To illustrate the equivalence between cross-correlation and strict convolution in deep learning, consider a convolutional layer that learns a kernel matrix $\mathbf{K}$ when performing cross-correlation to produce a specific output. If the same layer were to perform a strict mathematical convolution under identical conditions, it would learn a modified kernel $\mathbf{K}'$. This newly learned kernel $\mathbf{K}'$ is simply the original kernel $\mathbf{K}$ flipped both horizontally and vertically. Consequently, performing a strict convolution with the input and $\mathbf{K}'$ yields the exact same output as performing cross-correlation with the input and $\mathbf{K}$.