Convolutional Neural Networks using Logarithmic Data Representation

TL;DR

This paper introduces a logarithmic data representation for convolutional neural networks that allows encoding to 3 bits with minimal performance loss, improving efficiency and accuracy over fixed-point methods.

Contribution

It proposes a novel non-uniform logarithmic encoding scheme for weights and activations, enabling high-accuracy, low-bit neural network deployment on resource-constrained devices.

Findings

3-bit logarithmic encoding achieves near-original accuracy.

Logarithmic representation reduces hardware complexity by eliminating multipliers.

End-to-end training with log representation at 5 bits outperforms linear at the same bit-width.

Abstract

Recent advances in convolutional neural networks have considered model complexity and hardware efficiency to enable deployment onto embedded systems and mobile devices. For example, it is now well-known that the arithmetic operations of deep networks can be encoded down to 8-bit fixed-point without significant deterioration in performance. However, further reduction in precision down to as low as 3-bit fixed-point results in significant losses in performance. In this paper we propose a new data representation that enables state-of-the-art networks to be encoded to 3 bits with negligible loss in classification performance. To perform this, we take advantage of the fact that the weights and activations in a trained network naturally have non-uniform distributions. Using non-uniform, base-2 logarithmic representation to encode weights, communicate activations, and perform dot-products enables networks to 1) achieve higher classification accuracies than fixed-point at the same resolution and 2) eliminate bulky digital multipliers. Finally, we propose an end-to-end training procedure that uses log representation at 5-bits, which achieves higher final test accuracy than linear at 5-bits.