This episode explores Manifold-Constrained Hyper-Connections (mHC), a framework designed to solve the training instability and memory overhead issues found in existing Hyper-Connection architectures. We discuss how mHC uses the Sinkhorn-Knopp algorithm to project residual connections onto a doubly stochastic manifold, effectively restoring the "identity mapping" property essential for stable signal propagation. Finally, we examine the infrastructure-level optimizations—such as kernel fusion and selective recomputing—that allow mHC to achieve superior scalability and performance in large-scale foundation models.

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