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parse/train/BygkQeHKwB/BygkQeHKwB.md

@@ -81,7 +81,7 @@ $$
 \ell ( \mathbf { p } , t ) : = \log p _ { t } .
 $$
 
-We should warn that, while the cross-entropy is appropriate for bringing examples into the region of class $t$ during classifier training, its negative (6) is in general not appropriate for pulling them out during an attack. This is because this function is mostly flat in the class region. A common solution is to normalize the gradient of $\ell$ (Goodfellow et al., 2014; Rony et al., 2018), assuming it is nonzero. We consider more options in this work. A targeted attack on the other hand may use  $\log { p _ { t ^ { \prime } } }$ , which works fine because it brings examples into class $t ^ { \prime }$ region.
+We should warn that, while the cross-entropy is appropriate for bringing examples into the region of class $t$ during classifier training, its negative (6) is in general not appropriate for pulling them out during an attack. This is because this function is mostly flat in the class region. A common solution is to normalize the gradient of $\ell$ (Goodfellow et al., 2014; Rony et al., 2018), assuming it is nonzero. We consider more options in this work. A targeted attack on the other hand may use  $\log { p _ { t ^ { \prime } } }$ , which works fine because it brings examples into class $t ^ { \prime }$ region.
 
 Distortion. This work focuses on the 2-norm $\lVert \cdot \rVert$ as a measure of distortion. Alternatives like 1-norm and $\infty$ -norm are also common (Goodfellow et al., 2014; Carlini & Wagner, 2017). It is known that none is appropriate for measuring the imperceptibility of adversarial attacks, while more sophisticated measures like structural similarity (SSIM) (Wang et al., 2004) are limited too (Sharif et al., 2018). Measuring imperceptibility is arguably as difficult as classification itself.
 

parse/train/H1zxjsCqKQ/H1zxjsCqKQ.md

@@ -134,7 +134,7 @@ where $\nabla _ { \phi _ { D } } \hat { F } _ { D } \cdot \hat { J } _ { D }$ is
 
 # Algorithm 1 Gradient-based learning for the binary $F _ { 1 }$ score
 
-Require: classifier $h _ { \theta }$ , batch size $b$ , dataset $D$ , learning rate $\alpha$ , weight decay strength $\lambda$ $\begin{array} { r } { \hat { p ^ { + } }  \frac { 1 } { | D | } \sum _ { ( \pmb { x } , y ) \in D } \mathbb { I } ( y = 1 ) } \end{array}$ $\begin{array} { r } { p ^ { - }  \frac { 1 } { | D | } \sum _ { ( \pmb { x } , y ) \in D } \mathbb { I } ( y = 0 ) } \end{array}$ while terminating criterion not satisfied do Sample $B _ { + } \doteq \{ ( \pmb { x } _ { 1 } ^ { + } , 1 ) , . . . , ( \pmb { x } _ { b } ^ { + } , 1 ) \}$ from $D$ Sample $B _ { - } = \{ ( \pmb { x } _ { 1 } ^ { - } , 0 ) , . . . , ( \pmb { x } _ { b } ^ { - } , 0 ) \}$ from $D$ $\begin{array} { r } { \mathrm { f n }  \frac { p ^ { + } } { b } \sum _ { i = 1 } ^ { b } p _ { \theta } ( 0 | \pmb { x } _ { 1 } ^ { + } ) } \end{array}$ p b Pbi=1 pθ (1|x−1 ) δ ← ∇θ F1(fn, fp) − λ · |θ|
 θ ← θ + α · δ end while
+Require: classifier $h _ { \theta }$ , batch size $b$ , dataset $D$ , learning rate $\alpha$ , weight decay strength $\lambda$ $\begin{array} { r } { \hat { p ^ { + } }  \frac { 1 } { | D | } \sum _ { ( \pmb { x } , y ) \in D } \mathbb { I } ( y = 1 ) } \end{array}$ $\begin{array} { r } { p ^ { - }  \frac { 1 } { | D | } \sum _ { ( \pmb { x } , y ) \in D } \mathbb { I } ( y = 0 ) } \end{array}$ while terminating criterion not satisfied do Sample $B _ { + } \doteq \{ ( \pmb { x } _ { 1 } ^ { + } , 1 ) , . . . , ( \pmb { x } _ { b } ^ { + } , 1 ) \}$ from $D$ Sample $B _ { - } = \{ ( \pmb { x } _ { 1 } ^ { - } , 0 ) , . . . , ( \pmb { x } _ { b } ^ { - } , 0 ) \}$ from $D$ $\begin{array} { r } { \mathrm { f n }  \frac { p ^ { + } } { b } \sum _ { i = 1 } ^ { b } p _ { \theta } ( 0 | \pmb { x } _ { 1 } ^ { + } ) } \end{array}$ p b Pbi=1 pθ (1|x−1 ) δ ← ∇θ F1(fn, fp) − λ · |θ|
 θ ← θ + α · δ end while
 
 The binary $F$ -measure in fact belongs to a class of performance metrics that are well behaved functions of the confusion matrix. In this section, we propose a gradient-based learning algorithm that extends the approach illustrated in previous section to this class of performance metrics. We state theorems concerning the generalization and consistency of the proposed algorithm as well. We defer all proofs to appendix. We begin with a specification of this class of performance metrics, which relies on the definition of confusion matrix:
 

parse/train/SyrGJYlRZ/SyrGJYlRZ.md

@@ -417,7 +417,7 @@ According to Lemma 7 and 8, we have $\mathbb { E } ( \overline { { x } } _ { t }
 
 # C PROOF OF LEMMA 5
 
-Again we first present a proof of a multiple dimensional generalized version of Lemma 5. The proof of Lemma 5 is a one dimensional special case of Lemma 9. Lemma 9 also implies that for multiple dimension quadratics, the corresponding spectral radius ⇢(B ) = µ if (1pµ)2↵ $\begin{array} { r } { \frac { ( 1 - \sqrt { \mu } ) ^ { 2 } } { \alpha } \leq h \leq \frac { ( 1 + \sqrt { \mu } ) ^ { 2 } } { \alpha } } \end{array}$ on all the eigenvector directions with $h$ being the eigenvalue (curvature).
+Again we first present a proof of a multiple dimensional generalized version of Lemma 5. The proof of Lemma 5 is a one dimensional special case of Lemma 9. Lemma 9 also implies that for multiple dimension quadratics, the corresponding spectral radius ⇢(B ) = µ if (1pµ)2↵ $\begin{array} { r } { \frac { ( 1 - \sqrt { \mu } ) ^ { 2 } } { \alpha } \leq h \leq \frac { ( 1 + \sqrt { \mu } ) ^ { 2 } } { \alpha } } \end{array}$ on all the eigenvector directions with $h$ being the eigenvalue (curvature).
 
 Lemma 9. Let $\pmb { H } \in \mathbb { R } ^ { n \times n }$ be a symmetric matrix and $\rho ( B )$ be the spectral radius of matrix
 

parse/train/mfQxdSMWOF/mfQxdSMWOF.md

@@ -156,7 +156,7 @@ Orthoformer algorithm. The proposed approximation algorithm is outlined in Algor
 2: Ω1 = S(QTPk/ D)   
 3: Ω−12 = IterativeInverse(S(PTq Pk/ D), Niter)   
 4: Ω3 = S(PTq K/ D)   
-5: Y = Ω1 Ω−12 (Ω3V)

+5: Y = Ω1 Ω−12 (Ω3V)

 
 # 3.3 The Motionformer model