DeepSeek's recent paper introduces Manifold-Constrained Hyper-Connections (mHC) to address training instability in deep learning models with many layers. When stacking over 60 layers of learned mixing matrices, small amplifications can compound, leading to explosive growth in training gains. By projecting these matrices onto a "doubly stochastic" manifold using the Sinkhorn-Knopp algorithm, gains remain bounded regardless of depth, with just one iteration significantly reducing gain from 1016 to approximately 1. An interactive demo and PyTorch implementation are available for experimentation, illustrating how this approach effectively stabilizes training. This matters because it offers a solution to a critical challenge in scaling deep learning models safely and efficiently.
