Learning Algorithm for LesserDNN, a DNN with Quantized Weights

Abstract

This paper presents LesserDNN, a model that uses a set of floating-point values \{-1.0, -0.5, -0.25, -0.125, -0.0625, 0.0625, 0.125, 0.25, 0.5, 1.0\} as quantized weights, and a new learning algorithm for the proposed model.In previous studies on deep neural networks (DNNs) with quantized weights, because DNNs employ the gradient descent method as their learning algorithm, quantized weights were applied only during the inference stage.Due to differentiability properties, quantized weights cannot be used when the gradient descent method is applied during training.To address this issue, we devised an algorithm based on simulated annealing.Since simulated annealing has no differentiability requirements, LesserDNN can utilize quantized weights during training. With the use of quantized weights and this simulated annealing-based algorithm, the learning process becomes a combinatorial problem. The proposed algorithm was applied to train networks on the MNIST handwriting dataset. The tested models were trained with the simulated annealing-based algorithm and quantized weights, achieving the same level of accuracy as gradient descent-based comparison methods. Additionally, we conducted tests using the CIFAR-10 dataset, and achieved the good results to demonstrate the algorithm.Thus, LesserDNN has a simple design and small implementation scale because backpropagation is not applied. Moreover, this model achieves a high accuracy.