Post-training Quantization for Neural Networks with Provable Guarantees

TL;DR

This paper introduces a generalized post-training neural network quantization method, GPFQ, with provable error guarantees, demonstrating its effectiveness on various architectures and datasets with minimal accuracy loss.

Contribution

It extends GPFQ to handle general quantization alphabets and provides rigorous error analysis, including sparsity promotion and applicability to different architectures.

Findings

Quantized models show minor accuracy loss on ImageNet.

Error decays linearly with the number of weights in over-parameterized networks.

Modifications like bias correction improve quantization accuracy.

Abstract

While neural networks have been remarkably successful in a wide array of applications, implementing them in resource-constrained hardware remains an area of intense research. By replacing the weights of a neural network with quantized (e.g., 4-bit, or binary) counterparts, massive savings in computation cost, memory, and power consumption are attained. To that end, we generalize a post-training neural-network quantization method, GPFQ, that is based on a greedy path-following mechanism. Among other things, we propose modifications to promote sparsity of the weights, and rigorously analyze the associated error. Additionally, our error analysis expands the results of previous work on GPFQ to handle general quantization alphabets, showing that for quantizing a single-layer network, the relative square error essentially decays linearly in the number of weights -- i.e., level of over-parametrization. Our result holds across a range of input distributions and for both fully-connected and convolutional architectures thereby also extending previous results. To empirically evaluate the method, we quantize several common architectures with few bits per weight, and test them on ImageNet, showing only minor loss of accuracy compared to unquantized models. We also demonstrate that standard modifications, such as bias correction and mixed precision quantization, further improve accuracy.