mHC: Manifold-Constrained Hyper-Connections

TL;DR

This paper introduces mHC, a framework that constrains hyper-connections to a manifold to restore identity mapping, improve training stability, and enhance scalability in neural network architectures.

Contribution

mHC provides a novel manifold-constrained approach to hyper-connections, addressing stability and scalability issues while maintaining performance gains.

Findings

Effective training at scale demonstrated

Performance improvements over existing HC methods

Enhanced scalability and efficiency achieved

Abstract

Recently, studies exemplified by Hyper-Connections (HC) have extended the ubiquitous residual connection paradigm established over the past decade by expanding the residual stream width and diversifying connectivity patterns. While yielding substantial performance gains, this diversification fundamentally compromises the identity mapping property intrinsic to the residual connection, which causes severe training instability and restricted scalability, and additionally incurs notable memory access overhead. To address these challenges, we propose Manifold-Constrained Hyper-Connections (mHC), a general framework that projects the residual connection space of HC onto a specific manifold to restore the identity mapping property, while incorporating rigorous infrastructure optimization to ensure efficiency. Empirical experiments demonstrate that mHC is effective for training at scale, offering tangible performance improvements and superior scalability. We anticipate that mHC, as a flexible and practical extension of HC, will contribute to a deeper understanding of topological architecture design and suggest promising directions for the evolution of foundational models.