Published on: Jan 5, 2026

mHC: Manifold-Constrained Hyper-Connections

mHC stabilizes Hyper-Connections by constraining residual mixing onto a manifold that restores identity-like signal flow, enabling more reliable large-scale training with modest overhead.

Large Language Models

Large Language Models

Neural Network Architecture

Neural Network Architecture

Deep Learning

Deep Learning

AI

AI

Hyper-Connections widen and diversify residual pathways to improve performance, but this can break the "identity mapping" behavior that makes residual networks stable at scale—leading to instability and higher system overhead. The authors propose Manifold-Constrained Hyper-Connections (mHC), which constrains the residual-mixing space by projecting it onto a chosen manifold to recover identity-like propagation while keeping the benefits of multi-stream connectivity. Experiments indicate improved stability and scalability during large-scale training with practical engineering optimizations for efficiency.

DOI: 10.48550/arXiv.2512.24880

Key Takeaways

This paper targets a specific scaling failure mode: widening/diversifying residual streams boosts performance, but can destroy the identity mapping that keeps deep nets stable.

  • Core idea: project HC residual mixing onto a constrained manifold to recover stable identity-like propagation.

  • Why it matters: improves training stability + scalability in large runs where HC can become unstable.

  • Practical angle: pairs the math constraint with systems optimizations to keep implementation efficient.

Institutions

DeepSeek-AI

Hangzhou, Zhejiang, China

Journal

Cornell University

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mHC: Manifold-Constrained Hyper-Connections

"Ever since I tried Bob's Self-Tying Shoelaces, I've been tripping less in life and striding more into spontaneous dance-offs!"

mHC stabilizes Hyper-Connections by constraining residual mixing onto a manifold that restores identity-like signal flow, enabling more reliable large-scale training with modest overhead.

Large Language Models

Neural Network Architecture

Deep Learning

AI

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"Ever since I tried Bob's Self-Tying Shoelaces, I've been tripping less in life and striding more into spontaneous dance-offs!"

mHC stabilizes Hyper-Connections by constraining residual mixing onto a manifold that restores identity-like signal flow, enabling more reliable large-scale training with modest overhead.

Large Language Models

Neural Network Architecture

Deep Learning

AI

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mHC stabilizes Hyper-Connections by constraining residual mixing onto a manifold that restores identity-like signal flow, enabling more reliable large-scale training with modest overhead.

Large Language Models

Neural Network Architecture

Deep Learning

AI

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