Spectral-Sphere-Constrained Hyper-Connections

arXiv:2603.20896 · cs.LG, cs.AI · Submitted 2026-03-21 · Read on arXiv

cs.LG, cs.AI

Submitted: 2026-03-21

Updated: 2026-09-25

Code: https://github.com/karpathy/nanoGPT

Project page: http://skylion007.github.io/OpenWebTextCorpus

Terminology

• Spectral-Sphere-Constrained Hyper-Connections — 10× in this paper
• Manifold-Constrained Hyper-Connections — 8× in this paper
• Perplexity — 6× in this paper · explained in 3 episodes
• Cosine Similarity — 5× in this paper · explained in 3 episodes
• Core — 4× in this paper · explained in 2 episodes
• Adam — 3× in this paper · explained in 2 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Benchmark — 2× in this paper · explained in 2 episodes
• Decoupling — 2× in this paper · explained in 2 episodes
• Transformer — 2× in this paper · explained in 2 episodes
• AdamW Optimizer — 1× in this paper · explained in 1 episode
• Homogeneity — 1× in this paper · explained in 2 episodes
• Representation Learning — 1× in this paper · explained in 2 episodes
• Singular Value Decomposition (SVD) — 1× in this paper · explained in 2 episodes
• Structural Constraints — 1× in this paper · explained in 2 episodes
• Transfer Learning — 1× in this paper · explained in 10 episodes
• Transformer Models — 1× in this paper · explained in 2 episodes
• Zero-Shot Generalization — 1× in this paper · explained in 5 episodes

Sources

• mHC: Manifold-Constrained Hyper-Connections
• mHC-lite: You Don't Need 20 Sinkhorn-Knopp Iterations
• DeepSeek-V3 Technical Report
• LLaMA: Open and Efficient Foundation Language Models
• Hyper-Connections
• Frac-Connections: Fractional Extension of Hyper-Connections
• Layer by Layer: Uncovering Hidden Representations in Language Models
• The Homogeneity Trap: Spectral Collapse in Doubly-Stochastic Deep Networks
• The RefinedWeb Dataset for Falcon LLM: Outperforming Curated Corpora with Web Data, and Web Data Only

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