Quantized Convolutional Neural Networks Through the Lens of Partial Differential Equations

TL;DR

This paper introduces a PDE-inspired approach to improve quantized CNNs by applying edge-aware smoothing and stability analysis, resulting in networks that maintain performance with fewer resources.

Contribution

It proposes a novel PDE-based framework for enhancing quantized CNNs, emphasizing stability and edge-aware smoothing to preserve accuracy in low-resource settings.

Findings

Edge-aware smoothing reduces outliers in feature maps.

Stable quantized networks retain performance similar to full-precision models.

Stability can sometimes improve classification accuracy.

Abstract

Quantization of Convolutional Neural Networks (CNNs) is a common approach to ease the computational burden involved in the deployment of CNNs, especially on low-resource edge devices. However, fixed-point arithmetic is not natural to the type of computations involved in neural networks. In this work, we explore ways to improve quantized CNNs using PDE-based perspective and analysis. First, we harness the total variation (TV) approach to apply edge-aware smoothing to the feature maps throughout the network. This aims to reduce outliers in the distribution of values and promote piece-wise constant maps, which are more suitable for quantization. Secondly, we consider symmetric and stable variants of common CNNs for image classification, and Graph Convolutional Networks (GCNs) for graph node-classification. We demonstrate through several experiments that the property of forward stability preserves the action of a network under different quantization rates. As a result, stable quantized networks behave similarly to their non-quantized counterparts even though they rely on fewer parameters. We also find that at times, stability even aids in improving accuracy. These properties are of particular interest for sensitive, resource-constrained, low-power or real-time applications like autonomous driving.