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Hyperbolic Concept Bottleneck Models

NeurIPS 2026 · Label-efficient and robust learning › Recognition and long-tail · approach: Concept bottleneck models · 0 citations (OpenAlex)

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Proposes HypCBM, a post-hoc concept bottleneck that uses hyperbolic entailment-cone containment margins (frozen HyCoCLIP) as sparse, hierarchy-aware concept activations plus norm-scaled hierarchical interventions.

Problem

Standard concept bottleneck models embed concepts in flat Euclidean space as independent directions, which ignores concept hierarchies and yields redundant, logically inconsistent, sparsity-poor concept activations.

Approach

Reformulates concept activation as asymmetric containment: the normalized margin by which an image embedding lies inside a concept's hyperbolic entailment cone is used directly at test time (no training), and interventions on a parent concept propagate to descendants with a norm-dependent threshold.

Key results

• On ImageNet at ANEC-10, HypCBM reaches 34.6% vs 15.3% for LF-CBM (CLIP-20M), more than doubling accuracy in the sparse regime.
• On SUN397 at ANEC-20, HypCBM (HyCoCLIP-20M) gets 65.7% vs 58.8% for LF-CBM with CLIP-400M, despite 20x less data.
• Hierarchical consistency at eta_img=1.2 on SUN397 rises from 0.08 (LF-CBM) to 0.17 for HypCBM (+104.7%).

Surprising findings

• Euclidean LF-CBM on HyCoCLIP backbone performs worse than on CLIP at sparse budgets, and applying Euclidean-style activation to the hyperbolic backbone degrades performance.
• CLIP^RE, a hierarchy-aware Euclidean model trained on 20x more data, performs substantially worse than standard CLIP at strict concept budgets.

Limitations

• Relies on text-derived taxonomies (WordNet) that do not always match visual semantics; fine-grained CUB-200 performance is weak relative to CLIP-400M.
• Ablations do not fully disentangle the contributions of geometry versus activation design.
• Performance depends on the quality of available hyperbolic VLMs; strictness thresholds eta_img must be calibrated per dataset, with SUN397 tuned on validation data.

Experimental setup

Datasets: CIFAR-100 SUN397 ImageNet CUB-200-2011 GrIT-20M WordNet CIFAR100-C

Benchmarks: CIFAR-100 SUN397 ImageNet CUB-200-2011 CIFAR100-C

Metrics: ANEC-K accuracy peak accuracy linear probe accuracy hierarchical consistency Jaccard concept stability intervention confidence decay

Baselines: LF-CBM LF-CBM Matched CLIP^RE MERU LaBo CLIP-400M

Builds on: Post-hoc Concept Bottleneck Models LF-CBM MERU HyCoCLIP CLIP

Closest papers by meaning

• Energy-Based Concept Bottleneck Models: Unifying Prediction, Concept Intervention, and Probabilistic Interpretations (ICLR 2024 · similarity 0.89)
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• Sample-efficient Learning of Concepts with Theoretical Guarantees: from Data to Concepts without Interventions (NeurIPS 2025 · similarity 0.89)
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