Pooling and convolutional layers handle multi-channel input data in fundamentally different ways. In a convolutional layer, a multi-channel cross-correlation is performed: the kernel computes a two-dimensional cross-correlation with each input channel separately, but the results from all $c_ extrm{i}$ channels are then summed together to produce a single two-dimensional output per output channel. In contrast, the pooling layer processes each input channel independently—it applies the pooling window to every channel in isolation without combining information across channels. As a direct consequence, the number of output channels of a pooling layer always equals the number of input channels, whereas a convolutional layer's output channel count is determined by the number of kernels ($c_ extrm{o}$), which is independent of $c_ extrm{i}$. This architectural difference means pooling preserves the per-channel feature representations established by preceding convolutional layers, while convolution mixes cross-channel information to create new feature combinations.