Quantized Artificial Neural Networks Implemented with Spintronic Stochastic Computing

An Artificial Neural Network (ANN) inference involves matrix vector multiplications that require a very large number of multiply and accumulate operations, resulting in high energy cost and large device footprint. Stochastic computing (SC) offers a less resource-intensive ANN implementation and can be realized through stochastic-magnetic tunnel junctions (s-MTJ) that generate random numbers, where the energy barrier to switch between the up and down states is designed to be small. While s-MTJs have previously been used to implement SC-ANNs, these studies have been limited to architectures with continuously varying (analog) weights. We study the use of SC for matrix vector multiplication with quantized synaptic weights and outputs. We show that a quantized SC-ANN, implemented by using experimentally obtained s-MTJ bitstreams and using a limited number of discrete quantized states for both weights and hidden layer outputs in an ANN, can effectively reduce latency and energy consumption in SC compared to an analog implementation, while largely preserving accuracy. We implemented quantization with 5 and 11 quantized states, along with SC configured with stochastic bitstream lengths of 100 to 500 on neural networks with one and three hidden layers. Inference was performed on the MNIST dataset for both training with SC and without SC. Training with SC provided better accuracy for all cases. For the shortest bitstream of 100 bits, the highest accuracies were 92% for one hidden layer and over 96% for three hidden layers. The overall system attained its peak accuracy of 96.82% using a 400-bit stochastic bitstream with three hidden layers and demonstrated 9X improvement in latency to implement neuron activations and 2.6X improvement in energy consumption using the quantized SC approach compared to a similar s-MTJ based ANN architecture without quantization.