1. A method for computing a layer output for a convolutional neural network layer from a layer input using a two-dimensional systolic array, the convolutional neural network layer having a plurality of kernels, each kernel having a respective matrix structure of weights, the method comprising: receiving the layer input, the layer input comprising a plurality of activation inputs, the plurality of activation inputs represented as a multi-dimensional matrix comprising a plurality of depth levels, each depth level being a respective matrix of distinct activation inputs from the plurality of activation inputs; sending each respective kernel matrix structure to a distinct cell along a first dimension of the systolic array; for each depth level, sending the respective matrix of distinct activation inputs to a distinct cell along a second dimension of the systolic array; causing the systolic array to generate an accumulated output from the respective matrices sent to the cells; and generating the layer output from the accumulated output.