Effect of Weight Quantization on Learning Models by Typical Case Analysis
This work addresses the challenge of efficiently deploying large models on resource-limited devices, though it is incremental as it builds on existing quantization methods with theoretical insights.
The paper tackles the problem of selecting hyperparameters for weight quantization in learning models, using typical case analysis to find that an optimal quantization width minimizes error and that quantization delays overparameterization to mitigate overfitting.
This paper examines the quantization methods used in large-scale data analysis models and their hyperparameter choices. The recent surge in data analysis scale has significantly increased computational resource requirements. To address this, quantizing model weights has become a prevalent practice in data analysis applications such as deep learning. Quantization is particularly vital for deploying large models on devices with limited computational resources. However, the selection of quantization hyperparameters, like the number of bits and value range for weight quantization, remains an underexplored area. In this study, we employ the typical case analysis from statistical physics, specifically the replica method, to explore the impact of hyperparameters on the quantization of simple learning models. Our analysis yields three key findings: (i) an unstable hyperparameter phase, known as replica symmetry breaking, occurs with a small number of bits and a large quantization width; (ii) there is an optimal quantization width that minimizes error; and (iii) quantization delays the onset of overparameterization, helping to mitigate overfitting as indicated by the double descent phenomenon. We also discover that non-uniform quantization can enhance stability. Additionally, we develop an approximate message-passing algorithm to validate our theoretical results.