  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.
