Data augmentation (DA) is now a standard ingredient in modern machine learning pipelines, with extensive empirical evidence reporting improvements in generalization across modalities and tasks Mumuni and Mumuni (2022); Wang et al. (2025). It is often used to encode task-relevant symmetries directly into the training procedure, for instance by encouraging invariance to image rotations or other transformations of the input Shorten and Khoshgoftaar (2019); Chen et al. (2020). It has also been identified as one of the most effective regularization techniques across both supervised learning settings Bishop (1995); Cubuk et al. (2019); Mumuni and Mumuni (2022); Wang et al. (2025) and self-supervised/unsupervised learning Feng et al. (2021); Van Assel et al. (2025). Domain-specific augmentation pipelines have been central to progress in computer vision Shorten and Khoshgoftaar (2019); Kumar et al. (2024), natural language processing Feng et al. (2021); Shorten et al. (2021); Bayer et al. (2022), and time-series or audio applications Wen et al. (2020); Iwana and Uchida (2021); Iglesias et al. (2023). Despite these empirical successes, the benefits of DA remain highly task-and data-dependent, and augmentation schemes are often engineered in an ad hoc manner Fawzi et al. (2016); Cubuk et al. (2019); Lim et al. (2019); Hataya et al. (2020). In contrast with this rich empirical literature, comprehensive theoretical analyses of DA remain relatively scarce. Two classical starting points are, first, the interpretation of additive Gaussian noise as a form of explicit (ridge-like) regularization Bishop (1995); Lin et al. (2024), and second, the idea that leveraging distributional invariances and group structure in the learning objective helps decrease the variance of the model without increasing its bias Chen et al. (2020). Yet, when applied to modern and complex augmentation schemes, these works either provide only upper bounds on the generalization error Lin et al. (2024), or require very strong assumptions on the data distribution (e.g.

Though data augmentation has rapidly emerged as a key tool for optimization in modern machine learning, a clear picture of how augmentation schedules affect optimization and interact with optimization hyperparameters such as learning rate is nascent.

Successful adoption of deep learning (DL) in the wild requires models to be: (1) compact, (2) accurate, and (3) robust to distributional shifts. Unfortunately, efforts towards simultaneously meeting these requirements have mostly been unsuccessful. This raises an important question: "Is the inability to create Compact, Accurate, and Robust Deep neural networks (CARDs) fundamental?" To answer this question, we perform a large-scale analysis of popular model compression techniques which uncovers several intriguing patterns. Notably, in contrast to traditional pruning approaches (e.g., fine tuning and gradual magnitude pruning), we find that "lottery ticket-style" approaches can surprisingly be used to produce CARDs, including binary-weight CARDs. Specifically, we are able to create extremely compact CARDs that, compared to their larger counterparts, have similar test accuracy and matching (or better) robustness--simply by pruning and (optionally) quantizing. Leveraging the compactness of CARDs, we develop a simple domain-adaptive test-time ensembling approach (CARD-Deck) that uses a gating module to dynamically select appropriate CARDsfrom the CARD-Deckbased on their spectral-similarity with test samples. The proposed approach builds a "winning hand" of CARDsthat establishes a new state-of-the-art [8] on CIFAR-10-C accuracies (i.e., 96.8% standard and 92.75% robust) and CIFAR-100-C accuracies (i.e., 80.6% standard and 71.3% robust) with better memory usage than non-compressed baselines (pretrained CARDs available at [8]). Finally, we provide theoretical support for our empirical findings.

This view enables a structured variational approximation capturing dependencies across variables in the model.

For example, consider the "Mars rover mission" that uses laser-induced breakdown spectroscopy (LIBS)tosearchformicrobiallife.

Though data augmentation has rapidly emerged as a key tool for optimization in modern machine learning, a clear picture of how augmentation schedules affect optimization and interact with optimization hyperparameters such as learning rate is nascent. In the spirit of classical convex optimization and recent work on implicit bias, the present work analyzes the effect of augmentation on optimization in the simple convex setting of linear regression with MSE loss.We find joint schedules for learning rate and data augmentation scheme under which augmented gradient descent provably converges and characterize the resulting minimum. Our results apply to arbitrary augmentation schemes, revealing complex interactions between learning rates and augmentations even in the convex setting. Our approach interprets augmented (S)GD as a stochastic optimization method for a time-varying sequence of proxy losses. This gives a unified way to analyze learning rate, batch size, and augmentations ranging from additive noise to random projections. From this perspective, our results, which also give rates of convergence, can be viewed as Monro-Robbins type conditions for augmented (S)GD.