standard error 0.004), leave-one-cell-out error stayed at 2.43%, and the held-out miss is still 0.163 nats, about 40 times the cell's standard error.
What the data say instead: the compression excess at size 2 is +0.054 at H = 16 and +0.044 at H = 64. It does not grow with H, where a power law with the fitted exponent says it should (it was still rising at the smaller model: +0.083 to +0.099). The rule's form in H, not its constants, looks like the weak part at the wider size. The next step is two more H values (32 and 128) to see whether the excess saturates. Two seeds on five of the seven cells, one corpus and one extra size are the limits.
Log: research/lowcomm-training/LOG.md, milestone 6i.