In a multi-output channel cross-correlation, the result for each individual output channel is calculated independently from the other output channels, using its corresponding $c_ extrm{i} imes k_ extrm{h} imes k_ extrm{w}$ slice from the convolution kernel and the entire multi-channel input tensor. Specifically, the kernel slice performs a multi-channel cross-correlation with all $c_ extrm{i}$ channels of the input tensor to produce one channel of the output. While the computation for each channel is independent, the multiple output channels do not learn representations independently; rather, they are optimized jointly, meaning specific directions in the channel space may correspond to useful feature detections, such as edge detectors.