mlsanityData to 14 Oct 2026

SmoothHess: ReLU Network Feature Interactions via Stein's Lemma

arXiv 2311.00858 ↗First posted 1 Nov 2023cs.LGcited by 5

Not on the map. Why?

Abstract (arXiv)

Several recent methods for interpretability model feature interactions by looking at the Hessian of a neural network. This poses a challenge for ReLU networks, which are piecewise-linear and thus have a zero Hessian almost everywhere. We propose SmoothHess, a method of estimating second-order interactions through Stein's Lemma. In particular, we estimate the Hessian of the network convolved with a Gaussian through an efficient sampling algorithm, requiring only network gradient calls. SmoothHess is applied post-hoc, requires no modifications to the ReLU network architecture, and the extent of smoothing can be controlled explicitly. We provide a non-asymptotic bound on the sample complexity of our estimation procedure. We validate the superior ability of SmoothHess to capture interactions on benchmark datasets and a real-world medical spirometry dataset.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 51 of its 94 references that are in the map. First posted on arXiv 1 Nov 2023.

Builds on

51 of 94 references.

References · 51

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,364
  3. 2017A Unified Approach to Interpreting Model Predictionscited by 6,555
  4. 2016"Why Should I Trust You?": Explaining the Predictions of Any Classifiercited by 5,070
  5. 2016SGDR: Stochastic Gradient Descent with Warm Restartscited by 5,045
  6. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,349
  7. 2017Axiomatic Attribution for Deep Networkscited by 3,384
  8. 2021Convex optimizationcited by 2,515
  9. 2015Learning Deep Features for Discriminative Localizationcited by 2,436
  10. 2013Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Mapscited by 2,371
  11. 2017SmoothGrad: removing noise by adding noisecited by 1,109
  12. 2019Skin Lesion Analysis Toward Melanoma Detection 2018: A Challenge Hosted by the International Skin Imaging Collaboration (ISIC)cited by 669
38 more
  1. 2017Interpretation of Neural Networks is Fragilecited by 444
  2. 2014On the Number of Linear Regions of Deep Neural Networkscited by 381
  3. 2018Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problemcited by 323
  4. 2018Regularisation of Neural Networks by Enforcing Lipschitz Continuitycited by 314
  5. 2018On the Robustness of Interpretability Methodscited by 314
  6. 2016On the Expressive Power of Deep Neural Networkscited by 306
  7. 2019Explanations can be manipulated and geometry is to blamecited by 216
  8. 2017Bounding and Counting Linear Regions of Deep Neural Networkscited by 161
  9. 2019Deep ReLU Networks Have Surprisingly Few Activation Patternscited by 161
  10. 2019The Shapley Taylor Interaction Indexcited by 143
  11. 2017On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learningcited by 142
  12. 2017Procedural Content Generation via Machine Learning (PCGML)cited by 137
  13. 2020Reliable Post hoc Explanations: Modeling Uncertainty in Explainabilitycited by 125
  14. 2019Smooth Grad-CAM++: An Enhanced Inference Level Visualization Technique for Deep Convolutional Neural Network Modelscited by 118
  15. 2020Explaining Explanations: Axiomatic Feature Interactions for Deep Networkscited by 103
  16. 2019CXPlain: Causal Explanations for Model Interpretation under Uncertaintycited by 98
  17. 2017Detecting Statistical Interactions from Neural Network Weightscited by 80
  18. 2020How does this interaction affect me? Interpretable attribution for feature interactionscited by 73
  19. 2021Does Your Dermatology Classifier Know What It Doesn't Know? Detecting the Long-Tail of Unseen Conditionscited by 68
  20. 2018Mad Max: Affine Spline Insights into Deep Learningcited by 55
  21. 2020Evaluations and Methods for Explanation through Robustness Analysiscited by 51
  22. 2021Towards the Unification and Robustness of Perturbation and Gradient Based Explanationscited by 47
  23. 2020Towards Robust Explanations for Deep Neural Networkscited by 43
  24. 2020Smoothed Geometry for Robust Attributioncited by 38
  25. 2020Feature Interaction Interpretability: A Case for Explaining Ad-Recommendation Systems via Neural Interaction Detectioncited by 32
  26. 2019Understanding Impacts of High-Order Loss Approximations and Features in Deep Learning Interpretationcited by 22
  27. 2020Feature Removal Is a Unifying Principle for Model Explanation Methodscited by 21
  28. 2019Stein's Lemma for the Reparameterization Trick with Exponential Family Mixturescited by 18
  29. 2021Deep ReLU Networks Preserve Expected Lengthcited by 17
  30. 2023Explanations of Black-Box Models based on Directional Feature Interactionscited by 15
  31. 2021Context-Aware Legal Citation Recommendation using Deep Learningcited by 12
  32. 2022Match Cutting: Finding Cuts with Smooth Visual Transitionscited by 12
  33. 2020Explaining Local, Global, And Higher-Order Interactions In Deep Learningcited by 8
  34. 2021Hessian Estimation via Stein's Identity in Black-Box Problemscited by 8
  35. 2019Learning Global Pairwise Interactions with Bayesian Neural Networkscited by 6
  36. 2015Newton-Stein Method: An optimization method for GLMs via Stein's Lemmacited by 3
  37. 2020Hierarchical Verification for Adversarial Robustnesscited by 3
  38. 2023Active Learning for Classifying 2D Grid-Based Level Completabilitycited by 2

50 most cited of 51 All 51 (JSON)

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 3; 2026: 1.

5 papers.

  1. 2024Axiomatic Explainer Globalness via Optimal Transportcited by 2
  2. 2025Leveraging Machine Unlearning for Cost-Efficient Preference Alignmentcited by 2
  3. 2025OrdShap: Feature Position Importance for Sequential Black-Box Modelscited by 0
  4. 2025Feature-Function Curvature Analysis: A Geometric Framework for Explaining Differentiable Modelscited by 0
  5. 2026Local Stability and Gaussian Smoothing of Quantized Neural Networkscited by 0