Why Grok Groks: The 4/7 Threshold - A Geometric Theory of Delayed Generalization in Neural Networks
Abstract
A geometric theory explaining grokking as a phase transition at Φ* = 4/7 ≈ 0.571. Validated on NVIDIA H100 with 10/10 seeds achieving perfect generalization (mean grok step 6690 ± 1273). Connects neural network learning to Byzantine fault tolerance and the Velado algebra.
Fields of Study & Subjects
Neural Networks and Applications
Stochastic Gradient Optimization Techniques
Domain Adaptation and Few-Shot Learning
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 15 January 2026
- Language
- EN
- Document type
- Preprint