mHC
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Visualizing DeepSeek’s mHC Training Fix
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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.
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Interactive Visualization of DeepSeek’s mHC Stability
Read Full Article: Interactive Visualization of DeepSeek’s mHC Stability![[P] Interactive visualization of DeepSeek's mHC - why doubly stochastic constraints fix Hyper-Connection instability](https://www.tweakedgeek.com/wp-content/uploads/2026/01/featured-article-8316-300x171.png)
An interactive demo has been created to explore DeepSeek's mHC paper, addressing the instability in Hyper-Connections caused by the multiplication of learned matrices across multiple layers. This instability results in exponential amplification, reaching values as high as 10^16. The solution involves projecting these matrices onto a doubly stochastic manifold using the Sinkhorn-Knopp algorithm, which ensures that the composite mapping remains bounded, regardless of depth. Surprisingly, just one iteration of the Sinkhorn process is sufficient to stabilize the gain from 10^16 to approximately 1. This matters because it offers a practical method to enhance the stability and performance of deep learning models that utilize Hyper-Connections.
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DeepSeek’s mHC: A New Era in AI Architecture
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Since the introduction of ResNet in 2015, the Residual Connection has been a fundamental component in deep learning, providing a solution to the vanishing gradient problem. However, its rigid 1:1 input-to-computation ratio limits the model's ability to dynamically balance past and new information. DeepSeek's innovation with Manifold-Constrained Hyper-Connections (mHC) addresses this by allowing models to learn connection weights, offering faster convergence and improved performance. By constraining these weights to be "Double Stochastic," mHC ensures stability and prevents exploding gradients, outperforming traditional methods and reducing training time impact. This advancement challenges long-held assumptions in AI architecture, promoting open-source collaboration for broader technological progress.