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This paper theoretically demonstrates that two-layer neural networks trained on group composition tasks learn spectral representations, with neurons converging to irreducible representations and achieving rotational rank-one alignment, providing a representation-theoretic account of feature learning.
This paper provides a theoretical analysis of how neural networks learn structured representations during group composition tasks, proving that training dynamics drive neurons to converge to irreducible group representations with exponential convergence rates. The work establishes a representation-theoretic account of feature learning and characterizes a low-rank compression phenomenon for matrix-valued group representations.
This exploratory study empirically measures the symmetry–data exchange rate predicted by equivariance theory on controlled C_n-symmetric tasks, finding that wrong-group constraints are actively harmful, augmentation with test-time orbit averaging matches equivariant models exactly, and the empirical exchange rate is broadly consistent with theory but statistically inconclusive. The authors emphasize the study's exploratory nature and call for registered replications.
This paper introduces a theoretical framework to analyze the generalization error of canonization methods for symmetric data, proving that Hilbert curve serialization offers polynomial growth in covering number compared to exponential growth in lexicographical sorting.