  The inability of deep learning models to handle data drawn from unseen
distributions has sparked much interest in unsupervised out-of-distribution
(U-OOD) detection, as it is crucial for reliable deep learning models. Despite
considerable attention, theoretically-motivated approaches are few and far
between, with most methods building on top of some form of heuristic. Recently,
U-OOD was formalized in the context of data invariants, allowing a clearer
understanding of how to characterize U-OOD, and methods leveraging affine
invariants have attained state-of-the-art results on large-scale benchmarks.
Nevertheless, the restriction to affine invariants hinders the expressiveness
of the approach. In this work, we broaden the affine invariants formulation to
a more general case and propose a framework consisting of a normalizing
flow-like architecture capable of learning non-linear invariants. Our novel
approach achieves state-of-the-art results on an extensive U-OOD benchmark, and
we demonstrate its further applicability to tabular data. Finally, we show our
method has the same desirable properties as those based on affine invariants.
