arXiv:2608. 30417v2 Announce Type: replace Abstract: 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.
arXiv:2608.30417v1 Announce Type: new Abstract: We give a complete characterization of equivariant multi-head self-attention (MHSA): if an MHSA layer is equivariant to a symmetry group $G$, then $G$...
arXiv:2606. 27864v1 Announce Type: cross Abstract: Vision transformers have become a dominant architecture for visual recognition.
arXiv:2609.01129v1 Announce Type: new Abstract: We identify a recurrent algebraic regularity in Transformer attention: a sparse subset of effective OV operators $T=OV^\top$ nearly closes under compos...
arXiv:2609.01231v1 Announce Type: new Abstract: We prove that a multi-head scaled dot product attention can be viewed as a parameter identification strategy. The ratio of unidentified parameters to t...
arXiv:2409. 15600v3 Announce Type: replace Abstract: A representation of a molecule or material should be invariant to the symmetries of physics, unique, continuous, efficient and general.
arXiv:2606. 03003v1 Announce Type: cross Abstract: A latent world model built from an equivariant encoder $E$ and an equivariant predictor $f$ inherits a provable symmetry of its training loss: when the world's dynamics genuinely carries a group $G$ acting on latents by an orthogonal representation $\rho(g)$, the one-step prediction relMSE is exactly invariant across the whole group, so fitting the dynamics on a restricted slice of orientations mathematically determines it on the entire orbit (j\v{u} y\=i f\v{a}n s\=an).
arXiv:2207. 03116v4 Announce Type: replace Abstract: We introduce a general method for learning representations that are equivariant to symmetries of data.
arXiv:2606. 20547v1 Announce Type: new Abstract: We place the attention token on the group: a token is an element $g_i$ of a matrix Lie group $G$ -- a bare transformation, with no feature payload and no external action $\rho(g)$ carrying it.
Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields. Despite their remarkable capacity for representing geometric structures, ENNs suffer from degraded expressivity when processing symmetric inputs: the output representations are invariant to transformations that extend beyond the input's symmetries.
arXiv:2608. 12010v1 Announce Type: new Abstract: Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields.
The paper investigates how treating each entity in a graph or language model as having its own coordinate frame—viewed as a symmetry—constrains the form of attention mechanisms. It shows that with orthogonal transports, invariant attention scores depend only on norms and transported inner products, while equivariant messages lie in the span of the entity vectors and their transported counterparts. The authors demonstrate that standard attention corresponds to a flat shared frame, and that incorporating per‑entity frames allows relations to be represented as operators that compose via parallel transport, yielding empirical gains on synthetic relational tasks and natural language benchmarks.
arXiv:2410. 06665v4 Announce Type: replace-cross Abstract: This paper explores the characterization of equivariant linear layers for representations of permutations and related groups.