# Towards Robust Metrics for Concept Representation Evaluation

arXiv: https://arxiv.org/abs/2301.10367 · HTML: https://mlsanity.com/paper/2301.10367/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 41 references that are in the map.
- First posted on arXiv 25 Jan 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [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)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Towards Robust Interpretability with Self-Explaining Neural Networks](https://mlsanity.com/paper/1806.07538/) (2018)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [On Completeness-aware Concept-Based Explanations in Deep Neural Networks](https://mlsanity.com/paper/1910.07969/) (2019)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [Concept Whitening for Interpretable Image Recognition](https://mlsanity.com/paper/2002.01650/) (2020)
- [Explainable Machine Learning in Deployment](https://mlsanity.com/paper/1909.06342/) (2019)
- [Promises and Pitfalls of Black-Box Concept Learning Models](https://mlsanity.com/paper/2106.13314/) (2021)
- [Do Concept Bottleneck Models Learn as Intended?](https://mlsanity.com/paper/2105.04289/) (2021)
- [Learning Deep Disentangled Embeddings with the F-Statistic Loss](https://mlsanity.com/paper/1802.05312/) (2018)
- [Measuring Disentanglement: A Review of Metrics](https://mlsanity.com/paper/2012.09276/) (2020)
- [Now You See Me (CME): Concept-based Model Extraction](https://mlsanity.com/paper/2010.13233/) (2020)
- [Logic Explained Networks](https://mlsanity.com/paper/2108.05149/) (2021)
- [Is Disentanglement all you need? Comparing Concept-based & Disentanglement Approaches](https://mlsanity.com/paper/2104.06917/) (2021)
- [Benchmarks, Algorithms, and Metrics for Hierarchical Disentanglement](https://mlsanity.com/paper/2102.05185/) (2021)

## Built on by (most cited first, 29 of 29)

- [Interpretable Neural-Symbolic Concept Reasoning](https://mlsanity.com/paper/2304.14068/) (2023)
- [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)
- [Auxiliary Losses for Learning Generalizable Concept-based Models](https://mlsanity.com/paper/2311.11108/) (2023)
- [Interpretability is in the Mind of the Beholder: A Causal Framework for Human-interpretable Representation Learning](https://mlsanity.com/paper/2309.07742/) (2023)
- [A Comprehensive Survey on Self-Interpretable Neural Networks](https://mlsanity.com/paper/2501.15638/) (2025)
- [Interpretable Concept-Based Memory Reasoning](https://mlsanity.com/paper/2407.15527/) (2024)
- [Relational Concept Bottleneck Models](https://mlsanity.com/paper/2308.11991/) (2023)
- [If Concept Bottlenecks are the Question, are Foundation Models the Answer?](https://mlsanity.com/paper/2504.19774/) (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)
- [Leakage and Interpretability in Concept-Based Models](https://mlsanity.com/paper/2504.14094/) (2025)
- [Do Concept Bottleneck Models Respect Localities?](https://mlsanity.com/paper/2401.01259/) (2024)
- [A survey on Concept-based Approaches For Model Improvement](https://mlsanity.com/paper/2403.14566/) (2024)
- [There Was Never a Bottleneck in Concept Bottleneck Models](https://mlsanity.com/paper/2506.04877/) (2025)
- [Counterfactual Concept Bottleneck Models](https://mlsanity.com/paper/2402.01408/) (2024)
- [Improving Intervention Efficacy via Concept Realignment in Concept Bottleneck Models](https://mlsanity.com/paper/2405.01531/) (2024)
- [SUB: Benchmarking CBM Generalization via Synthetic Attribute Substitutions](https://mlsanity.com/paper/2507.23784/) (2025)
- [Can we Constrain Concept Bottleneck Models to Learn Semantically Meaningful Input Features?](https://mlsanity.com/paper/2402.00912/) (2024)
- [Foundations of Interpretable Models](https://mlsanity.com/paper/2508.00545/) (2025)
- [Learning Concept Bottleneck Models from Mechanistic Explanations](https://mlsanity.com/paper/2603.07343/) (2026)
- [Concepts' Information Bottleneck Models](https://mlsanity.com/paper/2602.14626/) (2026)
- [CNN-based explanation ensembling for dataset, representation and explanations evaluation](https://mlsanity.com/paper/2404.10387/) (2024)
- [Concept Labels Are Not Enough: Rethinking Concept Bottleneck Models through Representation Integrity](https://mlsanity.com/paper/2510.15770/) (2025)
- [Probing the Probes: Methods and Metrics for Concept Alignment](https://mlsanity.com/paper/2511.04312/) (2025)
- [Clarity: The Flexibility-Interpretability Trade-Off in Sparsity-aware Concept Bottleneck Models](https://mlsanity.com/paper/2601.21944/) (2026)
- [In Defense of Information Leakage in Concept-based Models](https://mlsanity.com/paper/2606.10669/) (2026)
- [Loss Invariance Determines What Concept Layers Encode: Volume Grounding in Echocardiography](https://mlsanity.com/paper/2607.25748/) (2026)
- [Limitations of Automated Simulatability: LLM Simulators Can Bypass Explanations](https://mlsanity.com/paper/2609.08585/) (2026)

## Abstract (arXiv)

Recent work on interpretability has focused on concept-based explanations, where deep learning models are explained in terms of high-level units of information, referred to as concepts. Concept learning models, however, have been shown to be prone to encoding impurities in their representations, failing to fully capture meaningful features of their inputs. While concept learning lacks metrics to measure such phenomena, the field of disentanglement learning has explored the related notion of underlying factors of variation in the data, with plenty of metrics to measure the purity of such factors. In this paper, we show that such metrics are not appropriate for concept learning and propose novel metrics for evaluating the purity of concept representations in both approaches. We show the advantage of these metrics over existing ones and demonstrate their utility in evaluating the robustness of concept representations and interventions performed on them. In addition, we show their utility for benchmarking state-of-the-art methods from both families and find that, contrary to common assumptions, supervision alone may not be sufficient for pure concept representations.