# Concept activation vectors: a unifying view and adversarial attacks

arXiv: https://arxiv.org/abs/2509.22755 · HTML: https://mlsanity.com/paper/2509.22755/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 19 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Acquisition of Chess Knowledge in AlphaZero](https://mlsanity.com/paper/2111.09259/) (2021)
- [Random Matrix Theory Proves that Deep Learning Representations of GAN-data Behave as Gaussian Mixtures](https://mlsanity.com/paper/2001.08370/) (2020)
- [Bridging the Human-AI Knowledge Gap: Concept Discovery and Transfer in AlphaZero](https://mlsanity.com/paper/2310.16410/) (2023)
- [Navigating Neural Space: Revisiting Concept Activation Vectors to Overcome Directional Divergence](https://mlsanity.com/paper/2202.03482/) (2022)
- [From Hope to Safety: Unlearning Biases of Deep Models via Gradient Penalization in Latent Space](https://mlsanity.com/paper/2308.09437/) (2023)
- [A Large Dimensional Analysis of Least Squares Support Vector Machines](https://mlsanity.com/paper/1701.02967/) (2017)
- [FastCAV: Efficient Computation of Concept Activation Vectors for Explaining Deep Neural Networks](https://mlsanity.com/paper/2505.17883/) (2025)
- [High-Dimensional Analysis of Bootstrap Ensemble Classifiers](https://mlsanity.com/paper/2505.14587/) (2025)

## Built on by (most cited first, 1 of 1)

- [α-TCAV: A Unified Framework for Testing with Concept Activation Vectors](https://mlsanity.com/paper/2605.15688/) (2026)

## Abstract (arXiv)

Concept Activation Vectors (CAVs) are a tool from explainable AI, offering a promising approach for understanding how human-understandable concepts are encoded in a model's latent spaces. They are computed from hidden-layer activations of inputs belonging either to a concept class or to non-concept examples. Adopting a probabilistic perspective, the distribution of the (non-)concept inputs induces a distribution over the CAV, making it a random vector in the latent space. This enables us to derive mean and covariance for different types of CAVs, leading to a unified theoretical view. This probabilistic perspective also reveals a potential vulnerability: CAVs can strongly depend on the rather arbitrary non-concept distribution, a factor largely overlooked in prior work. We illustrate this with a simple yet effective adversarial attack, underscoring the need for a more systematic study.