Zhu et al.: learnable depth-and-width hyper-connections

What changed

Expanded residual streams into multiple hidden vectors and learned their depth and width mixing, with input-dependent connection matrices in the dynamic variant.

Scientific scope

Expanded residual streams into multiple hidden vectors and learned their depth and width mixing, with input-dependent connection matrices in the dynamic variant. Residual and normalization architectures are inherited. This is original unconstrained HC, not later doubly-stochastic mHC. Finite training improvements do not prove optimal routing or universal absence of vanishing gradients/representation collapse.

Evidence

The linked original sources describe the stated contribution and its evidence limits. WRS has not independently rerun the experiments or certified a proof. Residual and normalization architectures are inherited. This is original unconstrained HC, not later doubly-stochastic mHC. Finite training improvements do not prove optimal routing or universal absence of vanishing gradients/representation collapse.

Contributors

• Source-listed authors and technical contributors · SCIENCE: Source-listed authors or explicitly credited technical contributors for the cited versions. Family entries retain source-specific attribution; a combined list is not one original-paper byline or equal individual work. Names alone do not establish resolved identities.

• Hyper-Connections

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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