@@ -95,41 +95,41 @@ Convolution is expressed as Equation
9595[ \[ equ: ch-deploy /conv-equation\] ] ( #equ:ch-deploy/conv-equation ) {reference-type="ref"
9696reference="equ: ch-deploy /conv-equation"}.
9797
98- $$ \tag{ equ:ch-deploy/conv-equation}
99- \bm {Y_{\rm conv}}=\bm {W_{\rm conv}}\cdot\bm {X_{\rm conv}}+\bm {B_{\rm conv}} $$
98+ $$ [ equ:ch-deploy/conv-equation]
99+ \mathbf {Y_{\rm conv}}=\mathbf {W_{\rm conv}}\cdot\mathbf {X_{\rm conv}}+\mathbf {B_{\rm conv}} $$
100100
101101Here, we do not need to understand what each variable means. Instead, we
102102only need to keep in mind that Equation
103103[ \[ equ: ch-deploy /conv-equation\] ] ( #equ:ch-deploy/conv-equation ) {reference-type="ref"
104104reference="equ: ch-deploy /conv-equation"} is an equation for
105- $\bm {Y_ {\rm conv}}$ with respect to $\bm {X_ {\rm conv}}$, and other
105+ $\mathbf {Y_ {\rm conv}}$ with respect to $\mathbf {X_ {\rm conv}}$, and other
106106symbols are constants.
107107
108108Equation
109109[ \[ equ: ch-deploy /bn-equation\] ] ( #equ:ch-deploy/bn-equation ) {reference-type="ref"
110110reference="equ: ch-deploy /bn-equation"} is about the computation of
111111Batchnorm:
112112
113- $$ \tag{ equ:ch-deploy/bn-equation}
114- \bm {Y_{\rm bn}}=\gamma\frac{\bm {X_{\rm bn}}-\mu_{\mathcal{B}}}{\sqrt{{\sigma_{\mathcal{B}}}^{2}+\epsilon}}+\beta $$
113+ $$ [ equ:ch-deploy/bn-equation]:
114+ \mathbf {Y_{\rm bn}}=\gamma\frac{\mathbf {X_{\rm bn}}-\mu_{\mathcal{B}}}{\sqrt{{\sigma_{\mathcal{B}}}^{2}+\epsilon}}+\beta $$
115115
116- Similarly, it is an equation for $\bm {Y_ {\rm bn}}$ with respect to
117- $\bm {X_ {\rm bn}}$. Other symbols in the equation represent constants.
116+ Similarly, it is an equation for $\mathbf {Y_ {\rm bn}}$ with respect to
117+ $\mathbf {X_ {\rm bn}}$. Other symbols in the equation represent constants.
118118
119119As shown in Figure
120120[ 2] ( #fig:ch-deploy/conv-bn-fusion ) {reference-type="ref"
121121reference="fig: ch-deploy /conv-bn-fusion"}, when the output of
122122Convolution is used as the input of Batchnorm, the formula of Batchnorm
123- is a function for $\bm {Y_ {\rm bn}}$ with respect to $\bm {X_ {\rm conv}}$.
124- After substituting $\bm {Y_ {\rm conv}}$ into $\bm {X_ {\rm bn}}$ and
123+ is a function for $\mathbf {Y_ {\rm bn}}$ with respect to $\mathbf {X_ {\rm conv}}$.
124+ After substituting $\mathbf {Y_ {\rm conv}}$ into $\mathbf {X_ {\rm bn}}$ and
125125uniting and extracting the constants, we obtain Equation
126126[ \[ equ: ch-deploy /conv-bn-equation-3\] ] ( #equ:ch-deploy/conv-bn-equation-3 ) {reference-type="ref"
127127reference="equ: ch-deploy /conv-bn-equation-3"}.
128128
129- $$ \tag{ equ:ch-deploy/conv-bn-equation-3}
130- \bm {Y_{\rm bn}}=\bm {A}\cdot\bm {X_{\rm conv}}+\bm {B} $$
129+ $$ [ equ:ch-deploy/conv-bn-equation-3]
130+ \mathbf {Y_{\rm bn}}=\mathbf {A}\cdot\mathbf {X_{\rm conv}}+\mathbf {B} $$
131131
132- Here, $\bm {A}$ and $\bm {B}$ are two matrices. It can be noticed that
132+ Here, $\mathbf {A}$ and $\mathbf {B}$ are two matrices. It can be noticed that
133133Equation
134134[ \[ equ: ch-deploy /conv-bn-equation-3\] ] ( #equ:ch-deploy/conv-bn-equation-3 ) {reference-type="ref"
135135reference="equ: ch-deploy /conv-bn-equation-3"} is a formula for computing
@@ -196,8 +196,8 @@ folding the constants, Batchnorm is defined as Equation
196196[ \[ equ: ch-deploy /replace-scale\] ] ( #equ:ch-deploy/replace-scale ) {reference-type="ref"
197197reference="equ: ch-deploy /replace-scale"}
198198
199- $$ \tag{ equ:ch-deploy/replace-scale}
200- \bm {Y_{bn}}=scale\cdot\bm {X_{bn}}+offset $$
199+ $$ [ equ:ch-deploy/replace-scale]
200+ \mathbf {Y_{bn}}=scale\cdot\mathbf {X_{bn}}+offset $$
201201
202202where ** scale** and ** offsets** are scalars. This simplified formula can
203203be mapped to a Scale operator.
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