A geometric theory demonstrates phase transitions in neural networks, connecting learning to fault tolerance.
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.
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Rafael Velado (2026) studied this question.
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