[2604.00316] Breaking Data Symmetry is Needed For Generalization in Feature Learning Kernels

Statistics > Machine Learning arXiv:2604.00316 (stat) [Submitted on 31 Mar 2026] Title:Breaking Data Symmetry is Needed For Generalization in Feature Learning Kernels Authors:Marcel Tomàs Bernal, Neil Rohit Mallinar, Mikhail Belkin View a PDF of the paper titled Breaking Data Symmetry is Needed For Generalization in Feature Learning Kernels, by Marcel Tom\`as Bernal and 2 other authors View PDF HTML (experimental) Abstract:Grokking occurs when a model achieves high training accuracy but generalization to unseen test points happens long after that. This phenomenon was initially observed on a class of algebraic problems, such as learning modular arithmetic (Power et al., 2022). We study grokking on algebraic tasks in a class of feature learning kernels via the Recursive Feature Machine (RFM) algorithm (Radhakrishnan et al., 2024), which iteratively updates feature matrices through the Average Gradient Outer Product (AGOP) of an estimator in order to learn task-relevant features. Our main experimental finding is that generalization occurs only when a certain symmetry in the training set is broken. Furthermore, we empirically show that RFM generalizes by recovering the underlying invariance group action inherent in the data. We find that the learned feature matrices encode specific elements of the invariance group, explaining the dependence of generalization on symmetry. Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG) Cite as: arXiv:2604.00316 [stat.ML]   (or ar...