深度神经网络中的卷积层Convolutional Layer的推导

Assuming :8x8 matrix，conv kernel : 3x3, ：Output。

，，

When padding = 1, stride=1

Y₁₂ = X₁₁W₂₁ + X₁₂W₂₂+ X₁₃W₂₃+ X₂₁W₃₁+ X₂₂W₃₂+ X₂₃W₃₃

Y₁₃ = X₁₂W₂₁ + X₁₃W₂₂+ X₁₄W₂₃+ X₂₂W₃₁+ X₂₃W₃₂+ X₂₄W₃₃

Y₁₄ = X₁₃W₂₁ + X₁₄W₂₂+ X₁₅W₂₃+ X₂₃W₃₁+ X₂₄W₃₂+ X₂₅W₃₃

Y₁₅ = X₁₄W₂₁ + X₁₅W₂₂+ X₁₆W₂₃+ X₂₄W₃₁+ X₂₅W₃₂+ X₂₆W₃₃

Y₁₆ = X₁₅W₂₁ + X₁₆W₂₂+ X₁₇W₂₃+ X₂₅W₃₁+ X₂₆W₃₂+ X₂₇W₃₃

Y₁₇ = X₁₆W₂₁ + X₁₇W₂₂+ X₁₈W₂₃+ X₂₆W₃₁+ X₂₇W₃₂+ X₂₈W₃₃

Y₁₈ = X₁₇W₂₁ + X₁₈W₂₂+X₂₇W₃₁+ X₂₈W₃₂

Y₂₁ = X₁₁W₁₂ + X₁₂W₁₃+ X₂₁W₂₂+ X₂₂W₂₃+ X₃₁W₃₂+ X₃₂W₃₃

Y₂₂ = X₁₁W₁₁ + X₁₂W₁₂+ X₁₃W₁₃+ X₂₁W₂₁+ X₂₂W₂₂+ X₂₃W₂₃+ X₃₁W₃₁+ X₃₂W₃₂+ X₃₃W₃₃

…

 

Now we know ，and calculate ,

 

Calculate

So,

 

That is,

 

: 3x3, So

padding=0

 

…

Let's calculate

 

 

: 3x3, So

 

Inference:

When padding = p, stride=1

Turn out to be

2. stride = 1, padding=p

Interesting.