# CHOQOLATE: Organizing Concept Bottleneck Latent Spaces with Choquet Integrals

arXiv: https://arxiv.org/abs/2609.37786 · HTML: https://mlsanity.com/paper/2609.37786/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in VLM benchmarks and visual reasoning, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 29 of its 53 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Placed in

- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 29 of 29)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (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)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [When and why vision-language models behave like bags-of-words, and what to do about it?](https://mlsanity.com/paper/2210.01936/) (2022)
- [The Platonic Representation Hypothesis](https://mlsanity.com/paper/2405.07987/) (2024)
- [Last Layer Re-Training is Sufficient for Robustness to Spurious Correlations](https://mlsanity.com/paper/2204.02937/) (2022)
- [Language in a Bottle: Language Model Guided Concept Bottlenecks for Interpretable Image Classification](https://mlsanity.com/paper/2211.11158/) (2022)
- [Debiasing Vision-Language Models via Biased Prompts](https://mlsanity.com/paper/2302.00070/) (2023)
- [Learning Multi-Level Features with Matryoshka Sparse Autoencoders](https://mlsanity.com/paper/2503.17547/) (2025)
- [Interpreting CLIP with Sparse Linear Concept Embeddings (SpLiCE)](https://mlsanity.com/paper/2402.10376/) (2024)
- [Does CLIP Bind Concepts? Probing Compositionality in Large Image Models](https://mlsanity.com/paper/2212.10537/) (2022)
- [Discover-then-Name: Task-Agnostic Concept Bottlenecks via Automated Concept Discovery](https://mlsanity.com/paper/2407.14499/) (2024)
- [Places: An Image Database for Deep Scene Understanding](https://mlsanity.com/paper/1610.02055/) (2016)
- [Identifying Interpretable Subspaces in Image Representations](https://mlsanity.com/paper/2307.10504/) (2023)
- [Coarse-to-Fine Concept Bottleneck Models](https://mlsanity.com/paper/2310.02116/) (2023)
- [If Concept Bottlenecks are the Question, are Foundation Models the Answer?](https://mlsanity.com/paper/2504.19774/) (2025)
- [CLIP-QDA: An Explainable Concept Bottleneck Model](https://mlsanity.com/paper/2312.00110/) (2023)
- [A k-additive Choquet integral-based approach to approximate the SHAP values for local interpretability in machine learning](https://mlsanity.com/paper/2211.02166/) (2022)
- [Benchmarking XAI Explanations with Human-Aligned Evaluations](https://mlsanity.com/paper/2411.02470/) (2024)
- [Enabling Explainable Fusion in Deep Learning with Fuzzy Integral Neural Networks](https://mlsanity.com/paper/1905.04394/) (2019)
- [Text Descriptions are Compressive and Invariant Representations for Visual Learning](https://mlsanity.com/paper/2307.04317/) (2023)
- [Enhancing Concept Localization in CLIP-based Concept Bottleneck Models](https://mlsanity.com/paper/2510.07115/) (2025)
- [Representation-Level Counterfactual Calibration for Debiased Zero-Shot Recognition](https://mlsanity.com/paper/2510.26466/) (2025)
- [Hoeffding Concept Bottleneck Models with Applications to Overhead Images](https://mlsanity.com/paper/2606.00082/) (2026)

## Abstract (arXiv)

Concept Bottleneck Models (CBMs) built on vision-language models such as CLIP represent a latent space as human-understandable concepts. These representations are unfaithful: related concepts are entangled, so individual scores do not reflect their intended meaning. We propose CHOQOLATE, an interpretable-by-design layer based on 2-additive Choquet integrals, which merges correlated concepts into compact nodes. Across four datasets, CHOQOLATE achieves a favorable accuracy-interpretability trade-off, with weight-sparse and semantically coherent nodes. A closed-form gradient derivation, backed by experiments, explains why Choquet layers drive this organization without explicit supervision. Choquet weights also map directly to Shapley values, which enables test-time intervention. On standard bias-mitigation benchmarks, suppressing spurious concepts after training performs on par with methods that require group annotations or retraining, while needing neither.