TBP-mHC: full expressivity for manifold-constrained hyper connections through transportation polytopes
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Computer Science > Machine Learning
Title:TBP-mHC: full expressivity for manifold-constrained hyper connections through transportation polytopes
Abstract:Hyper-Connections (HC) improve residual networks by introducing learnable mixing across multiple residual streams, but unconstrained mixing leads to training instability. Manifold-Constrained Hyper-Connections (mHC) address this by enforcing approximate double stochasticity via Sinkhorn normalization, while mHC-lite ensures exact constraints through convex combinations of permutation matrices at the cost of factorial complexity. KromHC reduces this cost using Kronecker-product parameterizations, but restricts the mixing matrices to a structured submanifold of the Birkhoff polytope .
We propose Transportation Birkhoff Polytope (TBP) parameterizations and their Recursive variants (RTBP), which construct exactly doubly stochastic mixing matrices with $(n-1)^2$ degrees of freedom. Our approach avoids iterative normalization and combinatorial explosion while preserving full expressivity of the Birkhoff polytope. Empirical results on language model pre-training' demonstrate competitive performance with improved stability and scalability.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2605.21724 [cs.LG] |
| (or arXiv:2605.21724v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.21724
arXiv-issued DOI via DataCite (pending registration)
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