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

arXiv: https://arxiv.org/abs/2602.02988 · HTML: https://mlsanity.com/paper/2602.02988/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 41 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 30 of 30)

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- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [DETRs Beat YOLOs on Real-time Object Detection](https://mlsanity.com/paper/2304.08069/) (2023)
- [I-BERT: Integer-only BERT Quantization](https://mlsanity.com/paper/2101.01321/) (2021)
- [Pretrained Language Models for Text Generation: A Survey](https://mlsanity.com/paper/2201.05273/) (2022)
- [OstQuant: Refining Large Language Model Quantization with Orthogonal and Scaling Transformations for Better Distribution Fitting](https://mlsanity.com/paper/2501.13987/) (2025)
- [Gemmini: Enabling Systematic Deep-Learning Architecture Evaluation via Full-Stack Integration](https://mlsanity.com/paper/1911.09925/) (2019)
- [Softermax: Hardware/Software Co-Design of an Efficient Softmax for Transformers](https://mlsanity.com/paper/2103.09301/) (2021)
- [I2MVFormer: Large Language Model Generated Multi-View Document Supervision for Zero-Shot Image Classification](https://mlsanity.com/paper/2212.02291/) (2022)
- [NN-LUT: Neural Approximation of Non-Linear Operations for Efficient Transformer Inference](https://mlsanity.com/paper/2112.02191/) (2021)
- [a survey on GPT-3](https://mlsanity.com/paper/2212.00857/) (2022)
- [LLMs for Translation: Historical, Low-Resourced Languages and Contemporary AI Models](https://mlsanity.com/paper/2503.11898/) (2025)

## Built on by (most cited first, 1 of 1)

- [Fast Polynomial Transcendentals for LLMs](https://mlsanity.com/paper/2610.00049/) (2026)

## Abstract (arXiv)

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.