SPFQ: A Stochastic Algorithm and Its Error Analysis for Neural Network Quantization
This work addresses the lack of comprehensive error analysis in quantization techniques for deep neural networks, providing theoretical guarantees that could benefit efficient deployment of large models.
The paper tackles the problem of neural network quantization by proposing a fast stochastic algorithm with linear computational complexity, and establishes full-network error bounds for the first time, showing that relative square quantization error decays linearly with over-parametrization and can be achieved with about log log N bits per weight.
Quantization is a widely used compression method that effectively reduces redundancies in over-parameterized neural networks. However, existing quantization techniques for deep neural networks often lack a comprehensive error analysis due to the presence of non-convex loss functions and nonlinear activations. In this paper, we propose a fast stochastic algorithm for quantizing the weights of fully trained neural networks. Our approach leverages a greedy path-following mechanism in combination with a stochastic quantizer. Its computational complexity scales only linearly with the number of weights in the network, thereby enabling the efficient quantization of large networks. Importantly, we establish, for the first time, full-network error bounds, under an infinite alphabet condition and minimal assumptions on the weights and input data. As an application of this result, we prove that when quantizing a multi-layer network having Gaussian weights, the relative square quantization error exhibits a linear decay as the degree of over-parametrization increases. Furthermore, we demonstrate that it is possible to achieve error bounds equivalent to those obtained in the infinite alphabet case, using on the order of a mere $\log\log N$ bits per weight, where $N$ represents the largest number of neurons in a layer.