Automatic mixed precision for optimizing gained time with constrained loss mean-squared-error based on model partition to sequential sub-graphs

TL;DR

This paper introduces an automatic mixed precision method for neural network quantization that optimizes inference time by modeling model partitioning and sensitivity, validated on large language models with hardware-aware predictions.

Contribution

It proposes a novel sensitivity metric based on a Taylor series expansion and an IP-based optimization for mixed precision configuration considering hardware constraints.

Findings

Effective sensitivity metric for layer-wise quantization

Hardware-aware time gain prediction model

Validated on large language models with real hardware

Abstract

Quantization is essential for Neural Network (NN) compression, reducing model size and computational demands by using lower bit-width data types, though aggressive reduction often hampers accuracy. Mixed Precision (MP) mitigates this tradeoff by varying the numerical precision across network layers. This study focuses on automatically selecting an optimal MP configuration within Post-Training Quantization (PTQ) for inference. The first key contribution is a novel sensitivity metric derived from a first-order Taylor series expansion of the loss function as a function of quantization errors in weights and activations. This metric, based on the Mean Square Error (MSE) of the loss, is efficiently calculated per layer using high-precision forward and backward passes over a small calibration dataset. The metric is additive across layers, with low calibration memory overhead as weight optimization is unnecessary. The second contribution is an accurate hardware-aware method for predicting MP time gain by modeling it as additive for sequential sub-graphs. An algorithm partitions the model graph into sequential subgraphs, measuring time gain for each configuration using a few samples. After calibrating per-layer sensitivity and time gain, an Integer Programming (IP) problem is formulated to maximize time gain while keeping loss MSE below a set threshold. Memory gain and theoretical time gain based on Multiply and Accumulate (MAC) operations are also considered. Rigorous experiments on the Intel Gaudi 2 accelerator validate the approach on several Large Language Models (LLMs).