Bias-Aware FP8 Format for Efficient Weight Representation in Post-Training Quantization

Abstract

Deep neural network (DNN) weights dominate memory consumption during inference, making their efficient numerical representation particularly important for resource-constrained Edge AI systems. Widely used 8-bit floating-point (FP8) formats, such as E5M2 and E4M3, provide representable ranges that are significantly wider than required for typical DNN weights, which exhibit low variance and a narrow effective support. Consequently, a substantial portion of the available representation range remains unused. Motivated by the observation that exponent bias scales representable values, we establish a general analytical framework linking FP representation with quantization theory by interpreting FP formats as piecewise-uniform quantizers, enabling systematic analysis of exponent bias effects on representation efficiency. The framework formalizes encoding and decoding rules for low-bit FP representations and provides analytical estimates of representation accuracy through derived expressions for mean squared error and signal-to-quantization-noise ratio (SQNR) as functions of data variance. The analysis shows that the maximum achievable SQNR, primarily determined by mantissa precision, is sustained over a variance range whose width is governed by the exponent–mantissa allocation, while its position is controlled by the exponent bias. This enables increased mantissa precision within a fixed bit budget by compensating for reduced variance coverage caused by fewer exponent bits through an appropriate bias selection that aligns the high-SQNR region with the statistical properties of the data. Based on these insights, we propose Bias-Aware FP8 for Weights (BA-FP8-W). Experimental results on ResNet-18 and DenseNet-121 demonstrate that BA-FP8-W achieves higher SQNR than E4M3 and E5M2 and delivers inference accuracy close to the FP32 baseline.