Elamur Research⌕
☰
home / papers / 2026 / Credal Concept Bottleneck Models for Epistemic–Aleatoric Uncertainty Decomposition

Credal Concept Bottleneck Models for Epistemic–Aleatoric Uncertainty Decomposition

Paper · 2026 · Tanmoy Mukherjee, Thomas Bailleux, Pierre Marquis et al.

Summary

Concept Bottleneck Models (CBMs) make predictions through interpretable intermediate concepts. They usually give each concept a single probability, so two kinds of uncertainty get mixed. One is epistemic: the model lacks knowledge that more data could supply. The other is aleatoric: the text itself is ambiguous. The authors propose CREDENCE, a CBM in which each concept is predicted as a probability interval (a credal set). The two uncertainty types come from separate parts of the model:

  • Epistemic uncertainty is the spread across several diverse LoRA-based concept heads on a frozen encoder.
  • Aleatoric uncertainty comes from a dedicated head trained to reproduce annotator disagreement.

These signals feed a routing policy:

  • confident cases are automated;
  • epistemically uncertain cases are flagged for more data;
  • ambiguous cases go to human reviewers;
  • the system abstains when both uncertainties are high.

On NLP tasks including CEBaB, epistemic scores correlate moderately with errors, and aleatoric scores closely follow human disagreement. Ablations show each signal depends only on its own component. This matters for subjective, high-stakes NLP, where fixable model gaps and inherent ambiguity call for different responses.

Key points

  • Architecture: a frozen encoder (encoder-only models and decoder-only LLMs were tested) with H=5 LoRA concept heads. The heads use different ranks (4, 8, 16, 32, 64) and different dropout settings, and their outputs are aggregated into concept intervals.
  • Main correlations: epistemic uncertainty vs. errors gives ρ = 0.287 (p < 10⁻³³). Aleatoric uncertainty vs. annotator disagreement gives ρ ≈ 0.785 (CEBaB, RoBERTa-base).
  • Ablations:
    • Removing the aleatoric head drops ρ_ale to 0.356 and leaves ρ_epi unchanged.
    • Making LoRA ranks or dropout identical across heads weakens ρ_epi (to about 0.21 and 0.20).
  • Without annotator labels: heteroscedastic NLL still reaches ρ_ale = 0.523. Agreement with CEBaB annotators' "unknown" rates is moderate (Cohen's κ = 0.47, Krippendorff's α = 0.45).
  • Interventions: targeting high-aleatoric concepts beats targeting high-epistemic ones across datasets.
  • Limitations: the method needs concept annotations and costs H× forward passes.
  • Code: github.com/Tankiit/Credal_Sets (branch ensemble-credal-cbm).

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🔬Centre National de la Recherche ScientifiqueParis · France168 works · 62,369 citations🎓Institut Universitaire de FranceParis · France5 works · 69 citations🔬Centre de Recherche en Informatique de LensLens · France2 works🎓Université d'ArtoisArras · France2 works

 Fields, topics and concepts

📚 Shelves 3The field of science this work belongs to (OpenAlex fields).Computer Science · 16,667 worksArtificial Intelligence · 16,194 worksComputer Vision and Pattern Recognition · 2,869 works

Cite

Cite as Tanmoy Mukherjee, Thomas Bailleux, Pierre Marquis and Zied Bouraoui. 2026. Credal Concept Bottleneck Models for Epistemic–Aleatoric Uncertainty Decomposition. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers).

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2026.acl-long.1991

@inproceedings{mukherjee2026credal,
  title = {{Credal Concept Bottleneck Models for Epistemic–Aleatoric Uncertainty Decomposition}},
  author = {Tanmoy Mukherjee, Thomas Bailleux, Pierre Marquis and Zied Bouraoui},
  booktitle = {Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)},
  year = {2026},
  doi = {10.18653/v1/2026.acl-long.1991},
  url = {https://doi.org/10.18653/v1/2026.acl-long.1991}
}

