Data Augmentation: A Fourier Analysis Perspective
arXiv:2606. 24418v1 Announce Type: new Abstract: Data augmentation is a simple and model-agnostic approach for exploiting known invariances in learning problems.
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.
arXiv:2606. 24418v1 Announce Type: new Abstract: Data augmentation is a simple and model-agnostic approach for exploiting known invariances in learning problems.
arXiv:2512. 20043v3 Announce Type: replace Abstract: Symmetry is fundamental to understanding physical systems and can improve performance and sample efficiency in machine learning.
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...
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.
arXiv:2407. 12288v5 Announce Type: replace-cross Abstract: The progress of machine learning over the past decade is undeniable.
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. 26273v1 Announce Type: new Abstract: Symmetries are important for many deep learning tasks, ranging from applications in the sciences to medical imaging.
arXiv:2609. 20883v1 Announce Type: new Abstract: Despite the widespread use and success of generative AI techniques today, theoretical guarantees on learning a distribution supported in $d$ dimensions from $n$ samples degrade as $O(n^{-1/\Theta(d)})$, though shown to be minimax optimal.
arXiv:2609.39512v1 Announce Type: new Abstract: The small-sample learning problem remains a fundamental challenge in machine learning because limited training data lead to unstable model estimation a...
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.
We study the problem of \emph{adversarially robust} PAC learning. In this framework, the learner observes independent samples from an unknown distribution over $\mathcal{X} \times \{0,1\}$, as in clas...
The paper introduces a PAC‑Bayesian, algorithm‑agnostic framework to quantify the value of privileged information (PI) in Learning Using Privileged Information (LUPI). By comparing the tightest achievable risk bounds with and without PI, the authors derive a training‑time metric that estimates the maximum potential gain from PI without requiring test data. Experiments in supervised and unsupervised settings show a strong correspondence between this metric and actual test‑time performance improvements.