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My understanding is that the width and the height represents a kernel (convolution matrix) that is convolved over the image. The depth is the number of these kernels. If that is the case, how would adjacent convolutional layers be connected, for Eg. If the first layer has a depth of 32, and the second has a depth of 64?

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starting from the input image, assume it has depth of 3 (RGB), if the first Conv layer has depth of 32, it means we have 32 recepetive fields (or filters) of n*n*3, where n is the size of the filter. and the same for the next layer. Example: suppose the input layer has dimensions 100*100*32, If the filter size is 5x5, then each neuron in the Conv layer will have weights to a [5x5x32] region in the input volume, for a total of 5*5*32 = 800 weights (and +1 bias parameter) and we have 64 of these filters (the depth of the second conv layer is 64). Notice that the extent of the connectivity along the depth axis must be 32, since this is the depth of the input volume.

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