Gradient Decomposition Methods for Training Neural Networks With Non-ideal Synaptic Devices

Abstract

While promising for high-capacity machine learning accelerators, memristor devices have non-idealities that prevent software-equivalent accuracies when used for online training. This work uses a combination of Mini-Batch Gradient Descent (MBGD) to average gradients, stochastic rounding to avoid vanishing weight updates, and decomposition methods to keep the memory overhead low during mini-batch training. Since the weight update has to be transferred to the memristor matrices efficiently, we also investigate the impact of reconstructing the gradient matrixes both internally (rank-seq) and externally (rank-sum) to the memristor array. Our results show that streaming batch principal component analysis (streaming batch PCA) and non-negative matrix factorization (NMF) decomposition algorithms can achieve near MBGD accuracy in a memristor-based multi-layer perceptron trained on the MNIST (Modified National Institute of Standards and Technology) database with only 3 to 10 ranks at significant memory savings. Moreover, NMF rank-seq outperforms streaming batch PCA rank-seq at low-ranks making it more suitable for hardware implementation in future memristor-based accelerators.

Hardware‐Mappable Cellular Neural Networks for Distributed Wavefront Detection in Next‐Generation Cardiac Implants

“…Stochastic rounding can be particularly useful in deep network training with low bit precision arithmetic. [ 31 , 32 ] A real template value a which lies between a lower weight level ( A 1 ) and upper weight level ( A 2 ) was stochastically rounded up to A 2 with probability ( a – A 1 )/( A 2 – A 1 ) and down to A 1 with probability ( A 2 – a )/( A 2 – A 1 ). The algorithm details are included in the supplemental materials.…”