# Controllable Concept Bottleneck Models

arXiv: https://arxiv.org/abs/2601.00451 · HTML: https://mlsanity.com/paper/2601.00451/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 65 references that are in the map.
- First posted on arXiv 1 Jan 2026.

## Builds on (most cited first, 30 of 45)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [A Survey on Multimodal Large Language Models](https://mlsanity.com/paper/2306.13549/) (2023)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (2019)
- [Remember What You Want to Forget: Algorithms for Machine Unlearning](https://mlsanity.com/paper/2103.03279/) (2021)
- [Post-hoc Concept Bottleneck Models](https://mlsanity.com/paper/2205.15480/) (2022)
- [Label-Free Concept Bottleneck Models](https://mlsanity.com/paper/2304.06129/) (2023)
- [Unrolling SGD: Understanding Factors Influencing Machine Unlearning](https://mlsanity.com/paper/2109.13398/) (2021)
- [Approximate Data Deletion from Machine Learning Models](https://mlsanity.com/paper/2002.10077/) (2020)
- [Opportunities and Challenges in Explainable Artificial Intelligence (XAI): A Survey](https://mlsanity.com/paper/2006.11371/) (2020)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [Machine Unlearning of Features and Labels](https://mlsanity.com/paper/2108.11577/) (2021)
- [Forgetting Outside the Box: Scrubbing Deep Networks of Information Accessible from Input-Output Observations](https://mlsanity.com/paper/2003.02960/) (2020)
- [Mixed-Privacy Forgetting in Deep Networks](https://mlsanity.com/paper/2012.13431/) (2020)
- [DeltaGrad: Rapid retraining of machine learning models](https://mlsanity.com/paper/2006.14755/) (2020)
- [Fast Approximate Natural Gradient Descent in a Kronecker-factored Eigenbasis](https://mlsanity.com/paper/1806.03884/) (2018)
- [Explaining Black Box Predictions and Unveiling Data Artifacts through Influence Functions](https://mlsanity.com/paper/2005.06676/) (2020)
- [Graph Unlearning](https://mlsanity.com/paper/2103.14991/) (2021)
- [Machine Unlearning for Random Forests](https://mlsanity.com/paper/2009.05567/) (2020)
- [DataInf: Efficiently Estimating Data Influence in LoRA-tuned LLMs and Diffusion Models](https://mlsanity.com/paper/2310.00902/) (2023)
- [FastIF: Scalable Influence Functions for Efficient Model Interpretation and Debugging](https://mlsanity.com/paper/2012.15781/) (2020)
- [An LLM can Fool Itself: A Prompt-Based Adversarial Attack](https://mlsanity.com/paper/2310.13345/) (2023)
- [Low-Cost High-Power Membership Inference Attacks](https://mlsanity.com/paper/2312.03262/) (2023)
- [Probabilistic Concept Bottleneck Models](https://mlsanity.com/paper/2306.01574/) (2023)
- [Understanding the Origins of Bias in Word Embeddings](https://mlsanity.com/paper/1810.03611/) (2018)
- [Deep Unlearning via Randomized Conditionally Independent Hessians](https://mlsanity.com/paper/2204.07655/) (2022)

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

- [Matryoshka Concept Bottleneck Models](https://mlsanity.com/paper/2605.20612/) (2026)
- [Bayesian Gated Non-Negative Contrastive Learning](https://mlsanity.com/paper/2605.28441/) (2026)

## Abstract (arXiv)

Concept Bottleneck Models (CBMs) have garnered much attention for their ability to elucidate the prediction process through a human-understandable concept layer. However, most previous studies focused on static scenarios where the data and concepts are assumed to be fixed and clean. In real-world applications, deployed models require continuous maintenance: we often need to remove erroneous or sensitive data (unlearning), correct mislabeled concepts, or incorporate newly acquired samples (incremental learning) to adapt to evolving environments. Thus, deriving efficient editable CBMs without retraining from scratch remains a significant challenge, particularly in large-scale applications. To address these challenges, we propose Controllable Concept Bottleneck Models (CCBMs). Specifically, CCBMs support three granularities of model editing: concept-label-level, concept-level, and data-level, the latter of which encompasses both data removal and data addition. CCBMs enjoy mathematically rigorous closed-form approximations derived from influence functions that obviate the need for retraining. Experimental results demonstrate the efficiency and adaptability of our CCBMs, affirming their practical value in enabling dynamic and trustworthy CBMs.