Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention
Transformer self-attention can be interpreted as a gradient flow on the unit sphere, in which tokens evolve under softmax interaction potentials and tend to form clusters. While prior work has established clustering behavior for single-head attention, the multi-head setting remains less understood due to geometric interference between heads, which invalidates standard monotonicity arguments. In this work, we develop a theoretical framework for multi-head self-attention dynamics and resolve several open questions. We show that, under suitable conditions on the score matrices, a natural multi-head energy functional is non-decreasing along both flat and spherical dynamics. We identify the ke...
| Authors | Ayan Pendharkar |
|---|---|
| Primary category | cs.LG |
| Published | 5 May 2026 |
| Last updated at source | 8 May 2026 |
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