Convolution

Convolution in Neural Networks: Dilated Convolution = replicating spectrum of filter dilated kernel size = (kernel_size - 1) * dilation + 1 leads to higher frequency resolution (number of unique points) strided convolution = conv plus downsampling

note that before downsampling, trailing entries are discarded.

of trailing entires discarded = stride - 1

therefore, the target size after conv only needs to be size - (stride - 1). Therefore, the input size after padding needs to be size - (stride - 1) + (kernel - 1), since the kernel takes away kernel - 1 units This is equal to size + kernel - stride, so the padding needs to be (kernel - stride)/2. if stride is even, we therefore want an even kernel.

Graph: X X X X X X X X - input [] X X X X X X X X [] - input after padding X X X X X X X - after conv, kernel size 4 X X X X - after downsampling

Otherwise: Two interpretations: 1—reverb (overlapping kernels) 2—flipping and shifting the ‘flipped’ kernel is a function. The x is the ‘offset’ and the y is the ‘weight’. i.e., how does input at time t + x affect output at time t.

Last Reviewed: 1/3/25