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.
arXiv:2604. 00316v2 Announce Type: replace-cross Abstract: Grokking occurs when a model achieves high training accuracy but generalization to unseen test points happens long after that.
arXiv:2609. 17926v1 Announce Type: new Abstract: The standard geometric derivation of neural scaling exponents takes the intrinsic dimension of a data manifold as its input.
The paper investigates how locality and weight sharing individually influence learning in convolutional neural networks using a teacher‑student framework. By comparing convolutional and locally connected students trained with online stochastic gradient descent, the authors derive exact dynamics in the large‑feature‑dimension limit. Key findings include that for uncorrelated inputs the convolutional student learns P‑times faster, locality reduces sample complexity, and spatial correlations diminish the advantage of weight sharing, leading to a dynamic trade‑off between the two architectures over time.
arXiv:2607. 03108v1 Announce Type: new Abstract: Post-hoc analysis of trained neural network weights often seeks to recover geometric structure directly from the parameters.
The paper investigates self‑supervised pre‑training that uses multiple data augmentations of the same unlabeled sample. It shows that pooling these dependent augmentations together yields statistical estimation error bounds that are never worse than, and sometimes better than, partitioning the data into independent subsets. The analysis explains why using many augmentations is practically advantageous, especially when their correlations have mild effects or reduce estimation variance.
arXiv:2606. 15219v1 Announce Type: new Abstract: In this work, we tackle the following question: Can neural networks trained with gradient-based methods achieve the optimal computational-statistical tradeoff in learning Gaussian single-index models?