References

38 references, 8 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

  1. Eldar D Abraham, Karel D’Oosterlinck, Amir Feder, Yair Gat, Atticus Geiger, Christopher Potts, Roi Reichart, and Zhengxuan Wu. 2022. Cebab: Estimating the causal effects of real-world concepts on nlp model behavior. In Advances in Neural Information Processing Systems, volume 35, pages 17582–17596.… find
  2. Joris Baan, Nico Daheim, Evgenia Ilia, Dennis Ulmer, Haau-Sing Li, Raquel Fernández, Barbara Plank, Rico Sennrich, Chrysoula Zerva, and Wilker Aziz. 2023. Uncertainty in natural language generation: From theory to applications. Preprint, arXiv:2307.15703. — [arXiv:2307.15703](https://arxiv.org/abs/2307.15703) find
  3. Thomas Bailleux, Tanmoy Mukherjee, Pierre Marquis, and Zied Bouraoui. 2025. Connecting concept layers and rationales to enhance language model interpretability. In Proceedings of the 14th Joint Conference on Lexical and Computational Semantics (*SEM 2025), pages 409–429, Suzhou, China. Association f… find
  4. Jasmijn Bastings, Wilker Aziz, and Ivan Titov. 2019. Interpretable neural predictions with differentiable binary variables. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pages 2963–2977, Florence, Italy. Association for Computational Linguistics.
  5. Katherine Maeve Collins, Matthew Barker, Mateo Espinosa Zarlenga, Naveen Raman, Umang Bhatt, Mateja Jamnik, Ilia Sucholutsky, Adrian Weller, and Krishnamurthy Dvijotham. 2023. Human uncertainty in concept-based ai systems. In Proceedings of the 2023 AAAI/ACM Conference on AI, Ethics, and Society, AI… find
  6. Adam Fisch, Robin Jia, and Tal Schuster. 2022. Uncertainty estimation for natural language processing. In COLING. find
  7. Yarin Gal and Zoubin Ghahramani. 2016. Dropout as a bayesian approximation: Representing model uncertainty in deep learning. In Proceedings of The 33rd International Conference on Machine Learning, volume 48 of Proceedings of Machine Learning Research, pages 1050–1059, New York, New York, USA. PMLR. find
  8. Chuan Guo, Geoff Pleiss, Yu Sun, and Kilian Q. Weinberger. 2017. On calibration of modern neural networks. In Proceedings of the 34th International Conference on Machine Learning, volume 70 of Proceedings of Machine Learning Research, pages 1321– 1330. PMLR. find
  9. Jianfeng He, Xuchao Zhang, Shuo Lei, Zhiqian Chen, Fanglan Chen, Abdulaziz Alhamadani, Bei Xiao, and ChangTien Lu. 2020. Towards more accurate uncertainty estimation in text classification. In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 8362–… find
  10. Edward J. Hu, Yelong Shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, and Weizhu Chen. 2021. Lora: Low-rank adaptation of large language models. Preprint, arXiv:2106.09685.
  11. Eyke Hüllermeier, Sébastien Destercke, and Mohammad Hossein Shaker. 2022. Quantification of credal uncertainty in machine learning: A critical analysis and empirical comparison. In Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, volume 180 of Proceedings of Mac… find
  12. Sarthak Jain and Byron C. Wallace. 2019. Attention is not Explanation. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers), pages 3543–3556, Minneapolis, Minnesota. Associa…
  13. Fabio Cuzzolin. 2024. Generalising realisability in statistical learning theory under epistemic uncertainty. Preprint, arXiv:2402.14759. — [arXiv:2402.14759](https://arxiv.org/abs/2402.14759) find
  14. Saurav Kadavath, Tom Conerly, Amanda Askell, Tom Henighan, Dawn Drain, Ethan Perez, Nicholas Schiefer, Zac Hatfield-Dodds, Nova DasSarma, Eli Tran-Johnson, Scott Johnston, Sheer El-Showk, Andy Jones, Nelson Elhage, Tristan Hume, Anna Chen, Yuntao Bai, Sam Bowman, Stanislav Fort, and 17 others. 2022.… find
  15. Stefan Depeweg, Jose-Miguel Hernandez-Lobato, Finale Doshi-Velez, and Steffen Udluft. 2018. Decomposition of uncertainty in Bayesian deep learning for efficient and risk-sensitive learning. In Proceedings Alex Kendall and Yarin Gal. 2017. What uncertainties do we need in bayesian deep learning for c…
  16. Giorgio Corani and Marco Zaffalon. 2008. Learning reliable classifiers from small or incomplete data sets: The naive credal classifier 2. Journal of Machine Learning Research, 9(20):581–621. find
  17. Eunji Kim, Dahuin Jung, Sangha Park, Siwon Kim, and Sungroh Yoon. 2023. Probabilistic concept bottleneck models. In Proceedings of the 40th International Conference on Machine Learning, volume 202 of Proceedings of Machine Learning Research, pages 16521–16540. PMLR. find
