Grokking Beyond the Euclidean Norm of Model Parameters
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| Format: | Preprint |
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2025
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| author | Notsawo, Pascal Jr Tikeng Dumas, Guillaume Rabusseau, Guillaume |
| author_facet | Notsawo, Pascal Jr Tikeng Dumas, Guillaume Rabusseau, Guillaume |
| contents | Grokking refers to a delayed generalization following overfitting when optimizing artificial neural networks with gradient-based methods. In this work, we demonstrate that grokking can be induced by regularization, either explicit or implicit. More precisely, we show that when there exists a model with a property $P$ (e.g., sparse or low-rank weights) that generalizes on the problem of interest, gradient descent with a small but non-zero regularization of $P$ (e.g., $\ell_1$ or nuclear norm regularization) results in grokking. This extends previous work showing that small non-zero weight decay induces grokking. Moreover, our analysis shows that over-parameterization by adding depth makes it possible to grok or ungrok without explicitly using regularization, which is impossible in shallow cases. We further show that the $\ell_2$ norm is not a reliable proxy for generalization when the model is regularized toward a different property $P$, as the $\ell_2$ norm grows in many cases where no weight decay is used, but the model generalizes anyway. We also show that grokking can be amplified solely through data selection, with any other hyperparameter fixed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_05718 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Grokking Beyond the Euclidean Norm of Model Parameters Notsawo, Pascal Jr Tikeng Dumas, Guillaume Rabusseau, Guillaume Machine Learning Artificial Intelligence I.2.6 Grokking refers to a delayed generalization following overfitting when optimizing artificial neural networks with gradient-based methods. In this work, we demonstrate that grokking can be induced by regularization, either explicit or implicit. More precisely, we show that when there exists a model with a property $P$ (e.g., sparse or low-rank weights) that generalizes on the problem of interest, gradient descent with a small but non-zero regularization of $P$ (e.g., $\ell_1$ or nuclear norm regularization) results in grokking. This extends previous work showing that small non-zero weight decay induces grokking. Moreover, our analysis shows that over-parameterization by adding depth makes it possible to grok or ungrok without explicitly using regularization, which is impossible in shallow cases. We further show that the $\ell_2$ norm is not a reliable proxy for generalization when the model is regularized toward a different property $P$, as the $\ell_2$ norm grows in many cases where no weight decay is used, but the model generalizes anyway. We also show that grokking can be amplified solely through data selection, with any other hyperparameter fixed. |
| title | Grokking Beyond the Euclidean Norm of Model Parameters |
| topic | Machine Learning Artificial Intelligence I.2.6 |
| url | https://arxiv.org/abs/2506.05718 |