The Illusion of Equivalency: Statistical Characterization of Quantization Effects in LLMs

Abstract

Post-Training Quantization has become widely used to compress large language models to make them deployable on resource-constrained devices. However, the evaluation of quantization methods mainly uses accuracy and perplexity, which cannot capture the behavioral changes in the quantized variants. In this work, we propose Correctness Agreement, a decision-level metric that can measure the intersection of correct predictions between the base model and its quantized variant. We use this metric across multiple models and quantization bit levels (8-bit to 2-bit), and we find that the base and quantized variants usually have a shift in behavior even when accuracy and perplexity are preserved. In order to explain this effect, we study the effect of quantization on the structure of the attention weights using statistical and distributional measures. The results reveal a breakpoint at low bit widths and show that query and key projections are more sensitive to quantization than the value and output projections. These results prove the illusion of equivalency between the base and quantized models and inspire behavioral evaluation beyond perplexity and accuracy for quantization methods.