In one embodiment, a method of simulating an operation of an artificial neural network on a binary neural network processor includes receiving a binary input vector for a layer including a probabilistic binary weight matrix and performing vector-matrix multiplication of the input vector with the probabilistic binary weight matrix, wherein the multiplication results are modified by simulated binary-neural-processing hardware noise, to generate a binary output vector, where the simulation is performed in the forward pass of a training algorithm for a neural network model for the binary-neural-processing hardware.