# A Unifying Framework of Concept-based Explainable AI with Completeness Guarantees

arXiv: https://arxiv.org/abs/2609.34750 · HTML: https://mlsanity.com/paper/2609.34750/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 32 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 26 of 26)

- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [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)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Language in a Bottle: Language Model Guided Concept Bottlenecks for Interpretable Image Classification](https://mlsanity.com/paper/2211.11158/) (2022)
- [Post-hoc Concept Bottleneck Models](https://mlsanity.com/paper/2205.15480/) (2022)
- [Label-Free Concept Bottleneck Models](https://mlsanity.com/paper/2304.06129/) (2023)
- [On Completeness-aware Concept-Based Explanations in Deep Neural Networks](https://mlsanity.com/paper/1910.07969/) (2019)
- [Neural Prototype Trees for Interpretable Fine-grained Image Recognition](https://mlsanity.com/paper/2012.02046/) (2020)
- [Explainable Artificial Intelligence: Understanding, Visualizing and Interpreting Deep Learning Models](https://mlsanity.com/paper/1708.08296/) (2017)
- [Scaling Monosemanticity: Extracting Interpretable Features from Claude 3 Sonnet](https://mlsanity.com/paper/2605.29358/) (2026)
- [CRAFT: Concept Recursive Activation FacTorization for Explainability](https://mlsanity.com/paper/2211.10154/) (2022)
- [From Attribution Maps to Human-Understandable Explanations through Concept Relevance Propagation](https://mlsanity.com/paper/2206.03208/) (2022)
- [Net2Vec: Quantifying and Explaining how Concepts are Encoded by Filters in Deep Neural Networks](https://mlsanity.com/paper/1801.03454/) (2018)
- [SAEBench: A Comprehensive Benchmark for Sparse Autoencoders in Language Model Interpretability](https://mlsanity.com/paper/2503.09532/) (2025)
- [Invertible Concept-based Explanations for CNN Models with Non-negative Concept Activation Vectors](https://mlsanity.com/paper/2006.15417/) (2020)
- [A Holistic Approach to Unifying Automatic Concept Extraction and Concept Importance Estimation](https://mlsanity.com/paper/2306.07304/) (2023)
- [Concept-based Explainable Artificial Intelligence: A Survey](https://mlsanity.com/paper/2312.12936/) (2023)
- [Concept Activation Regions: A Generalized Framework For Concept-Based Explanations](https://mlsanity.com/paper/2209.11222/) (2022)
- [Multi-dimensional concept discovery (MCD): A unifying framework with completeness guarantees](https://mlsanity.com/paper/2301.11911/) (2023)
- [Evaluating Readability and Faithfulness of Concept-based Explanations](https://mlsanity.com/paper/2404.18533/) (2024)
- [ConSim: Measuring Concept-Based Explanations' Effectiveness with Automated Simulatability](https://mlsanity.com/paper/2501.05855/) (2025)
- [FACE: Faithful Automatic Concept Extraction](https://mlsanity.com/paper/2510.11675/) (2025)
- [Towards Human-Understandable Multi-Dimensional Concept Discovery](https://mlsanity.com/paper/2503.18629/) (2025)
- [Subspace-Aware Sparse Autoencoders for Effective Mechanistic Interpretability](https://mlsanity.com/paper/2606.06333/) (2026)

## Abstract (arXiv)

Concept-based explanations describe neural network predictions through human-understandable properties of inputs called concepts. The field encompasses approaches that differ in how they define and represent concepts and connect them to model predictions. We introduce a theoretical framework that describes these approaches in a common mathematical language and supports a shared analysis of their properties. For concept discovery, which identifies concepts automatically within a latent space of a trained model, we employ a concept autoencoder view. An encoder extracts concept representations from the model's latent space, and a decoder uses them to reconstruct the original latent representation. The autoencoder's reconstruction error measures how accurately its decoder recovers the original latent representation. We revisit model completeness: how well the concepts can reproduce the model's outputs. We show that model incompleteness of the concepts can be bounded by the autoencoder's reconstruction error. The autoencoder view also provides a common way to define individual concept attributions, which measure each concept's contribution to a prediction. We establish when these attributions sum to the model's prediction, and bound the discrepancy otherwise, thus providing attribution completeness guarantees.