Feature Map

In a CNN, if we only apply a single convolution to the input, information will be lost; we are averaging nearby inputs, and the ReLU activation function clips results that are less than zero. Thus, we usually compute several convolutions in parallel. Each convolution produces a new set of hidden variables, termed a feature map or channel.

Part (a) and (b) of the figure shows this with two convolution kernels of size 3 and with zero padding.

• The first kernel computes a weighted sum of the nearest three pixels, and passes the results through the activation to produce results $h_1$ to $h_6$. These comprise the first channel.
• The second kernel computes a different weighted sum of the nearest three pixels, adds a different bias, and passes the results through the activation function to create hidden units $h_7$ to $h_{12}$. These comprise the second channel.

In general, the input and the hidden layers all have multiple channels (part (c) of figure). If the incoming layer has $C_i$ channels and we select a kernel size $K$ per channel, the hidden units in each output channel are computed as a weighted sum over all $C_i$ channels and $K$ kernel entries using a weight matrix $\Omega \in {\mathbb{R}}^{C_i\times K}$ and one bias. Hence, if there are $C_o$ channels in the next layer, then we need $\Omega \in {\mathbb{R}}^{C_i\times C_o\times K}$ weights and $\beta \in {\mathbb{R}}^{C_o}$ biases.