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Data augmentation (DA) is a powerful workhorse for bolstering performance in modern machine learning. Specific augmentations like translations and scaling in computer vision are traditionally believed to improve generalization by generating new (artificial) data from the same distribution. However, this traditional viewpoint does not explain the success of prevalent augmentations in modern machine learning (e.g. randomized masking, cutout, mixup), that greatly alter the training data distribution. In this work, we develop a new theoretical framework to characterize the impact of a general class of DA on underparameterized and overparameterized linear model generalization. Our framework reveals that DA induces implicit spectral regularization through a combination of two distinct effects: a) manipulating the relative proportion of eigenvalues of the data covariance matrix in a training-data-dependent manner, and b) uniformly boosting the entire spectrum of the data covariance matrix through ridge regression. These effects, when applied to popular augmentations, give rise to a wide variety of phenomena, including discrepancies in generalization between over-parameterized and under-parameterized regimes and differences between regression and classification tasks. Our framework highlights the nuanced and sometimes surprising impacts of DA on generalization, and serves as a testbed for novel augmentation design. 

The brain has long been divided into distinct areas based upon its local microstructure, or patterned composition of cells, genes, and proteins. While this taxonomy is incredibly useful and provides an essential roadmap for comparing two brains, there is also immense anatomical variability within areas that must be incorporated into models of brain architecture. In this work we leverage the expressive power of deep neural networks to create a data-driven model of intra- and inter-brain area variability. To this end, we train a convolutional neural network that learns relevant microstructural features directly from brain imagery. We then extract features from the network and fit a simple classifier to them, thus creating a simple, robust, and interpretable model of brain architecture. We further propose and show preliminary results for the use of features from deep neural networks in conjunction with unsupervised learning techniques to find fine-grained structure within brain areas. We apply our methods to micron-scale X-ray microtomography images spanning multiple regions in the mouse brain and demonstrate that our deep feature-based model can reliably discriminate between brain areas, is robust to noise, and can be used to reveal anatomically relevant patterns in neural architecture that the network wasn't trained to find.