Manuscript Psy03-D@1 · Psy03-D-v1.tex · theorem · 3e18951d
Theorem: Masked-gradient obstruction
Masked gradients and reference-preserving repair › Stored and effective parameters · lines 1312–1335 · proof included or linked
Psy03-D@1#thm:maskedgradient, Psy03-D@1#eq:maskedgradient
At every differentiability point,
Therefore every inactive coordinate has zero stored-weight loss derivative.
If a regrowth routine scores inactive coordinates using only accumulated absolute stored-weight derivatives and selects only strictly positive scores, it cannot select those coordinates through this interface.
Proof. The differential is
Apply the chain rule coordinatewise. Accumulating absolute zero derivatives still gives zero.
Displayed formulas in this passage
Psy03-D@1#eq:maskedgradient · line 1315
unlabeled · line 1330