One Pass Streaming Algorithm for Super Long Token Attention Approximation in Sublinear Space

• URL: http://arxiv.org/abs/2311.14652v2
• Date: Mon, 5 Feb 2024 18:30:30 GMT
• Title: One Pass Streaming Algorithm for Super Long Token Attention Approximation in Sublinear Space
• Authors: Raghav Addanki, Chenyang Li, Zhao Song, Chiwun Yang
• Abstract summary: Attention computation takes both the time complexity of $O(n2)$ and the space complexity of $O(n2)$ simultaneously. We introduce a new algorithm that only reads one pass of data in a streaming fashion. Notably, our algorithm exhibits exceptional memory-efficient performance with super-long tokens.
• Score: 11.735802740426294
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Attention computation takes both the time complexity of $O(n^2)$ and the space complexity of $O(n^2)$ simultaneously, which makes deploying Large Language Models (LLMs) in streaming applications that involve long contexts requiring substantial computational resources. In recent OpenAI DevDay (Nov 6, 2023), OpenAI released a new model that is able to support a 128K-long document, in our paper, we focus on the memory-efficient issue when context length $n$ is much greater than 128K ($n \gg 2^d$). Considering a single-layer self-attention with Query, Key, and Value matrices $Q, K, V \in \mathbb{R}^{n \times d}$, the polynomial method approximates the attention output $T \in \mathbb{R}^{n \times d}$. It accomplishes this by constructing $U_1, U_2 \in \mathbb{R}^{n \times t}$ to expedite attention ${\sf Attn}(Q, K, V)$ computation within $n^{1+o(1)}$ time executions. Despite this, computing the approximated attention matrix $U_1U_2^\top \in \mathbb{R}^{n \times n}$ still necessitates $O(n^2)$ space, leading to significant memory usage. In response to these challenges, we introduce a new algorithm that only reads one pass of the data in a streaming fashion. This method employs sublinear space $o(n)$ to store three sketch matrices, alleviating the need for exact $K, V$ storage. Notably, our algorithm exhibits exceptional memory-efficient performance with super-long tokens. As the token length $n$ increases, our error guarantee diminishes while the memory usage remains nearly constant. This unique attribute underscores the potential of our technique in efficiently handling LLMs in streaming applications.

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