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Algebraic Representability as the Limiting Regime of Grokking: An Exactly Solvable Model with Holomorphic Activations

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Neural networks trained on modular arithmetic exhibit grokking, a delayed transition from memorisation to generalisation known to depend on model capacity: too little and the network memorises slowly or not at all, too much and it generalises almost immediately. What happens at the extreme of this spectrum, when the architecture's expressible function class collapses to a finite-dimensional algebraic variety?

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arXiv Machine Learning
Jul 16

Algebraic Representability as the Limiting Regime of Grokking: An Exactly Solvable Model with Holomorphic Activations

arXiv:2607. 13749v1 Announce Type: new Abstract: Neural networks trained on modular arithmetic exhibit grokking, a delayed transition from memorisation to generalisation known to depend on model capacity: too little and the network memorises slowly or not at all, too much and it generalises almost immediately.

By Chon-Fai Kam, Xavier Cadet, Miloud Bessafi, Frederic Cadet
arXiv Machine Learning
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Beyond Neural Collapse: Task-Intrinsic Geometry Governs Neural Representations in Modular Arithmetic

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