Sigmoid Self-Attention is Better than Softmax Self-Attention: A Mixture-of-Experts Perspective
- URL: http://arxiv.org/abs/2502.00281v1
- Date: Sat, 01 Feb 2025 02:36:14 GMT
- Title: Sigmoid Self-Attention is Better than Softmax Self-Attention: A Mixture-of-Experts Perspective
- Authors: Fanqi Yan, Huy Nguyen, Pedram Akbarian, Nhat Ho, Alessandro Rinaldo,
- Abstract summary: This paper theoretically demonstrates that sigmoid self-attention is more sample-efficient than its softmax counterpart.
We show that ''experts'' in sigmoid self-attention require significantly less data to achieve the same approximation error as those in softmax self-attention.
- Score: 69.72942835553228
- License:
- Abstract: At the core of the popular Transformer architecture is the self-attention mechanism, which dynamically assigns softmax weights to each input token so that the model can focus on the most salient information. However, the softmax structure slows down the attention computation due to its row-wise nature, and inherently introduces competition among tokens: as the weight assigned to one token increases, the weights of others decrease. This competitive dynamic may narrow the focus of self-attention to a limited set of features, potentially overlooking other informative characteristics. Recent experimental studies have shown that using the element-wise sigmoid function helps eliminate token competition and reduce the computational overhead. Despite these promising empirical results, a rigorous comparison between sigmoid and softmax self-attention mechanisms remains absent in the literature. This paper closes this gap by theoretically demonstrating that sigmoid self-attention is more sample-efficient than its softmax counterpart. Toward that goal, we illustrate that each row of the self-attention matrix can be represented as a mixture of experts. Our analysis shows that ''experts'' in sigmoid self-attention require significantly less data to achieve the same approximation error as those in softmax self-attention. We corroborate our theoretical findings through extensive experiments on both synthetic and real-world datasets.
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