The Effects of Approximate Multiplication on Convolutional Neural Networks

TL;DR

This paper investigates how approximate multiplication affects CNN inference accuracy and efficiency, showing that certain approximations can significantly reduce energy consumption with minimal accuracy loss.

Contribution

It provides an analytical explanation for why approximate multipliers like Mitch-$w$6 maintain accuracy and demonstrates their effectiveness in CNN inference without retraining.

Findings

Approximate multipliers can achieve near-FP32 accuracy in CNNs.

Mitch-$w$6 reduces energy consumption by up to 80% compared to bfloat16.

Analytical justification that multiplications can be approximated while additions remain exact.

Abstract

This paper analyzes the effects of approximate multiplication when performing inferences on deep convolutional neural networks (CNNs). The approximate multiplication can reduce the cost of the underlying circuits so that CNN inferences can be performed more efficiently in hardware accelerators. The study identifies the critical factors in the convolution, fully-connected, and batch normalization layers that allow more accurate CNN predictions despite the errors from approximate multiplication. The same factors also provide an arithmetic explanation of why bfloat16 multiplication performs well on CNNs. The experiments are performed with recognized network architectures to show that the approximate multipliers can produce predictions that are nearly as accurate as the FP32 references, without additional training. For example, the ResNet and Inception-v4 models with Mitch-$w$6 multiplication produces Top-5 errors that are within 0.2% compared to the FP32 references. A brief cost comparison of Mitch-$w$6 against bfloat16 is presented, where a MAC operation saves up to 80% of energy compared to the bfloat16 arithmetic. The most far-reaching contribution of this paper is the analytical justification that multiplications can be approximated while additions need to be exact in CNN MAC operations.