# Understanding Inter-Concept Relationships in Concept-Based Models

arXiv: https://arxiv.org/abs/2405.18217 · HTML: https://mlsanity.com/paper/2405.18217/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 50 references that are in the map.
- First posted on arXiv 28 May 2024.

## Builds on (most cited first, 30 of 30)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [CheXpert: A Large Chest Radiograph Dataset with Uncertainty Labels and Expert Comparison](https://mlsanity.com/paper/1901.07031/) (2019)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Knowledge Graphs](https://mlsanity.com/paper/2003.02320/) (2020)
- [Does the Whole Exceed its Parts? The Effect of AI Explanations on Complementary Team Performance](https://mlsanity.com/paper/2006.14779/) (2020)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Post-hoc Concept Bottleneck Models](https://mlsanity.com/paper/2205.15480/) (2022)
- [Label-Free Concept Bottleneck Models](https://mlsanity.com/paper/2304.06129/) (2023)
- [Explanations can be manipulated and geometry is to blame](https://mlsanity.com/paper/1906.07983/) (2019)
- [Quantus: An Explainable AI Toolkit for Responsible Evaluation of Neural Network Explanations and Beyond](https://mlsanity.com/paper/2202.06861/) (2022)
- [Promises and Pitfalls of Black-Box Concept Learning Models](https://mlsanity.com/paper/2106.13314/) (2021)
- [What Do We Want From Explainable Artificial Intelligence (XAI)? -- A Stakeholder Perspective on XAI and a Conceptual Model Guiding Interdisciplinary XAI Research](https://mlsanity.com/paper/2102.07817/) (2021)
- [Probabilistic Concept Bottleneck Models](https://mlsanity.com/paper/2306.01574/) (2023)
- [Interactive Concept Bottleneck Models](https://mlsanity.com/paper/2212.07430/) (2022)
- [GlanceNets: Interpretabile, Leak-proof Concept-based Models](https://mlsanity.com/paper/2205.15612/) (2022)
- [Concept Embedding Models: Beyond the Accuracy-Explainability Trade-Off](https://mlsanity.com/paper/2209.09056/) (2022)
- [Concept-level Debugging of Part-Prototype Networks](https://mlsanity.com/paper/2205.15769/) (2022)
- [Now You See Me (CME): Concept-based Model Extraction](https://mlsanity.com/paper/2010.13233/) (2020)
- [Learning to Receive Help: Intervention-Aware Concept Embedding Models](https://mlsanity.com/paper/2309.16928/) (2023)
- [Human Uncertainty in Concept-Based AI Systems](https://mlsanity.com/paper/2303.12872/) (2023)
- [Towards Robust Metrics for Concept Representation Evaluation](https://mlsanity.com/paper/2301.10367/) (2023)
- [Trust in AI: Interpretability is not necessary or sufficient, while black-box interaction is necessary and sufficient](https://mlsanity.com/paper/2202.05302/) (2022)
- [Do Concept Bottleneck Models Respect Localities?](https://mlsanity.com/paper/2401.01259/) (2024)

## Built on by (most cited first, 13 of 13)

- [A Comprehensive Survey on Self-Interpretable Neural Networks](https://mlsanity.com/paper/2501.15638/) (2025)
- [Addressing Concept Mislabeling in Concept Bottleneck Models Through Preference Optimization](https://mlsanity.com/paper/2504.18026/) (2025)
- [SUB: Benchmarking CBM Generalization via Synthetic Attribute Substitutions](https://mlsanity.com/paper/2507.23784/) (2025)
- [LogicCBMs: Logic-Enhanced Concept-Based Learning](https://mlsanity.com/paper/2512.07383/) (2025)
- [B-cos LM: Efficiently Transforming Pre-trained Language Models for Improved Explainability](https://mlsanity.com/paper/2502.12992/) (2025)
- [A Comprehensive Survey on the Risks and Limitations of Concept-based Models](https://mlsanity.com/paper/2506.04237/) (2025)
- [On The Variability of Concept Activation Vectors](https://mlsanity.com/paper/2509.24058/) (2025)
- [Hierarchical Concept-based Interpretable Models](https://mlsanity.com/paper/2602.23947/) (2026)
- [Bridging Fairness and Explainability: Can Input-Based Explanations Promote Fairness in Hate Speech Detection?](https://mlsanity.com/paper/2509.22291/) (2025)
- [Digging Deeper: Learning Multi-Level Concept Hierarchies](https://mlsanity.com/paper/2603.10084/) (2026)
- [Metonymy in vision models undermines attention-based interpretability](https://mlsanity.com/paper/2605.06095/) (2026)
- [Formal Concept Lattices are Good Semantic Scaffolds for Concept-Based Learning](https://mlsanity.com/paper/2606.05471/) (2026)
- [ICON decomposition: Multivariate concept auditing reveals shortcuts that neural networks rely on](https://mlsanity.com/paper/2608.26083/) (2026)

## Abstract (arXiv)

Concept-based explainability methods provide insight into deep learning systems by constructing explanations using human-understandable concepts. While the literature on human reasoning demonstrates that we exploit relationships between concepts when solving tasks, it is unclear whether concept-based methods incorporate the rich structure of inter-concept relationships. We analyse the concept representations learnt by concept-based models to understand whether these models correctly capture inter-concept relationships. First, we empirically demonstrate that state-of-the-art concept-based models produce representations that lack stability and robustness, and such methods fail to capture inter-concept relationships. Then, we develop a novel algorithm which leverages inter-concept relationships to improve concept intervention accuracy, demonstrating how correctly capturing inter-concept relationships can improve downstream tasks.