# Mixture of Concept Bottleneck Experts

arXiv: https://arxiv.org/abs/2602.02886 · HTML: https://mlsanity.com/paper/2602.02886/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 60 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Builds on (most cited first, 30 of 36)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [The Mythos of Model Interpretability](https://mlsanity.com/paper/1606.03490/) (2016)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Label-Free Concept Bottleneck Models](https://mlsanity.com/paper/2304.06129/) (2023)
- [Zero-Shot Learning -- The Good, the Bad and the Ugly](https://mlsanity.com/paper/1703.04394/) (2017)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Efficient Large Scale Language Modeling with Mixtures of Experts](https://mlsanity.com/paper/2112.10684/) (2021)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [Promises and Pitfalls of Black-Box Concept Learning Models](https://mlsanity.com/paper/2106.13314/) (2021)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [Concept-based Explainable Artificial Intelligence: A Survey](https://mlsanity.com/paper/2312.12936/) (2023)
- [GlanceNets: Interpretabile, Leak-proof Concept-based Models](https://mlsanity.com/paper/2205.15612/) (2022)
- [How do Humans Understand Explanations from Machine Learning Systems? An Evaluation of the Human-Interpretability of Explanation](https://mlsanity.com/paper/1802.00682/) (2018)
- ["Help Me Help the AI": Understanding How Explainability Can Support Human-AI Interaction](https://mlsanity.com/paper/2210.03735/) (2022)
- [Concept Embedding Models: Beyond the Accuracy-Explainability Trade-Off](https://mlsanity.com/paper/2209.09056/) (2022)
- [Interpretable Neural-Symbolic Concept Reasoning](https://mlsanity.com/paper/2304.14068/) (2023)
- [Stochastic Concept Bottleneck Models](https://mlsanity.com/paper/2406.19272/) (2024)
- [CausalVAE: Structured Causal Disentanglement in Variational Autoencoder](https://mlsanity.com/paper/2004.08697/) (2020)
- [Logic Explained Networks](https://mlsanity.com/paper/2108.05149/) (2021)
- [Causal Concept Graph Models: Beyond Causal Opacity in Deep Learning](https://mlsanity.com/paper/2405.16507/) (2024)
- [Fine-grained Visual-textual Representation Learning](https://mlsanity.com/paper/1709.00340/) (2017)
- [Controllable Neural Symbolic Regression](https://mlsanity.com/paper/2304.10336/) (2023)
- [Preferential Mixture-of-Experts: Interpretable Models that Rely on Human Expertise as much as Possible](https://mlsanity.com/paper/2101.05360/) (2021)
- [Interpretable Mixture of Experts](https://mlsanity.com/paper/2206.02107/) (2022)
- [Interpretable Concept-Based Memory Reasoning](https://mlsanity.com/paper/2407.15527/) (2024)

## Built on by (most cited first, 2 of 2)

- [ConceptM3oE: Concept-Guided Multimodal Mixture of Experts for Interpretable Computational Pathology](https://mlsanity.com/paper/2605.24399/) (2026)
- [Graphical Design of Interpretable Architectures](https://mlsanity.com/paper/2608.18936/) (2026)

## Abstract (arXiv)

Concept Bottleneck Models (CBMs) promote interpretability by grounding predictions in human-understandable concepts. However, existing CBMs typically constrain their task predictor to a single expression whose functional form is set a priori, limiting both predictive accuracy and adaptability to diverse user needs. We propose Mixture of Concept Bottleneck Experts (M-CBE), a framework that generalizes existing CBMs along two dimensions: the number of expressions, referred to as experts, employed by the task predictor to map concepts to the task, and the functional form each expression takes, thus exposing an underexplored region of this design space. We investigate this region by instantiating two novel models: Linear M-CBE, which learns a finite set of linear expressions, and Symbolic M-CBE, which leverages symbolic regression to discover expert functions from data subject to user-specified operator vocabularies. Empirical evaluation demonstrates that varying the number of expressions and their functional form provides a robust framework for navigating the accuracy-interpretability trade-off.