SmoothGPTQ: Optimizing Diagonal Scaling for GPTQ Weight-Activation Quantization

Diagonal smoothing, as in SmoothQuant, is a useful tool for balancing the errors incurred from weights quantization and activations quantization. For weight quantization the error can be further reduced by accounting for the activations second-order statistics via GPTQ. Prior work have considered the optimization of diagonal smoothing parameters for round-to-nearest (RTN) quantization. In this work we develop a framework, termed SmoothGPTQ, for optimizing those parameters for GPTQ-quantized weights and RTN-quantized activations. We derive an approximate expression for the quantization mean-squared error MSE as a function of $S$. This expression is convex in log-scale and is therefore amenable to minimization, and its accuracy is established through experiments. Applying the developed SmoothGPTQ algorithm to various LLMs give state-of-the-art results for W4A4 INT quantization across various benchmarks.