A Statistical Theory of Gated Attention through the Lens of Hierarchical Mixture of Experts

• URL: http://arxiv.org/abs/2602.01468v1
• Date: Sun, 01 Feb 2026 22:22:13 GMT
• Title: A Statistical Theory of Gated Attention through the Lens of Hierarchical Mixture of Experts
• Authors: Viet Nguyen, Tuan Minh Pham, Thinh Cao, Tan Dinh, Huy Nguyen, Nhat Ho, Alessandro Rinaldo,
• Abstract summary: Gated attention has been empirically demonstrated to increase the expressiveness of low-rank mapping in standard attention.<n>We show that each entry in a gated attention matrix or a multi-head self-attention matrix can be written as a hierarchical mixture of experts.
• Score: 80.98474052840929
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Self-attention has greatly contributed to the success of the widely used Transformer architecture by enabling learning from data with long-range dependencies. In an effort to improve performance, a gated attention model that leverages a gating mechanism within the multi-head self-attention has recently been proposed as a promising alternative. Gated attention has been empirically demonstrated to increase the expressiveness of low-rank mapping in standard attention and even to eliminate the attention sink phenomenon. Despite its efficacy, a clear theoretical understanding of gated attention's benefits remains lacking in the literature. To close this gap, we rigorously show that each entry in a gated attention matrix or a multi-head self-attention matrix can be written as a hierarchical mixture of experts. By recasting learning as an expert estimation problem, we demonstrate that gated attention is more sample-efficient than multi-head self-attention. In particular, while the former needs only a polynomial number of data points to estimate an expert, the latter requires exponentially many data points to achieve the same estimation error. Furthermore, our analysis also provides a theoretical justification for why gated attention yields higher performance when a gate is placed at the output of the scaled dot product attention or the value map rather than at other positions in the multi-head self-attention architecture.

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