Efficacy of Local Linear Attention in Large Language Models

Determine the effectiveness of Local Linear Attention (LLA) when integrated into large language models, including assessing training feasibility and end-to-end performance at scale given the computational and numerical constraints introduced by the query-specific matrix inversion and associated kernel implementations.

Background

Local Linear Attention (LLA) is proposed as a more expressive attention mechanism derived from local linear regression, offering theoretical advantages over Softmax Attention and Linear Attention in bias-variance trade-offs and associative recall. The paper introduces FlashLLA, a hardware-efficient blockwise algorithm, and demonstrates empirical gains on synthetic and moderate-scale tasks.

However, the authors note that while LLA reduces memory consumption via blockwise computation and conjugate-gradient-based inversion, its computational and I/O costs remain high, and numerical sensitivity of matrix inversion presents challenges for low-precision kernels. Consequently, training and evaluating LLA within LLMs is not yet established, motivating a direct investigation into LLA’s scalability and practical efficacy in LLM contexts.