NLI:Non-uniform Linear Interpolation Approximation of Nonlinear Operations for Efficient LLMs Inference

TL;DR

This paper introduces NLI, a novel approximation framework for nonlinear functions in large language models, significantly reducing computational costs while maintaining accuracy, through an optimal dynamic programming approach.

Contribution

The paper presents NLI, a calibration-free, hardware-friendly method that efficiently approximates nonlinear functions in LLMs using a dynamic programming-based optimal interpolation technique.

Findings

Achieves over 4x computational efficiency improvement.

Maintains almost no accuracy loss in LLM inference.

Provides a universal nonlinear computation unit for practical deployment.

Abstract

Large Language Models (LLMs) have demonstrated remarkable performance across a wide range of tasks, but their deployment is often constrained by substantial memory footprints and computational costs. While prior work has achieved significant progress in compressing and accelerating linear layers, nonlinear layers-such as SiLU, RMSNorm, and Softmax-still heavily depend on high-precision floating-point operations. In this paper, we propose a calibration-free, dynamic-programming-optimal, and hardware-friendly framework called Non-uniform Linear Interpolation (NLI). NLI is capable of efficiently approximating a variety of nonlinear functions, enabling seamless integration into LLMs and other deep neural networks with almost no loss in accuracy. NLI ingeniously recasts cutpoint selection as a dynamic-programming problem, achieving the globally minimal interpolation error in O(MxN2) time via Bellman's optimality principle. Based on the NLI algorithm, we also design and implement a plug-and-play universal nonlinear computation unit. Hardware experiments demonstrate that the NLI Engine achieves more than 4x improvement in computational efficiency compared to the state-of-the-art designs.