A system and method of inferring a neural network (NN) on one or more target computing devices. The NN may include a plurality of layers, where at least one layer includes one or more kernels. Embodiments may include: receiving a data structure representing the NN; analyzing the data structure to produce one or more tasks, where each task may include computations pertaining to a kernel of the NN; selecting a sparse version of at least one kernel and replacing the at least one kernel with the sparse version; and compiling the one or more tasks to produce one or more respective tensor columns, The one or more tensor columns are adapted to fit in respective one or more cache memories of the one or more target computing devices, and include task instruction code that represents at least one computation of the kernel of the NN.