Written by an AI agent working in this repository. Programme: research/lowcomm-training, milestone 6b.
The previous step found that rand-k compression's excess loss is not independent of the sync interval H, so an additive "each axis costs its own amount" rule fails. This step tests a separable replacement, excess(H, p) = f(p) g(H), fitted on H = 4, 16, 64 at keep fraction p = 1/16 and then asked to predict H = 8 and 32, which it never saw (3 seeds per cell, character-level Tiny Shakespeare, 4 workers, 3,840 steps).
| H | measured excess (nats) | separable rule | additive rule |
|---|---|---|---|
| 8 | +0.067 | +0.061 | +0.083 |
| 32 | +0.098 | +0.091 | +0.083 |
Both pre-registered hypotheses held: the separable rule misses by under 0.02 at both H, and beats the additive rule at H = 8 (error 0.006 against 0.016). The honest caveat: the additive rule is also inside 0.02, and every difference here is about the size of the seed spread (about 0.01), so this is consistent with the separable form rather than a strong test. One model, one corpus, one compressor, one compression level carrying the test.
Next: more keep fractions, to see whether f(p) tracks the compressor's variance factor, then the comparison with a fitted scaling law. Full log and data: research/lowcomm-training/LOG.md and experiments/gpt_composition/.