Beyond Discreteness: Finite-Sample Analysis of Straight-Through Estimator for Quantization

TL;DR

This paper provides the first finite-sample theoretical analysis of the straight-through estimator (STE) for neural network quantization, revealing the importance of sample size and data complexity in ensuring successful training convergence.

Contribution

It introduces a finite-sample analysis of STE, deriving sample complexity bounds and exploring its behavior under label noise in neural network quantization.

Findings

Sample size critically affects STE success.

Derived data-dependent convergence guarantees.

Observed recurrence behavior of STE under label noise.

Abstract

Training quantized neural networks requires addressing the non-differentiable and discrete nature of the underlying optimization problem. To tackle this challenge, the straight-through estimator (STE) has become the most widely adopted heuristic, allowing backpropagation through discrete operations by introducing surrogate gradients. However, its theoretical properties remain largely unexplored, with few existing works simplifying the analysis by assuming an infinite amount of training data. In contrast, this work presents the first finite-sample analysis of STE in the context of neural network quantization. Our theoretical results highlight the critical role of sample size in the success of STE, a key insight absent from existing studies. Specifically, by analyzing the quantization-aware training of a two-layer neural network with binary weights and activations, we derive the sample complexity bound in terms of the data dimensionality that guarantees the convergence of STE-based optimization to the global minimum. Moreover, in the presence of label noises, we uncover an intriguing recurrence property of STE-gradient method, where the iterate repeatedly escape from and return to the optimal binary weights. Our analysis leverages tools from compressed sensing and dynamical systems theory.