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stalecos
confirmedshipPythonModel behavior & reasoningJuly 22, 2026
the question
Does GaLore's principal-angle refresh metric track the actual descent retained under a stale projector?
what came out
No. Retained descent equals the energy-weighted sum of squared cosines sum_j w_j cos^2(phi_j), decoupled from the frame-distance metric. When a tail direction rotates 85 degrees, the max principal angle predicts retention 0.003 while the true retained descent is 0.884, a 291x understatement that triggers refreshes too early.
method & receipts
- Result: confirmed
- Reproducible — one script re-runs the whole thing from scratch.
- Tested — a correctness/benchmark suite ships alongside the code.
→ read the code and re-run it
github.com/v-code01/stalecos