Streaming Attention Approximation via Discrepancy Theory

TL;DR

This paper introduces BalanceKV, a streaming algorithm for attention approximation in large language models that balances theoretical guarantees with empirical performance improvements for long-context token generation.

Contribution

The paper presents BalanceKV, a novel streaming algorithm based on geometric process and vector balancing theory, with proven lower bounds and practical advantages.

Findings

BalanceKV achieves strong theoretical approximation guarantees.

Empirical results show improved performance on long-context benchmarks.

BalanceKV outperforms existing attention approximation methods.

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.