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arXiv · 2510.01450

Local Linear Attention: An Optimal Interpolation of Linear and Softmax Attention For Test-Time Regression

Yifei Zuo·Yutong Yin·Zhichen Zeng·Ang Li·Banghua Zhu·Zhaoran Wang
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Abstract

Transformer architectures have achieved remarkable success in various domains. While efficient alternatives to Softmax Attention have been widely studied, the search for more expressive mechanisms grounded in theoretical insight-even at greater computational cost-has been relatively underexplored. In this work, we bridge this gap by proposing Local Linear Attention (LLA), a novel attention mechanism derived from nonparametric statistics through the lens of test-time regression. First, we show that LLA offers theoretical advantages over Linear and Softmax Attention for associative memory via a bias-variance trade-off analysis. Next, we address its computational challenges and propose two memory-efficient primitives to tackle the $Θ(n^2 d)$ and $Θ(n d^2)$ complexity. We then introduce FlashLLA, a hardware-efficient, blockwise algorithm that enables scalable and parallel computation on modern accelerators. In addition, we implement and profile a customized inference kernel that significantly reduces memory overheads. Finally, we empirically validate the advantages and limitations of LLA on test-time regression, in-context regression, associative recall and state tracking tasks. Experiment results demonstrate that LLA effectively adapts to non-stationarity, outperforming strong baselines in test-time training and in-context learning, and exhibiting promising evidence for its scalability and applicability in large-scale models. Code is available at https://github.com/Yifei-Zuo/Flash-LLA.

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Yifei Zuo, Yutong Yin, Zhichen Zeng, Ang Li, Banghua Zhu, Zhaoran Wang. 2025-10-01. Local Linear Attention: An Optimal Interpolation of Linear and Softmax Attention For Test-Time Regression. https://arxiv.org/abs/2510.01450

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