# There Was Never a Bottleneck in Concept Bottleneck Models

arXiv: https://arxiv.org/abs/2506.04877 · HTML: https://mlsanity.com/paper/2506.04877/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 60 references that are in the map.
- First posted on arXiv 5 Jun 2025.

## Builds on (most cited first, 30 of 43)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [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)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [DriveGPT4: Interpretable End-to-end Autonomous Driving via Large Language Model](https://mlsanity.com/paper/2310.01412/) (2023)
- [On Mutual Information Maximization for Representation Learning](https://mlsanity.com/paper/1907.13625/) (2019)
- [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)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [Emergence of Invariance and Disentanglement in Deep Representations](https://mlsanity.com/paper/1706.01350/) (2017)
- [A Theory of Usable Information Under Computational Constraints](https://mlsanity.com/paper/2002.10689/) (2020)
- [Information Dropout: Learning Optimal Representations Through Noisy Computation](https://mlsanity.com/paper/1611.01353/) (2016)
- [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)
- [Robustly Disentangled Causal Mechanisms: Validating Deep Representations for Interventional Robustness](https://mlsanity.com/paper/1811.00007/) (2018)
- [Interpretable Learning for Self-Driving Cars by Visualizing Causal Attention](https://mlsanity.com/paper/1703.10631/) (2017)
- [Learning Deep Disentangled Embeddings with the F-Statistic Loss](https://mlsanity.com/paper/1802.05312/) (2018)
- [On the Transfer of Inductive Bias from Simulation to the Real World: a New Disentanglement Dataset](https://mlsanity.com/paper/1906.03292/) (2019)
- [The Conditional Entropy Bottleneck](https://mlsanity.com/paper/2002.05379/) (2020)
- [GlanceNets: Interpretabile, Leak-proof Concept-based Models](https://mlsanity.com/paper/2205.15612/) (2022)
- [To Compress or Not to Compress- Self-Supervised Learning and Information Theory: A Review](https://mlsanity.com/paper/2304.09355/) (2023)
- [VLG-CBM: Training Concept Bottleneck Models with Vision-Language Guidance](https://mlsanity.com/paper/2408.01432/) (2024)
- [A Closer Look at the Intervention Procedure of Concept Bottleneck Models](https://mlsanity.com/paper/2302.14260/) (2023)

## Built on by (most cited first, 8 of 8)

- [In-Context Learning Operates as Concept Subspace Learning](https://mlsanity.com/paper/2605.18830/) (2026)
- [The Standard Interpretable Model: A general theory of interpretable machine learning to deductively design interpretable methods using Lagrangian mechanics](https://mlsanity.com/paper/2606.12289/) (2026)
- [Exploring Concept Subspace for Self-explainable Text-Attributed Graph Learning](https://mlsanity.com/paper/2604.11986/) (2026)
- [In Defense of Information Leakage in Concept-based Models](https://mlsanity.com/paper/2606.10669/) (2026)
- [S2COPE: Self-Supervised Concept Discovery via Preference Learning](https://mlsanity.com/paper/2606.14586/) (2026)
- [Assessing Reliability of Symbol Detection in Concept Bottleneck Models](https://mlsanity.com/paper/2606.16535/) (2026)
- [On the Faithfulness of Post-Hoc Concept Bottleneck Models](https://mlsanity.com/paper/2606.30498/) (2026)
- [Loss Invariance Determines What Concept Layers Encode: Volume Grounding in Echocardiography](https://mlsanity.com/paper/2607.25748/) (2026)

## Abstract (arXiv)

Deep learning representations are often difficult to interpret, which can hinder their deployment in sensitive applications. Concept Bottleneck Models (CBMs) have emerged as a promising approach to mitigate this issue by learning representations that support target task performance while ensuring that each component predicts a concrete concept from a predefined set. In this work, we argue that CBMs do not impose a true bottleneck: the fact that a component can predict a concept does not guarantee that it encodes only information about that concept. This shortcoming raises concerns regarding interpretability and the validity of intervention procedures. To overcome this limitation, we propose Minimal Concept Bottleneck Models (MCBMs), which incorporate an Information Bottleneck (IB) objective to constrain each representation component to retain only the information relevant to its corresponding concept. This IB is implemented via a variational regularization term added to the training loss. As a result, MCBMs yield more interpretable representations, support principled concept-level interventions, and remain consistent with probability-theoretic foundations.