An apparatus includes circuitry configured to: partition an input tensor into one or more block tensors; partition at least one of the block tensors into one or more continuation bands, the one or more continuation bands being associated with a caching counter having a value; store the one or more continuation bands in a cache managed using a cache manager; retrieve, prior to a convolution or pooling operation on a current block tensor, the one or more continuation bands of a previous block tensor from the cache that are adjacent to a current block tensor; concatenate the retrieved continuation bands with the current block tensor; apply the convolution or pooling operation on the current block tensor after the concatenation; decrease the respective caching counter value of the retrieved continuation bands; and clear the continuation bands from the cache when its respective caching counter reaches a value of zero.