Beyond Residual Connections: Manifold-Constrained Hyper-Connections for Robust Speaker Representation Learning

Residual connections are fundamental to deep speaker recogni- tion models, such as ECAPA-TDNN and ResNet. However, standard identity mapping limits information flow to a sin- gle path, constraining representation capacity. We introduce Manifold-Constrained Hyper-Connections (mHC), reformulat- ing residual paths as a multi-stream evolution where informa- tion is mixed through a doubly stochastic matrix. By employing Sinkhorn-Knopp iterations, mHC ensures energy conservation by preserving signal intensity and feature mean, which stabi- lizes gradients and mitigates signal degradation in complex net- works. We evaluate mHC by replacing standard residual con- nections in backbones including ECAPA-TDNN, ResNet-34, Res2Net, and E-Res2Net. Extensive experiments on VoxCeleb1 demonstrate that mHC connections consistently enhance per- formance across all architectures, highlighting its effectiveness for robust speaker representation learning.