Grokking as a First Order Phase Transition in Two Layer Networks

Fuente: arXiv
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Main Authors: Rubin, Noa, Seroussi, Inbar, Ringel, Zohar
Format: Preprint
Published: 2023
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author Rubin, Noa
Seroussi, Inbar
Ringel, Zohar
author_facet Rubin, Noa
Seroussi, Inbar
Ringel, Zohar
contents A key property of deep neural networks (DNNs) is their ability to learn new features during training. This intriguing aspect of deep learning stands out most clearly in recently reported Grokking phenomena. While mainly reflected as a sudden increase in test accuracy, Grokking is also believed to be a beyond lazy-learning/Gaussian Process (GP) phenomenon involving feature learning. Here we apply a recent development in the theory of feature learning, the adaptive kernel approach, to two teacher-student models with cubic-polynomial and modular addition teachers. We provide analytical predictions on feature learning and Grokking properties of these models and demonstrate a mapping between Grokking and the theory of phase transitions. We show that after Grokking, the state of the DNN is analogous to the mixed phase following a first-order phase transition. In this mixed phase, the DNN generates useful internal representations of the teacher that are sharply distinct from those before the transition.
format Preprint
id arxiv_https___arxiv_org_abs_2310_03789
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Grokking as a First Order Phase Transition in Two Layer Networks
Rubin, Noa
Seroussi, Inbar
Ringel, Zohar
Machine Learning
Disordered Systems and Neural Networks
A key property of deep neural networks (DNNs) is their ability to learn new features during training. This intriguing aspect of deep learning stands out most clearly in recently reported Grokking phenomena. While mainly reflected as a sudden increase in test accuracy, Grokking is also believed to be a beyond lazy-learning/Gaussian Process (GP) phenomenon involving feature learning. Here we apply a recent development in the theory of feature learning, the adaptive kernel approach, to two teacher-student models with cubic-polynomial and modular addition teachers. We provide analytical predictions on feature learning and Grokking properties of these models and demonstrate a mapping between Grokking and the theory of phase transitions. We show that after Grokking, the state of the DNN is analogous to the mixed phase following a first-order phase transition. In this mixed phase, the DNN generates useful internal representations of the teacher that are sharply distinct from those before the transition.
title Grokking as a First Order Phase Transition in Two Layer Networks
topic Machine Learning
Disordered Systems and Neural Networks
url https://arxiv.org/abs/2310.03789