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

ICLR 2026 · Large language models › Reasoning and chain of thought · approach: Efficient LLM serving

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Proposes NLI, a calibration-free dynamic-programming-optimal non-uniform linear interpolation LUT scheme for nonlinear ops (SiLU, RMSNorm, Softmax) in LLMs, plus a 28nm hardware engine with two-level address translation.

Problem

Nonlinear layers (SiLU, RMSNorm, Softmax) in LLMs still require high-precision floating-point computation, and existing LUT-based approximations (NN-LUT) are calibration-dependent and fail on LLM activation outliers beyond their training range.

Approach

Cast the selection of LUT cutpoints over the FP16 grid as a dynamic program minimizing additive mean relative interpolation error (Bellman recursion, O(MN^2)), giving a calibration-free LUT; combine with a fixed two-level (macro/uniform micro) layout so hardware needs only 10 comparators.

Key results

• On Qwen2.5-7B, NLI keeps MMLU 70.67 and GSM8k 43.97 (FP32: 70.56, 44.28), while NN-LUT collapses to 25.51 MMLU and 0 GSM8k with perplexity 28194.
• Hardware: NLI engine area 7787 um^2 vs 23238 (NN-LUT) and 23647 (RI-LUT) at 28nm, 1 GHz, 34 mW power.
• NLI engine reports 3.78 efficiency vs 0.94 (NN-LUT) and 0.88 (RI-LUT), i.e., about 4.02x and 4.29x higher.

Surprising findings

• Naive NN-LUT collapses on Qwen models with SiLU inputs beyond its training range, with perplexity up to 7.0e4 on Qwen2.5-32B.
• Uniform 259-point and curvature-based 259-point layouts degrade substantially on Qwen2.5-7B MMLU/GSM8k relative to the DP-based layout.

Limitations

• Macro-only DP with 11 cutpoints fails (MMLU 21.14, GSM8k 0), so the method depends on a fixed 259-entry two-level layout rather than the DP alone.
• Hardware evaluation is limited to synthesis (SMIC 28nm) without end-to-end chip measurements; NN-LUT and RI-LUT were re-implemented since the original NN-LUT code is not public.
• Values outside the [-150,150] LLM-typical domain are clamped, which may matter for rare outliers; the paper claims negligible impact without detailed analysis.

Experimental setup

Datasets: Wikitext-2 ARC-c ARC-e BoolQ PIQA HellaSwag OBQA LAMBADA SIQA WinoGrande MMLU HumanEval

Benchmarks: Wikitext-2 ARC-c ARC-e BoolQ PIQA HellaSwag OBQA LAMBADA SIQA WinoGrande MMLU HumanEval

Metrics: accuracy perplexity area (um^2) power (mW) efficiency (throughput/(area x power))

Baselines: NN-LUT RI-LUT Uniform 259 Curvature 259 Macro-only DP (M=11) Non-uniform 259 (DP)

Builds on: NN-LUT I-BERT Softermax linear LUT fitting

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