  18. Pang Wei Koh, Thao Nguyen, Yew Siang Tang, Stephen Mussmann, Emma Pierson, Been Kim, and Percy Liang. 2020. Concept bottleneck models. In Proceedings of the 37th International Conference on Machine Learning, volume 119 of Proceedings of Machine Learning Research, pages 5338–5348. PMLR. find
  19. Lorenz Kuhn, Yarin Gal, and Sebastian Farquhar. 2023. Semantic uncertainty: Linguistic invariances for uncertainty estimation in natural language generation. Preprint, arXiv:2302.09664. find
  20. Balaji Lakshminarayanan, Alexander Pritzel, and Charles Blundell. 2017. Simple and scalable predictive uncertainty estimation using deep ensembles. In Advances in Neural Information Processing Systems, volume 30. Curran Associates, Inc. find
  21. Tao Lei, Regina Barzilay, and Tommi Jaakkola. 2016. Rationalizing neural predictions. In Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing, pages 107–117, Austin, Texas. Association for Computational Linguistics.
  22. Isaac Levi. 1980. The Enterprise of Knowledge. MIT Press. find
  23. Josh Magnus Ludan, Qing Lyu, Yue Yang, Liam Dugan, Mark Yatskar, and Chris Callison-Burch. 2024. Interpretable-by-design text understanding with iteratively generated concept bottleneck. Preprint, arXiv:2310.19660. find
  24. Scott M Lundberg and Su-In Lee. 2017. A unified approach to interpreting model predictions. In Advances in Neural Information Processing Systems, volume 30. Curran Associates, Inc.
  25. Thomas Mortier, Eyke Hüllermeier, Krzysztof Dem-bczyński, and Willem Waegeman. 2022. Set-valued prediction in hierarchical classification with constrained representation complexity. In Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, volume 180 of Proceedings o… find
  26. Intelligence, volume 216 of Proceedings of Machine Learning Research, pages 1795–1804. PMLR. find
  27. Murat Sensoy, Lance Kaplan, and Melih Kandemir. 2018. Evidential deep learning to quantify classification uncertainty. In Advances in Neural Information Processing Systems, volume 31. Curran Associates, Inc. find
  28. Mohammad Hossein Shaker and Eyke Hüllermeier. 2020. Aleatoric and epistemic uncertainty with random forests. Preprint, arXiv:2001.00893. — [arXiv:2001.00893](https://arxiv.org/abs/2001.00893) find
  29. Chung-En Sun, Tuomas Oikarinen, Berk Ustun, and Tsui-Wei Weng. 2025. Concept bottleneck large language models. Preprint, arXiv:2412.07992. — [arXiv:2412.07992](https://arxiv.org/abs/2412.07992) find
  30. Mukund Sundararajan, Ankur Taly, and Qiqi Yan. 2017. Axiomatic attribution for deep networks. Preprint, arXiv:1703.01365. find
  31. Dennis Ulmer. 2024. On uncertainty in natural language processing. Preprint, arXiv:2410.03446. — [arXiv:2410.03446](https://arxiv.org/abs/2410.03446) find
  32. P. Walley. 1991. Statistical Reasoning with Imprecise Probabilities. Chapman & Hall/CRC Monographs on Statistics & Applied Probability. Taylor & Francis. find
  33. Sarah Wiegreffe and Yuval Pinter. 2019. Attention is not not explanation. In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP), pages 11–20, Hong Kong, China. Association for…
  34. Yijun Xiao and William Yang Wang. 2019. Quantifying uncertainties in natural language processing tasks. Proceedings of the AAAI Conference on Artificial Intelligence, 33(01):7322–7329. find
  35. Marco Zaffalon, Giorgio Corani, and Denis Mauá. 2012. Evaluating credal classifiers by utility-discounted predictive accuracy. International Journal of Approximate Reasoning, 53(8):1282–1301. Imprecise Probability: Theories and Applications (ISIPTA’11). find
  36. Marco Tulio Ribeiro, Sameer Singh, and Carlos Guestrin. 2016. "why should i trust you?": Explaining the predictions of any classifier. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’16, page 1135–1144, New York, NY, USA. Association for Co…
  37. Yusuf Sale, Michele Caprio, and Eyke Hüllermeier. 2023. Is the volume of a credal set a good measure for epistemic uncertainty? In Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial *Table 8: Complete mathematical notation for the CREDENCE framework.* Symbol Type Section §3 §3 §… find
  38. CREDENCE: Ensemble Components H N (k) [0, 1] p h r h N Number of ensemble heads (default: 5) Probability for concept k predicted by head h LoRA rank for head h (varies across heads: 4, 8, 16, 32, 64) §3.1 §3.1 App. B CREDENCE: Aleatoric Uncertainty (k) [0, 1] σ θ Predicted aleatoric uncertainty (amb… find

Updated

↑ back to top

This page in Markdown → https://md.research.elamur.ai/free/en/papers/mukherjee-2026-credal-concept-bottleneck-models-epistemic/