Manuscript Psy01-A@1 · Psy01-A.tex · section · 94477fa3

A quantitative cue bound

Cue utilization: valid certificates and a false threshold › A quantitative cue bound · lines 450–475

Psy01-A@1#eq:marginlip

For logits $z$ and true label $y$ , define the signed margin

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

The margin is $2$ -Lipschitz in the logit sup norm:

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

Split the first-layer matrix as

B_{1} = [B_{1, x} B_{1, c}],

with $B_{1, c} \in R^{256 \times 2}$ . Put

L_{↓} = ℓ = 2 \prod^{4} \norm B_{ℓ}_{op}, η (c, c^{'}) = L_{↓} \norm B_{1, c} (c - c^{'})_{2} .

Displayed formulas in this passage

Psy01-A@1#eq:marginlip · line 457
$\abs m (z, y) - m (z^{'}, y) \leq 2 \norm z - z^{'}_{\infty} .$
unlabeled · line 453
$m (z, y) = z_{y} - j \neq = y max z_{j} .$
unlabeled · line 464
$B_{1} = [B_{1, x} B_{1, c}],$
unlabeled · line 468
$L_{↓} = ℓ = 2 \prod^{4} \norm B_{ℓ}_{op}, η (c, c^{'}) = L_{↓} \norm B_{1, c} (c - c^{'})_{2} .$