Manuscript Psy03-B@1 · Psy03-B-v1.tex · section · 8ca3caf9

Common-protection challenge paths

Biased-noise and full-state perturbation certificates › Common-protection challenge paths · lines 1003–1020

Psy03-B@1#eq:marginlip

The factor $q^{4 - r}$ includes multiplication immediately after noise injection and at each subsequent hidden layer. The reference forward pass still contains the common protection offset.

For true-label margin

m (z, y) = z_{y} - j \neq = y max z_{j},

one has

\abs m (z, y) - m (z^{'}, y) \leq 2 \norm z - z^{'}_{\infty} .

Displayed formulas in this passage

unlabeled · line 1011
$m (z, y) = z_{y} - j \neq = y max z_{j},$
Psy03-B@1#eq:marginlip · line 1015
$\abs m (z, y) - m (z^{'}, y) \leq 2 \norm z - z^{'}_{\infty} .$

Nearby in this section

section: Common-protection challenge paths
corollary: Corollary: Biased-noise path bound
theorem: Theorem: Sufficient challenge-survival certificate
section: Common-protection challenge paths