# KromHC: Manifold-Constrained Hyper-Connections with Kronecker-Product Residual Matrices

arXiv: https://arxiv.org/abs/2601.21579 · HTML: https://mlsanity.com/paper/2601.21579/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 48 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models](https://mlsanity.com/paper/2304.06364/) (2023)
- [Muon is Scalable for LLM Training](https://mlsanity.com/paper/2502.16982/) (2025)
- [DataComp-LM: In search of the next generation of training sets for language models](https://mlsanity.com/paper/2406.11794/) (2024)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [DeepNet: Scaling Transformers to 1,000 Layers](https://mlsanity.com/paper/2203.00555/) (2022)
- [Training Very Deep Networks](https://mlsanity.com/paper/1507.06228/) (2015)
- [mHC: Manifold-Constrained Hyper-Connections](https://mlsanity.com/paper/2512.24880/) (2025)
- [Hyper-Connections](https://mlsanity.com/paper/2409.19606/) (2024)
- [Tensor Networks Meet Neural Networks: A Survey and Future Perspectives](https://mlsanity.com/paper/2302.09019/) (2023)
- [ResiDual: Transformer with Dual Residual Connections](https://mlsanity.com/paper/2304.14802/) (2023)
- [MUDDFormer: Breaking Residual Bottlenecks in Transformers via Multiway Dynamic Dense Connections](https://mlsanity.com/paper/2502.12170/) (2025)
- [LoTR: Low Tensor Rank Weight Adaptation](https://mlsanity.com/paper/2402.01376/) (2024)
- [The Defeat of the Winograd Schema Challenge](https://mlsanity.com/paper/2201.02387/) (2022)
- [Cross-Layer Retrospective Retrieving via Layer Attention](https://mlsanity.com/paper/2302.03985/) (2023)
- [Highway Transformer: Self-Gating Enhanced Self-Attentive Networks](https://mlsanity.com/paper/2004.08178/) (2020)
- [TensorGPT: Efficient Compression of Large Language Models based on Tensor-Train Decomposition](https://mlsanity.com/paper/2307.00526/) (2023)
- [mHC-lite: You Don't Need 20 Sinkhorn-Knopp Iterations](https://mlsanity.com/paper/2601.05732/) (2026)
- [TensorLLM: Tensorising Multi-Head Attention for Enhanced Reasoning and Compression in LLMs](https://mlsanity.com/paper/2501.15674/) (2025)
- [Residual Matrix Transformers: Scaling the Size of the Residual Stream](https://mlsanity.com/paper/2506.22696/) (2025)

## Built on by (most cited first, 11 of 11)

- [JPmHC Dynamical Isometry via Orthogonal Hyper-Connections](https://mlsanity.com/paper/2602.18308/) (2026)
- [Spectral-Sphere-Constrained Hyper-Connections](https://mlsanity.com/paper/2603.20896/) (2026)
- [go-mHC: Direct Parameterization of Manifold-Constrained Hyper-Connections via Generalized Orthostochastic Matrices](https://mlsanity.com/paper/2604.02309/) (2026)
- [Analyzing Stream Collapse in Hyper-Connections: From Diagnosis to Mitigation](https://mlsanity.com/paper/2606.03483/) (2026)
- [TBP-mHC: full expressivity for manifold-constrained hyper connections through transportation polytopes](https://mlsanity.com/paper/2605.21724/) (2026)
- [Tensorizing Engram: Sharing Latents Across N-Gram Embeddings is Beneficial in LLMs](https://mlsanity.com/paper/2606.08347/) (2026)
- [Manifold-Constrained Hyper-Connections for Parameter-Efficient Finetuning](https://mlsanity.com/paper/2607.18130/) (2026)
- [TEMPER: Tensorized Efficient Manifold-constrained Parameterization for Expressive Residual Routing](https://mlsanity.com/paper/2608.07851/) (2026)
- [oHC: Orthogonal Hyper-Connections on SO(4) via Quaternions](https://mlsanity.com/paper/2609.02672/) (2026)
- [CliffSearch: Structured Agentic Co-Evolution over Theory and Code for Scientific Algorithm Discovery](https://mlsanity.com/paper/2604.01210/) (2026)
- [The Birkhoff Geometry of Manifold-Constrained Hyper-Connections: Two Channels, Vertex Viscosity, and Sinkhorn as a Retraction](https://mlsanity.com/paper/2610.06653/) (2026)

## Abstract (arXiv)

The success of Hyper-Connections (HC) in neural networks (NN) has also highlighted issues related to training instability and restricted scalability. The Manifold-Constrained Hyper-Connections (mHC) mitigate these challenges by projecting the residual connection space onto a Birkhoff polytope, however, it faces two issues: 1) its iterative Sinkhorn-Knopp (SK) algorithm does not always yield exactly doubly stochastic residual matrices; 2) mHC incurs a prohibitive O(n3C) parameter complexity with n as the width of the residual stream and C as the feature dimension. The recently proposed mHC-lite reparametrizes the residual matrix via the Birkhoff-von-Neumann theorem to guarantee double stochasticity, but also faces a factorial explosion in its parameter complexity, O left( nC · n! right). To address both challenges, we propose KromHC, which uses the Kronecker products of smaller doubly stochastic matrices to parametrize the residual matrix in mHC. By enforcing manifold constraints across the factor residual matrices along each mode of the tensorized residual stream, KromHC guarantees exact double stochasticity of the residual matrices while reducing parameter complexity to only O(n2C). Experiments show that KromHC matches or even outperforms other state-of-the-art (SOTA) mHC variants, while requiring significantly fewer trainable parameters. The code is at https://github.com/wz1119/KromHC.