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

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 \underline{N}on-uniform \underline{L}inear \underline{I}nterpolation (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 \emph{globally} minimal interpolation error in $\mathcal{O}(M \times N^2)$ 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 4× improvement in computational efficiency compared to the state-of-the-art designs.