To Augment or Not to Augment? Diagnosing Distributional Symmetry Breaking
This work addresses a foundational issue in machine learning for researchers and practitioners by critically assessing the assumptions behind symmetry-aware techniques, though it is incremental in refining existing evaluation methods.
The paper tackles the problem of evaluating when symmetry-aware methods like data augmentation are beneficial by developing a metric to quantify dataset anisotropy, revealing high alignment in benchmark point cloud datasets and showing that symmetry-breaking can hinder invariant methods even with invariant labels.
Symmetry-aware methods for machine learning, such as data augmentation and equivariant architectures, encourage correct model behavior on all transformations (e.g. rotations or permutations) of the original dataset. These methods can improve generalization and sample efficiency, under the assumption that the transformed datapoints are highly probable, or "important", under the test distribution. In this work, we develop a method for critically evaluating this assumption. In particular, we propose a metric to quantify the amount of anisotropy, or symmetry-breaking, in a dataset, via a two-sample neural classifier test that distinguishes between the original dataset and its randomly augmented equivalent. We validate our metric on synthetic datasets, and then use it to uncover surprisingly high degrees of alignment in several benchmark point cloud datasets. We show theoretically that distributional symmetry-breaking can actually prevent invariant methods from performing optimally even when the underlying labels are truly invariant, as we show for invariant ridge regression in the infinite feature limit. Empirically, we find that the implication for symmetry-aware methods is dataset-dependent: equivariant methods still impart benefits on some anisotropic datasets, but not others. Overall, these findings suggest that understanding equivariance -- both when it works, and why -- may require rethinking symmetry biases in the data.