The subspace cut at the third length: still a leak, no longer a revelation¶
subspace-split-cpp-256-c256.json. The same registered split at 256 examples a client, on 32 C++
clients over nine projects, against 126 groupings.
| 128 examples, 48 clients, 1,716 groupings | 256 examples, 32 clients, 126 groupings | |
|---|---|---|
| the whole update | 0.542, p 0.39 | 0.906, p 0.040 |
| shared half, best cell | 0.917, family-wise p 0.0012 | 0.906, family-wise p 0.032 |
| residual, best cell | 1.000, family-wise p 0.0006 | 1.000, family-wise p 0.008, the floor |
Both halves still identify the organization, and the residual is still perfect at rank 1. What changes is what they are being compared against: at 128 examples the intact update identified nothing, so cutting it was what made the source readable; at 256 the intact update identifies too.
So the cut's effect is regime-dependent, and the sharper claim belongs to the shorter length. At the training length where a whole update hides its source, splitting it along the subspace clients share exposes that source. At the length where everything is exposed, the split neither helps nor hides. A defence evaluated only at long local training would therefore report that its cut costs nothing, and be right about the wrong regime.