An alternative mathematical perspective on grouped convolutions is to view them as operations involving a block-diagonal matrix for the convolutional weights. By restricting the connections between input and output channels to independent groups, the overall weight matrix essentially becomes block-diagonal, where each block corresponds to the convolution weights of a single group. This structural constraint enforces sparsity, which reduces computational cost and allows for an increase in the size of the activations (number of channels) without a quadratic penalty.