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mhc-algorithm
Implement mHC (Manifold-Constrained Hyper-Connections) for stabilizing deep network training. Use when implementing residual connection improvements with doubly stochastic matrices via Sinkhorn-Knopp algorithm. Based on DeepSeek's 2025 paper (arXiv:2512.24880).
tasks-extra/mhc-layer-impl/environment/skills/mhc-algorithm/SKILL.md
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# mHC: Manifold-Constrained Hyper-Connections
## Overview
mHC (Manifold-Constrained Hyper-Connections) stabilizes deep network training by constraining residual mixing matrices to be **doubly stochastic**. It provides:
- **Stable Training**: Lower gradient norm variance via doubly stochastic constraints
- **Multiple Streams**: Hyper-Connections with learnable mixing across residual streams
- **Sinkhorn Projection**: Log-space Sinkhorn-Knopp algorithm for doubly stochastic projection
- **GPT Integration**: Pattern for wrapping attention and MLP layers
Two components:
- **HyperConnections Module**: Core PyTorch module with H_res, H_pre, H_post matrices
- **Sinkhorn-Knopp**: Log-space projection to doubly stochastic manifold