# Relational Concept Bottleneck Models

arXiv: https://arxiv.org/abs/2308.11991 · HTML: https://mlsanity.com/paper/2308.11991/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 38 references that are in the map.
- First posted on arXiv 23 Aug 2023.

## Builds on (most cited first, 21 of 21)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [On Completeness-aware Concept-Based Explanations in Deep Neural Networks](https://mlsanity.com/paper/1910.07969/) (2019)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Promises and Pitfalls of Black-Box Concept Learning Models](https://mlsanity.com/paper/2106.13314/) (2021)
- [RNNLogic: Learning Logic Rules for Reasoning on Knowledge Graphs](https://mlsanity.com/paper/2010.04029/) (2020)
- [Probabilistic Concept Bottleneck Models](https://mlsanity.com/paper/2306.01574/) (2023)
- [GlanceNets: Interpretabile, Leak-proof Concept-based Models](https://mlsanity.com/paper/2205.15612/) (2022)
- [DeepStochLog: Neural Stochastic Logic Programming](https://mlsanity.com/paper/2106.12574/) (2021)
- [Interpretable Neural-Symbolic Concept Reasoning](https://mlsanity.com/paper/2304.14068/) (2023)
- [Efficient Probabilistic Logic Reasoning with Graph Neural Networks](https://mlsanity.com/paper/2001.11850/) (2020)
- [Multi-dimensional concept discovery (MCD): A unifying framework with completeness guarantees](https://mlsanity.com/paper/2301.11911/) (2023)
- [Logic Explained Networks](https://mlsanity.com/paper/2108.05149/) (2021)
- [Towards Robust Metrics for Concept Representation Evaluation](https://mlsanity.com/paper/2301.10367/) (2023)
- [Towards Neural Theorem Proving at Scale](https://mlsanity.com/paper/1807.08204/) (2018)
- [Dividing and Conquering a BlackBox to a Mixture of Interpretable Models: Route, Interpret, Repeat](https://mlsanity.com/paper/2307.05350/) (2023)
- [Relational Reasoning Networks](https://mlsanity.com/paper/2106.00393/) (2021)
- [Enhancing Embedding Representations of Biomedical Data using Logic Knowledge](https://mlsanity.com/paper/2303.13566/) (2023)

## Built on by (most cited first, 15 of 15)

- [Causal Concept Graph Models: Beyond Causal Opacity in Deep Learning](https://mlsanity.com/paper/2405.16507/) (2024)
- [A Comprehensive Survey on Self-Interpretable Neural Networks](https://mlsanity.com/paper/2501.15638/) (2025)
- [If Concept Bottlenecks are the Question, are Foundation Models the Answer?](https://mlsanity.com/paper/2504.19774/) (2025)
- [Counterfactual Concept Bottleneck Models](https://mlsanity.com/paper/2402.01408/) (2024)
- [Towards Reasonable Concept Bottleneck Models](https://mlsanity.com/paper/2506.05014/) (2025)
- [Grounding Methods for Neural-Symbolic AI](https://mlsanity.com/paper/2507.08216/) (2025)
- [Quantifying the Accuracy-Interpretability Trade-Off in Concept-Based Sidechannel Models](https://mlsanity.com/paper/2510.05670/) (2025)
- [RESOLVE: Relational Reasoning with Symbolic and Object-Level Features Using Vector Symbolic Processing](https://mlsanity.com/paper/2411.08290/) (2024)
- [Learning Label-Efficient Interpretable Medical Image Diagnosis via Semi-supervised Hypergraph Concept Bottleneck Model](https://mlsanity.com/paper/2606.01698/) (2026)
- [Vision-Language Models Encode Clinical Guidelines for Concept-Based Medical Reasoning](https://mlsanity.com/paper/2603.08921/) (2026)
- [DCG-Net: Dual Cross-Attention with Concept-Value Graph Reasoning for Interpretable Medical Diagnosis](https://mlsanity.com/paper/2603.20325/) (2026)
- [Concept Graph Convolutions: Message Passing in the Concept Space](https://mlsanity.com/paper/2604.20082/) (2026)
- [Hyperbolic Concept Bottleneck Models](https://mlsanity.com/paper/2605.06440/) (2026)
- [Measuring What Matters: Synthetic Benchmarks for Concept Bottleneck Models](https://mlsanity.com/paper/2606.04326/) (2026)
- [Formal Concept Lattices are Good Semantic Scaffolds for Concept-Based Learning](https://mlsanity.com/paper/2606.05471/) (2026)

## Abstract (arXiv)

The design of interpretable deep learning models working in relational domains poses an open challenge: interpretable deep learning methods, such as Concept Bottleneck Models (CBMs), are not designed to solve relational problems, while relational deep learning models, such as Graph Neural Networks (GNNs), are not as interpretable as CBMs. To overcome these limitations, we propose Relational Concept Bottleneck Models (R-CBMs), a family of relational deep learning methods providing interpretable task predictions. As special cases, we show that R-CBMs are capable of both representing standard CBMs and message-passing GNNs. To evaluate the effectiveness and versatility of these models, we designed a class of experimental problems, ranging from image classification to link prediction in knowledge graphs. In particular we show that R-CBMs (i) match generalization performance of existing relational black-boxes, (ii) support the generation of quantified concept-based explanations, (iii) effectively respond to test-time interventions, and (iv) withstand demanding settings including out-of-distribution scenarios, limited training data regimes, and scarce concept supervisions.