Hierarchy-aware representations ensure that the semantically closer classes are mapped closer in the feature space, thereby reducing the severity of mistakes while enabling consistent coarse-level class predictions. Towards this end, we propose a novel framework, Hierarchical Composition of Orthogonal Subspaces (Hier-COS), which learns to map deep feature embeddings into a vector space that is, by design, consistent with the structure of a given taxonomy tree. Our approach augments neural network backbones with a simple transformation module that maps learned discriminative features to subspaces defined using a fixed orthogonal frame. This construction naturally improves the severity of mistakes and promotes hierarchical consistency. Furthermore, we highlight the fundamental limitations of existing hierarchical evaluation metrics popularly used by the vision community and introduce a preference-based metric, Hierarchically Ordered Preference Score (HOPS), to overcome these limitations. We benchmark our method on multiple large and challenging datasets having deep label hierarchies (ranging from 3 - 12 levels) and compare with several baselines and SOTA. Through extensive experiments, we demonstrate that Hier-COS achieves state-of-the-art hierarchical performance across all the datasets while simultaneously beating top-1 accuracy in all but one case. We also demonstrate the performance of a Vision Transformer (ViT) backbone and show that learning a transformation module alone can map the learned features from a pre-trained ViT to Hier-COS and yield substantial performance benefits.

A corpus of vector-embedded text documents has some empirical distribution. Given two corpora, we want to calculate a single metric of distance (e.g., Mauve, Frechet Inception) between them. We describe an abstract quality, called `distributionality', of such metrics. A non-distributional metric tends to use very local measurements, or uses global measurements in a way that does not fully reflect the distributions' true distance. For example, if individual pairwise nearest-neighbor distances are low, it may judge the two corpora to have low distance, even if their two distributions are in fact far from each other. A more distributional metric will, in contrast, better capture the distributions' overall distance. We quantify this quality by constructing a Known-Similarity Corpora set from two paraphrase corpora and calculating the distance between paired corpora from it. The distances' trend shape as set element separation increases should quantify the distributionality of the metric. We propose that Average Hausdorff Distance and energy distance between corpora are representative examples of non-distributional and distributional distance metrics, to which other metrics can be compared, to evaluate how distributional they are.