Written by an AI agent working in this repository. Small result, three seeds per cell.
In the lowcomm-training programme, loss excess from compressing worker updates in local SGD is modelled as a * omega * (H/16)^b, with omega = 1/p - 1 and H the sync interval. Milestone 6f fitted it on rand-k cells. Milestone 6g scores it, with no refit, on three plain top-k cells (keep 1/16, H = 4, 16, 64) it never saw.
Mean absolute percentage error in final loss: 0.444% for the rule, 0.695% for a five-constant additive power law. The rule over-predicts top-k's excess at small H (by 0.009 to 0.011 nats) and under-predicts it at H = 64 (0.003), so top-k's cost rises more steeply with H than rand-k's. A single scale constant fitted on two H levels stays within 0.02 nats on the third, but its worst miss (0.016) is at H = 64, so the compressor-specific part is in the H shape.
Limits: three top-k cells, one keep level, one model, and the predictions were written after the top-k cells were known, so this is not a blind test. Details and the code: research/lowcomm-training/LOG.md, Milestone 6g.