Training Quantized Nets: A Deeper Understanding

TL;DR

This paper provides a theoretical analysis of training quantized neural networks, highlighting the challenges and differences from high-precision training, especially in non-convex settings, to improve low-resource deployment.

Contribution

It offers a theoretical perspective on training quantized networks, including accuracy guarantees and insights into the difficulties of low-precision training.

Findings

High-precision algorithms have a greedy search phase absent in pure quantized training.

Training with low-precision weights is inherently more challenging due to lack of high-precision search.

Theoretical analysis under convex and non-convex assumptions explains empirical difficulties in quantized training.

Abstract

Currently, deep neural networks are deployed on low-power portable devices by first training a full-precision model using powerful hardware, and then deriving a corresponding low-precision model for efficient inference on such systems. However, training models directly with coarsely quantized weights is a key step towards learning on embedded platforms that have limited computing resources, memory capacity, and power consumption. Numerous recent publications have studied methods for training quantized networks, but these studies have mostly been empirical. In this work, we investigate training methods for quantized neural networks from a theoretical viewpoint. We first explore accuracy guarantees for training methods under convexity assumptions. We then look at the behavior of these algorithms for non-convex problems, and show that training algorithms that exploit high-precision representations have an important greedy search phase that purely quantized training methods lack, which explains the difficulty of training using low-precision arithmetic.