mlsanityData to 7 Oct 2026

Concept Gradient: Concept-based Interpretation Without Linear Assumption

arXiv 2208.14966 ↗First posted 31 Aug 2022cs.LGcited by 20

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Abstract (arXiv)

Concept-based interpretations of black-box models are often more intuitive for humans to understand. The most widely adopted approach for concept-based interpretation is Concept Activation Vector (CAV). CAV relies on learning a linear relation between some latent representation of a given model and concepts. The linear separability is usually implicitly assumed but does not hold true in general. In this work, we started from the original intent of concept-based interpretation and proposed Concept Gradient (CG), extending concept-based interpretation beyond linear concept functions. We showed that for a general (potentially non-linear) concept, we can mathematically evaluate how a small change of concept affecting the model's prediction, which leads to an extension of gradient-based interpretation to the concept space. We demonstrated empirically that CG outperforms CAV in both toy examples and real world datasets.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). Builds on 34 of its 54 references that are in the map. First posted on arXiv 31 Aug 2022.

Builds on

34 of 54 references.

References · 34

  1. 2017Axiomatic Attribution for Deep Networkscited by 3,350
  2. 2013Visualizing and Understanding Convolutional Networkscited by 2,278
  3. 2017Understanding Black-box Predictions via Influence Functionscited by 1,714
  4. 2017Learning Important Features Through Propagating Activation Differencescited by 1,454
  5. 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,324
  6. 2017Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)cited by 1,309
  7. 2017SmoothGrad: removing noise by adding noisecited by 1,097
  8. 2020Concept Bottleneck Modelscited by 1,022
  9. 2018RISE: Randomized Input Sampling for Explanation of Black-box Modelscited by 825
  10. 2018This Looks Like That: Deep Learning for Interpretable Image Recognitioncited by 731
  11. 2020Estimating Training Data Influence by Tracing Gradient Descentcited by 565
  12. 2017Zero-Shot Learning -- A Comprehensive Evaluation of the Good, the Bad and the Uglycited by 536
22 more
  1. 2019Counterfactual Visual Explanationscited by 312
  2. 2019On the (In)fidelity and Sensitivity for Explanationscited by 309
  3. 2018Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negativescited by 261
  4. 2017Real Time Image Saliency for Black Box Classifierscited by 246
  5. 2019On Completeness-aware Concept-Based Explanations in Deep Neural Networkscited by 239
  6. 2019FACE: Feasible and Actionable Counterfactual Explanationscited by 232
  7. 2020Concept Whitening for Interpretable Image Recognitioncited by 225
  8. 2018Representer Point Selection for Explaining Deep Neural Networkscited by 187
  9. 2017Visualizing Deep Neural Network Decisions: Prediction Difference Analysiscited by 166
  10. 2019Explaining Classifiers with Causal Concept Effect (CaCE)cited by 135
  11. 2019Towards Realistic Individual Recourse and Actionable Explanations in Black-Box Decision Making Systemscited by 128
  12. 2018Grounding Visual Explanationscited by 92
  13. 2014Falling Rule Listscited by 58
  14. 2020Evaluations and Methods for Explanation through Robustness Analysiscited by 51
  15. 2018Interpreting Black Box Predictions using Fisher Kernelscited by 48
  16. 2021DISSECT: Disentangled Simultaneous Explanations via Concept Traversalscited by 37
  17. 2018Contrastive Explanations with Local Foil Treescited by 34
  18. 2020Debiasing Concept-based Explanations with Causal Analysiscited by 32
  19. 2021Best of both worlds: local and global explanations with human-understandable conceptscited by 22
  20. 2019EDUCE: Explaining model Decisions through Unsupervised Concepts Extractioncited by 13
  21. 2021Cause and Effect: Hierarchical Concept-based Explanation of Neural Networkscited by 8
  22. 2019Functional Transparency for Structured Data: a Game-Theoretic Approachcited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 3; 2024: 7; 2025: 8; 2026: 1.

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  1. 2022Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Taskcited by 417
  2. 2024Usable XAI: 10 Strategies Towards Exploiting Explainability in the LLM Eracited by 45
  3. 2023Bridging the Human-AI Knowledge Gap: Concept Discovery and Transfer in AlphaZerocited by 41
  4. 2024LG-CAV: Train Any Concept Activation Vector with Language Guidancecited by 9
  5. 2024A survey on Concept-based Approaches For Model Improvementcited by 8
  6. 2024Large Language Models are Interpretable Learnerscited by 7
  7. 2023Selective Concept Models: Permitting Stakeholder Customisation at Test-Timecited by 6
  8. 2024Concept-based Analysis of Neural Networks via Vision-Language Modelscited by 6
  9. 2025Debugging and Runtime Analysis of Neural Networks with VLMs (A Case Study)cited by 3
  10. 2025On The Variability of Concept Activation Vectorscited by 3
  11. 2025Nonparametric Identification of Latent Conceptscited by 3
  12. 2023Explaining Deep Neural Networks for Bearing Fault Detection with Vibration Conceptscited by 2
8 more
  1. 2025Adaptive Diagnostic Reasoning Framework for Pathology with Multimodal Large Language Modelscited by 2
  2. 2024LatentExplainer: Explaining Latent Representations in Deep Generative Models with Multimodal Large Language Modelscited by 1
  3. 2025Concept-Based Mechanistic Interpretability Using Structured Knowledge Graphscited by 1
  4. 2025Concept-Based Interpretability for Toxicity Detectioncited by 1
  5. 2024An Axiomatic Approach to Model-Agnostic Concept Explanationscited by 0
  6. 2025Concept Learning for Cooperative Multi-Agent Reinforcement Learningcited by 0
  7. 2025Probing the Probes: Methods and Metrics for Concept Alignmentcited by 0
  8. 2026Improving Adversarial Robustness of Attribution via Implicit Regularizationcited by 0