FP=xINT:Representing Neural Networks via Low-Bit Series Basis Functions

TL;DR

This paper introduces FP=xINT, a novel series expansion framework for neural network quantization that accurately approximates full-precision models using low-bit basis models, improving performance at extremely low bit settings.

Contribution

First application of series expansion to neural network quantization, enabling rapid, calibration-free approximation of full-precision models with theoretical convergence guarantees.

Findings

Achieves state-of-the-art low-bit quantization performance

4-bit ResNet-50 surpasses original accuracy, reaching 77.03%

Ensures operation parallelism and model accuracy restoration

Abstract

Post-Training Quantization (PTQ) converts pre-trained Full-Precision (FP) models into quantized versions without training. While existing methods reduce size and computational costs, they also significantly degrade performance and quantization efficiency at extremely low settings due to quantization noise. We introduce a deep model series expansion framework to address this issue, enabling rapid and accurate approximation of unquantized models without calibration sets or fine-tuning. This is the first use of series expansion for neural network quantization. Specifically, our method expands the FP model into multiple low-bit basis models. To ensure accurate quantization, we develop low-bit basis model expansions at different granularities (tensor, layer, model), and theoretically confirm their convergence to the dense model, thus restoring FP model accuracy. Additionally, we design AbelianAdd/Mul operations between isomorphic models in the low-bit expansion, forming an Abelian group to ensure operation parallelism and commutativity. The experiments show that our algorithm achieves state-of-the-art performance in low-bit settings; for example, 4-bit quantization of ResNet-50 surpasses the original accuracy, reaching 77.03%. The code will be made public.