The paper introduces Orthogonal Hyper-Connections (oHC), a new approach that replaces the single residual stream of a Transformer with multiple parallel streams mixed by a rotation matrix from the group SO(n). By constraining the mixing matrix to SO(n) and parameterizing it with unit quaternions for four streams, oHC prevents both amplification and attenuation of residuals, maintaining training stability and preserving stream diversity. Experiments show that oHC outperforms the single-stream baseline, manifold-constrained Hyper-Connections, and identity-fixed Hyper-Connections across a wide range of downstream tasks.
arXiv:2601. 21579v2 Announce Type: replace-cross Abstract: The success of Hyper-Connections (HC) in neural networks (NN) has also highlighted issues related to training instability and restricted scalability.
By Wuyang Zhou, Yuxuan Gu, Giorgos Iacovides, Danilo Mandic
The paper introduces Spectral‑Sphere‑Constrained Hyper‑Connections (s²HC), a new method for controlling the residual matrices used in Hyper‑Connections (HC). Unlike previous doubly stochastic constraints that caused identity degeneration, expressivity bottlenecks, and parameterization inefficiencies, s²HC confines these matrices to a spectral norm sphere, restoring flexibility over subdominant spectra and eliminating unstable Sinkhorn‑Knopp iterations. This approach preserves training stability while allowing expressive, non‑degenerate residual matrices.
By Zhaoyi Liu, Haichuan Zhang, Ang Li
arXiv:2601. 02451v2 Announce Type: replace-cross Abstract: Graph Neural Networks (GNNs) suffer from over-smoothing in deep architectures and expressiveness bounded by the 1-Weisfeiler-Leman (1-WL) test.
By Subhankar Mishra
arXiv:2607. 14530v1 Announce Type: new Abstract: Hyper-Connections (HC) expand the residual stream of Transformers into $N$ parallel streams, providing a form of memory scaling beyond model width and depth.
By Xiangdong Zhang, Xiaohan Qin, Sunan Zou, Tuo Dai, Xiaoming Shi, Huaijin Wu, Yebin Yang, Zhuo Xia, Shaofeng Zhang, Lin Yao, Yuliang Liu, Yu Cheng, Junchi Yan
arXiv:2606. 26538v1 Announce Type: cross Abstract: Deep Transformers are composed of uniformly stacked residual blocks, yet their deepest layers often add little value.
By Huzama Ahmad, Cao Viet Hai Nam, Se-Young Yun