CNNs: Practice and Extra Details¶

Prof. Forrest Davis

Question: Apply the following kernel to the input matrix with stride 1:

Kernel: $\left[\begin{array}{cc} 10 & 1\\ 0 & 2 \end{array}\right]$

input: $\left[\begin{array}{cccccc} 1 & 0 & 4 & 3 & 4 & 3\\ 3 & 4 & 3 & 1 & 0 & 2\\ 1 & 4 & 3 & 4 & 2 & 3\\ \end{array}\right]$

||

Recall, last class I applied a simple edge detection algorithm which subtracting each pixel by the value to its left.

Question Give a 1D kernel that accomplishes this task

||

Question: What is the shape of the output of this kernel with a stride of 1?

||

Question: Give a general expression for the shape of the output after applying a kernel

||

Floating-point operations are any mathematical operation (e.g., +, *, -, /) or assignment involving floating-point numbers
Ignoring assignment here, a matrix multiplication implementation of our edge detection operation applied to a image of shape 320 X 280 would require more than 16 billion floating-point operations

Question: How many floating-point operations does our convolution trick require (again ignoring assignment)?

||

Padding¶

How do we prevent the reduction in image size caused by convolution (e.g., we lost one row and one column in our first example in the handout)?

Question: Try to come up with an approach that resolves this (and give the resultant convolution) for the example below

Stride: 2

Kernel: $\left[\begin{array}{cc} 1 & 2\\ 0 & 2 \end{array}\right]$

input: $\left[\begin{array}{cccc} 3 & 1 & 2 & 4 \\ 2 & 2 & 4 & 0 \\ 3 & 2 & 2 & 1 \\ 3 & 4 & 4 & 0 \\ \end{array}\right]$

||