Per-Tensor Fixed-Point Quantization of the Back-Propagation Algorithm

Charbel Sakr, Naresh Shanbhag

Abstract: The high computational and parameter complexity of neural networks makes their training very slow and difficult to deploy on energy and storage-constrained comput- ing systems. Many network complexity reduction techniques have been proposed including fixed-point implementation. However, a systematic approach for design- ing full fixed-point training and inference of deep neural networks remains elusive. We describe a precision assignment methodology for neural network training in which all network parameters, i.e., activations and weights in the feedforward path, gradients and weight accumulators in the feedback path, are assigned close to minimal precision. The precision assignment is derived analytically and enables tracking the convergence behavior of the full precision training, known to converge a priori. Thus, our work leads to a systematic methodology of determining suit- able precision for fixed-point training. The near optimality (minimality) of the resulting precision assignment is validated empirically for four networks on the CIFAR-10, CIFAR-100, and SVHN datasets. The complexity reduction arising from our approach is compared with other fixed-point neural network designs.

Keywords: deep learning, reduced precision, fixed-point, quantization, back-propagation algorithm

TL;DR: We analyze and determine the precision requirements for training neural networks when all tensors, including back-propagated signals and weight accumulators, are quantized to fixed-point format.

Data: [CIFAR-10](https://paperswithcode.com/dataset/cifar-10), [CIFAR-100](https://paperswithcode.com/dataset/cifar-100), [SVHN](https://paperswithcode.com/dataset/svhn)