Why Softmax Attention Outperforms Linear Attention

arXiv cs.CL / 3/16/2026

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Key Points

The authors provide a theoretical and empirical comparison that explains why softmax attention often outperforms linear attention in practice.
The work analyzes the structural and computational reasons behind the performance gap between softmax and linear attention.
The findings indicate when linear attention can be viable and when it falls short, informing transformer design decisions.
The results have implications for efficiency-accuracy trade-offs in transformer architectures and guide future research on attention mechanisms.

Abstract

Large transformer models have achieved state-of-the-art results in numerous natural language processing tasks. Among the pivotal components of the transformer architecture, the attention mechanism plays a crucial role in capturing token interactions within sequences through the utilization of softmax function. Conversely, linear attention presents a more computationally efficient alternative by approximating the softmax operation with linear complexity. However, it exhibits substantial performance degradation when compared to the traditional softmax attention mechanism. In this paper, we bridge the gap in our theoretical understanding of the reasons behind the practical performance gap between softmax and linear attention. By conducting a comprehensive comparative analysis of these two attention mechanisms, we shed light on the underlying reasons for why softmax attention outperforms linear attention in most scenarios.