Streaming Attention Approximation via Discrepancy Theory

Ekaterina Kochetkova, Kshiteej Sheth, Insu Han, Amir Zandieh, Michael Kapralov

Keywords: Attention approximation, Long-context Attention, Large Language Models, Discrepancy theory, Self-Balancing Walk

TL;DR: We design a geometric sampling framework to enhance memory efficiency and precision in long-context LLMs.

Abstract:

Large language models (LLMs) have achieved impressive success, but their high memory requirements present challenges for long-context token generation. In this paper we study the streaming complexity of attention approximation, a key computational primitive underlying token generation.

Our main contribution is BalanceKV, a streaming algorithm for $\epsilon$-approximating attention computations based on geometric process for selecting a balanced collection of Key and Value tokens as per Banaszczyk's vector balancing theory. We complement our algorithm with space lower bounds for streaming attention computation. Besides strong theoretical guarantees, BalanceKV exhibits empirically validated performance improvements over existing methods, both for attention approximation and end-to-end performance on various long context benchmarks.

Primary Area: Theory (e.g., control theory, learning theory, algorithmic game theory)

Submission Number: 21347