Log-Linear Attention

• URL: http://arxiv.org/abs/2506.04761v1
• Date: Thu, 05 Jun 2025 08:44:51 GMT
• Title: Log-Linear Attention
• Authors: Han Guo, Songlin Yang, Tarushii Goel, Eric P. Xing, Tri Dao, Yoon Kim,
• Abstract summary: This paper develops log-linear attention, an attention mechanism that balances linear attention's efficiency and the expressiveness of softmax attention.<n>We show that with a particular growth function, log-linear attention admits a similarly matmul-rich parallel form whose compute cost is log-linear in sequence length.<n>Log-linear attention is a general framework and can be applied on top of existing linear attention variants.
• Score: 81.09631871212211
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The attention mechanism in Transformers is an important primitive for accurate and scalable sequence modeling. Its quadratic-compute and linear-memory complexity however remain significant bottlenecks. Linear attention and state-space models enable linear-time, constant-memory sequence modeling and can moreover be trained efficiently through matmul-rich parallelization across sequence length. However, at their core these models are still RNNs, and thus their use of a fixed-size hidden state to model the context is a fundamental limitation. This paper develops log-linear attention, an attention mechanism that balances linear attention's efficiency and the expressiveness of softmax attention. Log-linear attention replaces the fixed-size hidden state with a logarithmically growing set of hidden states. We show that with a particular growth function, log-linear attention admits a similarly matmul-rich parallel form whose compute cost is log-linear in sequence length. Log-linear attention is a general framework and can be applied on top of existing linear attention variants. As case studies, we instantiate log-linear variants of two recent architectures -- Mamba-2 and Gated DeltaNet -- and find they perform well compared to their linear-time variants.

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