Flattening the Parent Bias: Hierarchical Semantic Segmentation in the Poincaré Ball

Class embeddings in the Euclidean space (a) exhibit non-uniform properties of the separation margin: the average distance of a pixel embedding of one class to the decision boundaries of the other classes varies substantially (e.g.

). This creates an implicit parent bias in hierarchical segmentation, which prefers grouping one set of classes over the other, in terms of the parent-level segmentation accuracy. In contrast, in hyperbolic space characterized by the Poincaré ball (b), the separation margins between the class embeddings are more uniform, e.g. the hyperbolic distance of embeddings A and B of two different classes to the decision boundary (a gyroplane) of another class is approximately equal, d A H ≈ d B H . This may explain the strong generalization of the parent-level predictions, observed in practice, in terms of the segmentation accuracy and calibration quality.