# Mhc

> Implements Manifold-Constrained Hyper-Connections (mHC) using Doubly Stochastic Matrices to improve deep learning stability.

- Skill: `diegosouzapw/mhc` (Agent Skill, multi-file: 2 files)
- Install (CLI): `npx skillmds@latest add diegosouzapw/mhc`
- Raw SKILL.md: https://api.skillmd.com/api/skills/diegosouzapw/mhc/raw
- Safety review: PASS (external: skill-scanner PASS, skillspector PASS)
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: AI & ML, Coding & Dev Tools, Model Training & Fine-tuning
- Tags: Deep Learning, Doubly Stochastic Matrices, Jax, Residual Connections, Sinkhorn Knopp
- Author: diegosouzapw (https://skillmd.com/u/diegosouzapw)
- Updated: 2026-08-22
- Page: https://skillmd.com/skills/diegosouzapw/mhc

---

# mHC Skill

Manifold-Constrained Hyper-Connections (mHC) uses Doubly Stochastic Matrices to improve Deep Learning stability.

## Contents

- [Examples](examples.md)
    - Full JAX implementation of `sinkhorn_knopp` and `mhc_layer_forward`.
- [Deep Theory](reference.md)
    - Motivation, stability proofs, and scalability arguments.

## Usage

Use this skill when implementing Deep Transformers (1000+ layers) where standard residual connections fail (Gradient Vanishing, Representation Collapse).

```python
# Quick Ref: Sinkhorn-Knopp (See examples.md for full context)
def sinkhorn_knopp(log_matrix, n_iters=20):
    M = jnp.exp(log_matrix)
    def body(i, m):
        m /= m.sum(axis=1, keepdims=True)
        m /= m.sum(axis=0, keepdims=True)
        return m
    return jax.lax.fori_loop(0, n_iters, body, M)
```