# Concept Embedding Models: Beyond the Accuracy-Explainability Trade-Off

arXiv: https://arxiv.org/abs/2209.09056 · HTML: https://mlsanity.com/paper/2209.09056/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 52 references that are in the map.
- First posted on arXiv 19 Sep 2022.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Towards Robust Interpretability with Self-Explaining Neural Networks](https://mlsanity.com/paper/1806.07538/) (2018)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [The (Un)reliability of saliency methods](https://mlsanity.com/paper/1711.00867/) (2017)
- [On Completeness-aware Concept-Based Explanations in Deep Neural Networks](https://mlsanity.com/paper/1910.07969/) (2019)
- [Concept Whitening for Interpretable Image Recognition](https://mlsanity.com/paper/2002.01650/) (2020)
- [Grad-CAM: Why did you say that?](https://mlsanity.com/paper/1611.07450/) (2016)
- [Promises and Pitfalls of Black-Box Concept Learning Models](https://mlsanity.com/paper/2106.13314/) (2021)
- [Learning how to explain neural networks: PatternNet and PatternAttribution](https://mlsanity.com/paper/1705.05598/) (2017)
- [Nonlinear Information Bottleneck](https://mlsanity.com/paper/1705.02436/) (2017)
- [Explanation Methods in Deep Learning: Users, Values, Concerns and Challenges](https://mlsanity.com/paper/1803.07517/) (2018)
- [GCExplainer: Human-in-the-Loop Concept-based Explanations for Graph Neural Networks](https://mlsanity.com/paper/2107.11889/) (2021)
- [Deep Supervision with Intermediate Concepts](https://mlsanity.com/paper/1801.03399/) (2018)
- [Trust in AI: Interpretability is not necessary or sufficient, while black-box interaction is necessary and sufficient](https://mlsanity.com/paper/2202.05302/) (2022)

## Built on by (most cited first, 30 of 61)

- [Label-Free Concept Bottleneck Models](https://mlsanity.com/paper/2304.06129/) (2023)
- [Getting aligned on representational alignment](https://mlsanity.com/paper/2310.13018/) (2023)
- [Explainable Artificial Intelligence (XAI) 2.0: A Manifesto of Open Challenges and Interdisciplinary Research Directions](https://mlsanity.com/paper/2310.19775/) (2023)
- [Probabilistic Concept Bottleneck Models](https://mlsanity.com/paper/2306.01574/) (2023)
- [A Closer Look at the Intervention Procedure of Concept Bottleneck Models](https://mlsanity.com/paper/2302.14260/) (2023)
- [Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcuts](https://mlsanity.com/paper/2305.19951/) (2023)
- [Interpretable Neural-Symbolic Concept Reasoning](https://mlsanity.com/paper/2304.14068/) (2023)
- [Multi-dimensional concept discovery (MCD): A unifying framework with completeness guarantees](https://mlsanity.com/paper/2301.11911/) (2023)
- [Human Uncertainty in Concept-Based AI Systems](https://mlsanity.com/paper/2303.12872/) (2023)
- [BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcuts](https://mlsanity.com/paper/2402.12240/) (2024)
- [Auxiliary Losses for Learning Generalizable Concept-based Models](https://mlsanity.com/paper/2311.11108/) (2023)
- [Energy-Based Concept Bottleneck Models: Unifying Prediction, Concept Intervention, and Probabilistic Interpretations](https://mlsanity.com/paper/2401.14142/) (2024)
- [Causal Concept Graph Models: Beyond Causal Opacity in Deep Learning](https://mlsanity.com/paper/2405.16507/) (2024)
- [A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcuts](https://mlsanity.com/paper/2406.10368/) (2024)
- [State2Explanation: Concept-Based Explanations to Benefit Agent Learning and User Understanding](https://mlsanity.com/paper/2309.12482/) (2023)
- [Learning Discrete Concepts in Latent Hierarchical Models](https://mlsanity.com/paper/2406.00519/) (2024)
- [Causally Reliable Concept Bottleneck Models](https://mlsanity.com/paper/2503.04363/) (2025)
- [Understanding Inter-Concept Relationships in Concept-Based Models](https://mlsanity.com/paper/2405.18217/) (2024)
- [Shortcuts and Identifiability in Concept-based Models from a Neuro-Symbolic Lens](https://mlsanity.com/paper/2502.11245/) (2025)
- [Dissecting Generalized Category Discovery: Multiplex Consensus under Self-Deconstruction](https://mlsanity.com/paper/2508.10731/) (2025)
- [Tuning-Free Accountable Intervention for LLM Deployment -- A Metacognitive Approach](https://mlsanity.com/paper/2403.05636/) (2024)
- [Dividing and Conquering a BlackBox to a Mixture of Interpretable Models: Route, Interpret, Repeat](https://mlsanity.com/paper/2307.05350/) (2023)
- [Learning with Explanation Constraints](https://mlsanity.com/paper/2303.14496/) (2023)
- [Concept-Centric Transformers: Enhancing Model Interpretability through Object-Centric Concept Learning within a Shared Global Workspace](https://mlsanity.com/paper/2305.15775/) (2023)
- [Selective Concept Models: Permitting Stakeholder Customisation at Test-Time](https://mlsanity.com/paper/2306.08424/) (2023)
- [SHARCS: Shared Concept Space for Explainable Multimodal Learning](https://mlsanity.com/paper/2307.00316/) (2023)
- [Improving Intervention Efficacy via Concept Realignment in Concept Bottleneck Models](https://mlsanity.com/paper/2405.01531/) (2024)
- [Towards Multi-dimensional Explanation Alignment for Medical Classification](https://mlsanity.com/paper/2410.21494/) (2024)
- [OCRT: Boosting Foundation Models in the Open World with Object-Concept-Relation Triad](https://mlsanity.com/paper/2503.18695/) (2025)
- [SUB: Benchmarking CBM Generalization via Synthetic Attribute Substitutions](https://mlsanity.com/paper/2507.23784/) (2025)

## Abstract (arXiv)

Deploying AI-powered systems requires trustworthy models supporting effective human interactions, going beyond raw prediction accuracy. Concept bottleneck models promote trustworthiness by conditioning classification tasks on an intermediate level of human-like concepts. This enables human interventions which can correct mispredicted concepts to improve the model's performance. However, existing concept bottleneck models are unable to find optimal compromises between high task accuracy, robust concept-based explanations, and effective interventions on concepts -- particularly in real-world conditions where complete and accurate concept supervisions are scarce. To address this, we propose Concept Embedding Models, a novel family of concept bottleneck models which goes beyond the current accuracy-vs-interpretability trade-off by learning interpretable high-dimensional concept representations. Our experiments demonstrate that Concept Embedding Models (1) attain better or competitive task accuracy w.r.t. standard neural models without concepts, (2) provide concept representations capturing meaningful semantics including and beyond their ground truth labels, (3) support test-time concept interventions whose effect in test accuracy surpasses that in standard concept bottleneck models, and (4) scale to real-world conditions where complete concept supervisions are scarce.