The E$\Delta$-MHC-Geo Transformer: Adaptive Geodesic Operations with Guaranteed Orthogonality

ArXi:2605.06729v1 Announce Type: cross We present the E$\Delta$-MHC-Geo Transformer, a novel architecture that unifies Manifold-Constrained Hyper-Connections (mHC), Deep Delta Learning (DDL), and the Cayley transform to obtain input-adaptive, unconditionally orthogonal residual connections. Unlike DDL, whose Householder operator is orthogonal only at $\beta \in \{0,2\}$, our Data-Dependent Cayley rotation $Q(x)=(I+(\beta/2)A(x))^{-1}(I-(\beta/2)A(x))$ preserves orthogonality for all $\beta$ and all inputs. To handle negation, an eigenvalue $-1$ case that Cayley provably excludes, we.