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Assume I have an input of size $32 \times 32 \times 3$ and pass it to a convolution layer. Now, if my kernel size were to be $5 \times 5 \times 3$ and the depth of my convolution layer were to be 1, only one feature map would be produced for the image. Here, each neuron would have $5 \times 5 \times 3 = 75$ weights (+1 bias).

If I wanted to calculate multiple feature maps in this layer, say 3, is each local section (in this example, $5 \times 5 \times 3$) of the image looked on by three different neurons and each of their weights trained individually? And what would be the output volume of this layer?

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Each feature map (or kernel) is independent of each other. If you had $3$ of these filters, your output shape would be $(28, 28, 3)$ (given the appropriate amount of padding and stride) with a total of $75*3=225$ trainable weights.

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