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Relational Concept Bottleneck Models
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Proposes Relational Concept Bottleneck Models (R-CBMs), a family of interpretable relational deep learning models that generalize CBMs and message-passing GNNs, and evaluates them on synthetic image relational tasks and relational graph benchmarks.
Problem
Interpretable deep models for relational domains: CBMs process one entity at a time and cannot handle relational tasks, while relational models like GNNs are not interpretable.
Approach
Extends concept bottlenecks to relational settings with a hypergraph of atom dependencies and message passing that updates atom predictions; task predictors are relational (e.g., logic rules via DCR), and max aggregation gives existential-quantifier semantics for explanations.
Key results
- On Hanoi, R-CBM-Linear and R-CBM-Deep reach 100% ROC-AUC versus ~55% for standard CBMs, while Flat-CBM breaks on OOD tower sizes.
- R-DCR reaches 98.77% ROC-AUC on RPS and 99.99% on Hanoi, and under concept/rule interventions R-DCR perfectly predicts adversarial RPS samples (100%).
- On Citeseer under 25% supervision, R-CBM-Linear achieves 16.92% accuracy versus 7.70% for the relational black-box.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use a relational concept bottleneck rather than a standard CBM | relational task prediction · Hanoi | ROC-AUC: 54.58 -> 100.00 | Helped |
| use a relational concept bottleneck rather than a standard CBM | relational task prediction · RPS | ROC-AUC: 64.48 -> 98.77 | Helped |
| use a linear rather than deep task predictor | R-CBM · RPS | ROC-AUC: 100.00 -> 51.04 | Hurt |
| use an interpretable rule predictor instead of an embedding-based black-box predictor | R-CBM · WN18RR | MRR: 0.49 -> 0.47 | Hurt |
| apply concept and rule interventions | R-DCR · RPS adversarial test samples | ROC-AUC: 54.47 \pm 1.64 -> 100.00 \pm 0.00 | Helped |
| apply concept and rule interventions | R-DCR · Hanoi adversarial test samples | ROC-AUC: 49.48 \pm 0.35 -> 100.00 \pm 0.00 | Helped |
| apply concept intervention | R-CBM-Linear · RPS adversarial test samples | ROC-AUC: 49.46 \pm 1.11 -> 47.83 \pm 2.19 | Hurt |
| use a relational CBM instead of a relational black-box | node classification · Citeseer, 50% supervision | accuracy: 46.46 \pm 2.01 -> 57.07 \pm 3.74 | Helped |
| use a relational CBM instead of a relational black-box | node classification · Citeseer, 25% supervision | accuracy: 7.70 \pm 0.0 -> 16.92 \pm 4.83 | Helped |
| increase the number of test-time Hanoi disks from 3 to 7 after training with 3 disks | R-CBM · Hanoi out-of-distribution test | ROC-AUC: \sim 100\% -> around \sim 85\% | Hurt |
| reduce supervision to 5 labeled atoms per predicate (ablation) | R-DCR-Low · Hanoi | ROC-AUC: 99.99 -> 90.62 | Hurt |
| reduce supervision to 5 labeled atoms per predicate (ablation) | R-DCR-Low · RPS | ROC-AUC: 98.77 -> 98.11 | No clear effect |
Surprising findings
- Standard CBMs barely beat random (~55% ROC-AUC) on relational tasks, and perfect concept predictions do not suffice for them to solve the task.
- Flat-CBM with a linear predictor performs near random on RPS (50.74% ROC-AUC).
Limitations
- Limited scalability to very large domains, shared with relational systems.
- Requires manually defined relational concept bottleneck templates, acting as an inductive bias.
- R-DCR-Low performance drops on Hanoi when learning binary relational concepts from 5 examples.
Experimental setup
Datasets: Rock-Paper-Scissors (self-built) Tower of Hanoi (self-built) Cora Citeseer PubMed Countries S1/S2 WN18RR FB15k-237
Benchmarks: Rock-Paper-Scissors Tower of Hanoi Cora Citeseer PubMed Countries S1 Countries S2 WN18RR FB15k-237
Metrics: ROC-AUC accuracy MRR Hits@1 Hits@10 completeness score
Baselines: CBM-Linear CBM-Deep DCR Flat-CBM Feedforward Relational GCN black-box DeepStochLog DistMult ConvE ComplEx RNNLogic RLogic
Builds on: Concept Bottleneck Models Deep Concept Reasoner Graph Convolutional Networks DeepStochLog
Closest papers by meaning
- Energy-Based Concept Bottleneck Models: Unifying Prediction, Concept Intervention, and Probabilistic Interpretations (ICLR 2024 · similarity 0.88)
- Learning to Intervene on Concept Bottlenecks (ICML 2024 · similarity 0.88)
- Explanation Bottleneck Models (AAAI 2025 · similarity 0.87)
- Hyperbolic Concept Bottleneck Models (NeurIPS 2026 · similarity 0.87)
- Show and Tell: Visually Explainable Deep Neural Nets via Spatially-Aware Concept Bottleneck Models (CVPR 2025 · similarity 0.87)
- VLG-CBM: Training Concept Bottleneck Models with Vision-Language Guidance (NeurIPS 2024 · similarity 0.87)
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