Inherent Trade-offs when Enforcing Correct Data Symmetries in Multi-head Self-attention
We give a complete characterization of equivariant multi-head self-attention (MHSA): if an MHSA layer is equivariant to a symmetry group $G$, then $G$ can only act by permuting head-clusters, with QK and OV matrices satisfying an equivariance constraint tied to the group action. As a consequence, we prove that any fixed MHSA architecture that achieves exact equivariance by polynomially parameterizing unconstrained MHSA parameters inevitably leads to expressivity loss within the class of equivariant maps: the equivariance locus of unconstrained MHSA forms a union of extremely many Zariski-irreducible components in a reduced parameter space, and any single architecture covers at most one. F...
| Authors | Tīkun Ông, Georg Bökman |
|---|---|
| Primary category | cs.LG |
| Published | 31 August 2026 |
| Last updated at source | 15 October 2026 |
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