Delays in generalization match delayed changes in representational geometry

Xingyu Zheng, Kyle Daruwalla, Ari S Benjamin, David Klindt
Proceedings of UniReps: the Second Edition of the Workshop on Unifying Representations in Neural Models, PMLR 285:324-334, 2024.

Abstract

Delayed generalization, also known as "grokking", has emerged as a well-replicated phenomenon in overparameterized neural networks. Recent theoretical works associated grokking with the transition from lazy to rich learning regime, measured as the change in the Neural Tangent Kernel (NTK) from its initial state. Here, we present an empirical study on image classification tasks. Surprisingly, we demonstrate that the NTK deviates from its initial state significantly before the onset of grokking, i.e., before test performance increases, suggesting that rich learning does occur before generalization. To explain this difference, we instead look at the representational geometry of the network, and find that grokking coincides in time with a rapid increase in manifold capacity and improved effective geometry metrics. Notably, this sharp transition is absent when generalization is not delayed. Our findings on real data show that lazy and rich training regimes can become decoupled from sudden generalization. In contrast, changes in representational geometry remain tightly linked and may therefore better explain grokking dynamics.

Cite this Paper

BibTeX
@InProceedings{pmlr-v285-zheng24a, title = {Delays in generalization match delayed changes in representational geometry}, author = {Zheng, Xingyu and Daruwalla, Kyle and Benjamin, Ari S and Klindt, David}, booktitle = {Proceedings of UniReps: the Second Edition of the Workshop on Unifying Representations in Neural Models}, pages = {324--334}, year = {2024}, editor = {Fumero, Marco and Domine, Clementine and Lähner, Zorah and Crisostomi, Donato and Moschella, Luca and Stachenfeld, Kimberly}, volume = {285}, series = {Proceedings of Machine Learning Research}, month = {14 Dec}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v285/main/assets/zheng24a/zheng24a.pdf}, url = {https://proceedings.mlr.press/v285/zheng24a.html}, abstract = {Delayed generalization, also known as "grokking", has emerged as a well-replicated phenomenon in overparameterized neural networks. Recent theoretical works associated grokking with the transition from lazy to rich learning regime, measured as the change in the Neural Tangent Kernel (NTK) from its initial state. Here, we present an empirical study on image classification tasks. Surprisingly, we demonstrate that the NTK deviates from its initial state significantly before the onset of grokking, i.e., before test performance increases, suggesting that rich learning does occur before generalization. To explain this difference, we instead look at the representational geometry of the network, and find that grokking coincides in time with a rapid increase in manifold capacity and improved effective geometry metrics. Notably, this sharp transition is absent when generalization is not delayed. Our findings on real data show that lazy and rich training regimes can become decoupled from sudden generalization. In contrast, changes in representational geometry remain tightly linked and may therefore better explain grokking dynamics.} }
Endnote
%0 Conference Paper %T Delays in generalization match delayed changes in representational geometry %A Xingyu Zheng %A Kyle Daruwalla %A Ari S Benjamin %A David Klindt %B Proceedings of UniReps: the Second Edition of the Workshop on Unifying Representations in Neural Models %C Proceedings of Machine Learning Research %D 2024 %E Marco Fumero %E Clementine Domine %E Zorah Lähner %E Donato Crisostomi %E Luca Moschella %E Kimberly Stachenfeld %F pmlr-v285-zheng24a %I PMLR %P 324--334 %U https://proceedings.mlr.press/v285/zheng24a.html %V 285 %X Delayed generalization, also known as "grokking", has emerged as a well-replicated phenomenon in overparameterized neural networks. Recent theoretical works associated grokking with the transition from lazy to rich learning regime, measured as the change in the Neural Tangent Kernel (NTK) from its initial state. Here, we present an empirical study on image classification tasks. Surprisingly, we demonstrate that the NTK deviates from its initial state significantly before the onset of grokking, i.e., before test performance increases, suggesting that rich learning does occur before generalization. To explain this difference, we instead look at the representational geometry of the network, and find that grokking coincides in time with a rapid increase in manifold capacity and improved effective geometry metrics. Notably, this sharp transition is absent when generalization is not delayed. Our findings on real data show that lazy and rich training regimes can become decoupled from sudden generalization. In contrast, changes in representational geometry remain tightly linked and may therefore better explain grokking dynamics.
APA
Zheng, X., Daruwalla, K., Benjamin, A.S. & Klindt, D.. (2024). Delays in generalization match delayed changes in representational geometry. Proceedings of UniReps: the Second Edition of the Workshop on Unifying Representations in Neural Models, in Proceedings of Machine Learning Research 285:324-334 Available from https://proceedings.mlr.press/v285/zheng24a.html.

Related Material