Hyperbolic Concept Bottleneck Models

2026-05-07

AI Summary

This work addresses the limitation of existing concept bottleneck models, which treat concepts as orthogonal dimensions in Euclidean space and thereby ignore their inherent semantic hierarchies. To overcome this, the authors propose the Hyperbolic Concept Bottleneck Model (HypCBM), the first framework to integrate hyperbolic geometry into concept bottleneck learning. HypCBM leverages asymmetric inclusion relationships via entailment cones to model concept activations, automatically generating sparse and hierarchy-consistent representations without requiring additional supervision or learnable modules. The model further incorporates an adaptive scaling rule that enables faithful hierarchical propagation of human interventions. Experimental results demonstrate that HypCBM achieves performance on par with Euclidean post-hoc models using only 1/20 of the training data, while significantly improving hierarchical consistency and robustness to input perturbations.

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.

Problem

• Concept Bottleneck Models
• hyperbolic space
• semantic hierarchies
• interpretability
• concept representation

Innovation

• Hyperbolic space
• Concept Bottleneck Models
• Semantic hierarchies
• Geometric containment
• Interpretability