arXiv:2606. 24418v1 Announce Type: new Abstract: Data augmentation is a simple and model-agnostic approach for exploiting known invariances in learning problems.
arXiv:2609.08133v1 Announce Type: cross Abstract: In nonconvex optimization problems arising in geometric machine learning, data augmentation is commonly used to promote invariance by averaging empir...
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 investigates sparse data augmentation for nonconvex optimization in geometric machine learning. It shows that using a small, fixed sample of transformations—obtained before optimization—allows gradient descent to achieve an ε‑stationary point of the fully augmented objective with ≤ O((log|G|+log(1/δ))/ε²) transformation queries. This is more efficient than both full augmentation and standard group‑SGD, which require O(1/ε⁴) queries.
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: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:2511. 09432v2 Announce Type: replace Abstract: Machine learning (ML) models achieve remarkable performance but remain hard to interpret due to their scale and complexity.
arXiv:2606. 09049v1 Announce Type: cross Abstract: We propose the data augmented bootstrap (DAB), a framework for constructing confidence intervals from approximately invariant transformations of the data.
We propose the data augmented bootstrap (DAB), a framework for constructing confidence intervals from approximately invariant transformations of the data. As special cases, DAB recovers popular methods that rely on exact group symmetries, such as conformal prediction, wild bootstrap for Maximum Mean Discrepancy U-statistics and the recently proposed SymmPI.
arXiv:2505. 19809v3 Announce Type: replace-cross Abstract: In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency.
The paper investigates fundamental limits of algorithmic principles in multiclass learning, specifically proper learning and regularization. It shows that learning cannot always be reduced to proper learning even with an enlarged hypothesis class, that proper learners may need a sublinear number of errors that can be arbitrarily large, and that regularization (SRM or local) is not universally sufficient. The authors also provide a positive theory giving sufficient conditions for SRM learnability and a characterization via integrability of revealed preferences.
arXiv:2406. 13944v2 Announce Type: replace-cross Abstract: This paper establishes the generalization error of pooled min-$\ell_2$-norm interpolation in transfer learning, where data from diverse distributions are available.
arXiv:2510. 17303v2 Announce Type: replace Abstract: Symmetries are known to improve the empirical performance of machine learning models, yet theoretical guarantees explaining these gains remain limited.