Gating Enables Curvature: A Geometric Expressivity Gap in Attention
Multiplicative gating is widely used in neural architectures and has recently been applied to attention layers to improve performance and training stability in large language models. Despite the success of gated attention, the mathematical implications of gated attention mechanisms remain poorly understood. We study attention through the geometry of its representations by modeling outputs as mean parameters of Gaussian distributions and analyzing the induced Fisher--Rao geometry. We show that ungated attention operator is restricted to intrinsically flat statistical manifolds due to its affine structure, while multiplicative gating enables non-flat geometries, including positively curved ...
| Authors | Satwik Bathula, Anand A. Joshi |
|---|---|
| Primary category | cs.LG |
| Published | 16 April 2026 |
| Last updated at source | 16 April 2026 |
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