kNN Attention Demystified: A Theoretical Exploration for Scalable Transformers
Keywords: efficient transformers, self-attention mechanism, sublinear algorithms, sampling, k-nearest neighbors
TL;DR: This paper proposes a theoretical framework for kNN attention and develops novel algorithms for sub-quadratic attention gradient estimation in Transformers.
Abstract: Despite their power, Transformers face challenges with long sequences due to the quadratic complexity of self-attention. To address this limitation, methods like $k$-Nearest-Neighbor ($k$NN) attention have been introduced [Roy et al., 2017], enabling each token to attend to only its $k$ closest tokens. While $k$NN attention has shown empirical success in making Transformers more efficient, its exact approximation guarantees have not been theoretically analyzed. In this work, we establish a theoretical framework for $k$NN attention, reformulating self-attention as expectations over softmax distributions and leveraging lazy Gumbel sampling [Mussmann et al., 2017] with $k$NN indices for efficient approximation. Building on this framework, we also propose novel sub-quadratic algorithms that approximate self-attention gradients by leveraging efficient sampling techniques, such as Markov Chain-based estimation. Finally, we demonstrate the practical effectiveness of these algorithms through empirical experiments, showcasing their benefits in both training and inference.
Primary Area: foundation or frontier models, including LLMs
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Submission Number: 932
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