Why Grok Groks: The 4/7 Threshold - A Geometric Theory of Delayed Generalization in Neural Networks

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.

Keywords

Velado algebra, grokking, Fisher-Rao geometry, memorization, deep learning, Byzantine consensus, neural networks, generalization, phase transitions

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