doubly stochastic
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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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