Hyperbolic Concept Bottleneck Models

TL;DR

Hyperbolic Concept Bottleneck Models (HypCBM) improve interpretability and hierarchical consistency in neural networks by embedding concepts in hyperbolic space, enabling sparse, hierarchy-aware activations without extra supervision.

Contribution

The paper introduces HypCBM, a novel hyperbolic embedding framework that captures concept hierarchies and enhances interpretability and robustness in concept bottleneck models.

Findings

HypCBM rivals Euclidean models trained on 20 times more data in sparse regimes.

HypCBM exhibits stronger hierarchical consistency.

HypCBM shows improved robustness to input corruptions.

Abstract

Concept Bottleneck Models (CBMs) have become a popular approach to enable interpretability in neural networks by constraining classifier inputs to a set of human-understandable concepts. While effective, current models embed concepts in flat Euclidean space, treating them as independent, orthogonal dimensions. Concepts, however, are highly structured and organized in semantic hierarchies. To resolve this mismatch, we propose Hyperbolic Concept Bottleneck Models (HypCBM), a post-hoc framework that grounds the bottleneck in this structure by reformulating concept activation as asymmetric geometric containment in hyperbolic space. Rather than treating entailment cones as a pre-training penalty, we show they encode a natural test-time activation signal: the margin of inclusion within a concept's entailment cone yields sparse, hierarchy-aware activations without any additional supervision or learned modules. We further introduce an adaptive scaling law for hierarchically faithful interventions, propagating user corrections coherently through the concept tree. Empirically, HypCBM rivals post-hoc Euclidean models trained on 20$\times$ more data in sparse regimes required for human interpretability, with stronger hierarchical consistency and improved robustness to input corruptions.