name: mhc
description: Implements Manifold-Constrained Hyper-Connections (mHC) to solve residual connection issues using Doubly Stochastic Matrices.

mHC Skill

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

Contents

• Examples
  • Full JAX implementation of sinkhorn_knopp and mhc_layer_forward.
• Deep Theory
  • 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).

# 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)