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arXiv:2610.08420v1 Announce Type: new Abstract: We establish a polynomial sample complexity separation between symmetry-aware and symmetry-agnostic feature learning. We study growing-rank multi-index...
arXiv:2606. 24418v1 Announce Type: new Abstract: Data augmentation is a simple and model-agnostic approach for exploiting known invariances in learning problems.
arXiv:2609.07031v1 Announce Type: new Abstract: Learning with group invariances is central to many scientific and geometric learning problems, yet its computational foundations remain poorly understo...
The paper introduces a statistical learning theory for size generalization in models that handle variable-size structured data such as sets and graphs. It proves an exponential separation in sample complexity: polynomial in-domain learning yields only logarithmic decay in size-generalization error, while an exponential source condition restores polynomial decay. These results provide dimension‑free scaling laws and optimal minimax bounds for transferring learning across input sizes.
arXiv:2606. 28573v1 Announce Type: new Abstract: Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions.
arXiv:2602. 02431v2 Announce Type: replace-cross Abstract: It is folklore that reusing training data more than once can improve the statistical efficiency of gradient-based learning.