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:2609. 02672v1 Announce Type: cross Abstract: Hyper-Connections (HC) replace the single residual stream of a Transformer with $n$ parallel ones, mixing them at every layer with a learned $n \times n$ residual matrix.
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.
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.
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.
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.
arXiv:2608. 07851v1 Announce Type: new Abstract: Residual connections rely on a static residual pathway, and are essential for training deep neural networks.
arXiv:2606. 26538v1 Announce Type: cross Abstract: Deep Transformers are composed of uniformly stacked residual blocks, yet their deepest layers often add little value.
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...
We investigate how each component of the Transformer feedforward block architecture design determines how much rank survives across depth at initialization. We reinterpret skip connections and normalization, long understood as controlling magnitude, as mechanisms for preserving gradient rank across depth, since the very matrix multiplications and nonlinear activations that make the network expressive also reduce the rank.
arXiv:2606. 07574v1 Announce Type: cross Abstract: Manifold-constrained hyper-connections (mHCs) have recently been proposed as a principled extension of hyper-connections, where the residual mixing matrices are constrained to be doubly stochastic via projection onto the Birkhoff polytope.
arXiv:2607. 14018v1 Announce Type: cross Abstract: We investigate how each component of the Transformer feedforward block architecture design determines how much rank survives across depth at initialization.
The paper investigates how the four‑stream manifold‑constrained hyper‑connection (mHC) residual pathway in DeepSeek‑V4‑Flash is actually used. It finds that read/write routing is concentrated, typically involving only two streams per block, and that the dominant stream shifts across layers while representations stay directionally distinct. Residual mixing is modest, mainly in early layers, and late mixing contributes little to performance, whereas early mixing is crucial for perplexity and task scores.