FastCAV: Efficient Computation of Concept Activation Vectors for Explaining Deep Neural Networks

Abstract

Concepts such as objects, patterns, and shapes are how humans understand the world. Building on this intuition, concept-based explainability methods aim to study representations learned by deep neural networks in relation to human-understandable concepts. Here, Concept Activation Vectors (CAVs) are an important tool and can identify whether a model learned a concept or not. However, the computational cost and time requirements of existing CAV computation pose a significant challenge, particularly in large-scale, high-dimensional architectures. To address this limitation, we introduce FastCAV, a novel approach that accelerates the extraction of CAVs by up to 63.6× (on average 46.4×). We provide a theoretical foundation for our approach and give concrete assumptions under which it is equivalent to established SVM-based methods. Our empirical results demonstrate that CAVs calculated with FastCAV maintain similar performance while being more efficient and stable. In downstream applications, i.e., concept-based explanation methods, we show that FastCAV can act as a replacement leading to equivalent insights. Hence, our approach enables previously infeasible investigations of deep models, which we demonstrate by tracking the evolution of concepts during model training.

Accelerate CAV-Extraction!

Quantitative Comparison

To empirically compare FastCAV with SVM-based computation, we evaluate a broad spectrum of model architectures trained on ImageNet. We split our investigation into four dimensions: computational time, accuracy, inter-method similarity, and intra-method robustness.

Comparing our approach FastCAV with SVM-based computation. Bold values indicate better results. "N/A" indicates that no results were produced due to the overall computational time exceeding four days. More details can be found in our paper!

Qualitative Comparison

FastCAV can act as a more efficient drop-in replacement for downstream applications of CAVs. Examples include Testing with Concept Activation Vectors (TCAV) or Automatic Concept-based Explanations (ACE).

Testing for Class Relevant Concepts with TCAV

TCAV scores for various GoogleNet layers. We compare the concepts "polka-dotted", "striped", and "zigzagged" for the class ladybug using FastCAV against the established SVM approach. We mark CAVs that are not statistically significant with "*". The insights into the GoogleNet model are consistent between both our approach and the SVM-based method. Nevertheless, we observe lower standard deviations and faster computation speed for FastCAV.

Automatic Concept Discovery with ACE

Comparison of the most salient concepts discovered by ACE using either our FastCAV or the established SVM-CAV. Here, we use class lionfish and display the two most salient concepts. We find the discovered patches between both approaches similar and congruent with the original observation in (Ghorbani et al., 2019).

Tracking CAVs During Training Using FastCAV

FastCAV enables previously infeasible analyses for models with high dimensional activation spaces. To show this, we train a ResNet50 on ImageNet from scratch and track the evolution of learned concepts during training.

We find the learning of concepts aligns with a simultaneous increase in predictive performance, suggesting that the model is learning to recognize and utilize relevant information for predictions. We observe similar trends for specific concept examples, although the results exhibit increased variability across the training steps compared to the average across concepts. Notably, we observe stark increases in average CAV accuracy after each epoch, where the learning rate is reduced during training.

Furthermore, we observe that early and middle layers have a higher likelihood of learning textures compared to later layers, supporting previous findings (Kim et al., 2018; Ghorbani et al., 2019; Bau et al., 2017). Our observations demonstrate that FastCAV can be used to study the learning dynamics of deep neural networks in a more fine-grained manner and for abstract concepts.

BibTeX

If you find our work useful, please consider citing our paper!

      
@inproceedings{schmalwasser2025fastcav,
  title={FastCAV: Efficient Computation of Concept Activation Vectors for Explaining Deep Neural Networks},
  author={Laines Schmalwasser and Niklas Penzel and Joachim Denzler and Julia Niebling},
  booktitle = {Proceedings of the 42nd International Conference on Machine Learning (ICML)},
  year = {2025},
  url={}
}

FastCAV Efficient Computation of Concept Activation Vectors for Explaining Deep Neural Networks