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Understanding Deep Convolutional Networks

arXiv 1601.04920 ↗First posted 19 Jan 2016stat.ML cs.CV cs.LGcited by 76

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Abstract (arXiv)

Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities. A mathematical framework is introduced to analyze their properties. Computations of invariants involve multiscale contractions, the linearization of hierarchical symmetries, and sparse separations. Applications are discussed.

Key facts. Cited by 76 papers in the map (data through 14 Oct 2026). First posted on arXiv 19 Jan 2016.

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Citing papers per year: 2021: 18; 2022: 25; 2023: 9; 2024: 11; 2025: 9; 2026: 4.

76 papers.

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  1. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 608
  2. 2022Data-driven emergence of convolutional structure in neural networkscited by 29
  3. 2023Physics-Informed Computer Vision: A Review and Perspectivescited by 28
  4. 2022Learning sparse features can lead to overfitting in neural networkscited by 23
  5. 2021Theory of Deep Convolutional Neural Networks III: Approximating Radial Functionscited by 22
  6. 2021Low-Fidelity End-to-End Video Encoder Pre-training for Temporal Action Localizationcited by 20
  7. 2021Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNscited by 18
  8. 2022Automatic Data Augmentation via Invariance-Constrained Learningcited by 17
  9. 2021Scaling Properties of Deep Residual Networkscited by 16
  10. 2021Parametric Scattering Networkscited by 16
  11. 2021Relative stability toward diffeomorphisms indicates performance in deep netscited by 12
  12. 2024High-dimensional learning of narrow neural networkscited by 12
38 more
  1. 2021On the Regularity of Attentioncited by 11
  2. 2022Wavelet Conditional Renormalization Groupcited by 11
  3. 2023Covariance properties under natural image transformations for the generalized Gaussian derivative model for visual receptive fieldscited by 8
  4. 2022Tailoring Self-Supervision for Supervised Learningcited by 7
  5. 2024How Deep Networks Learn Sparse and Hierarchical Data: the Sparse Random Hierarchy Modelcited by 7
  6. 2022Statistical Hypothesis Testing Based on Machine Learning: Large Deviations Analysiscited by 6
  7. 2022Normalization effects on deep neural networkscited by 6
  8. 2021Sparsity in long-time control of neural ODEscited by 5
  9. 2022Convolutional Neural Networks for Spherical Signal Processing via Spherical Haar Tight Frameletscited by 5
  10. 2022Decision boundaries and convex hulls in the feature space that deep learning functions learn from imagescited by 5
  11. 2022Equilibrium Aggregation: Encoding Sets via Optimizationcited by 5
  12. 2022Generalized Permutants and Graph GENEOscited by 5
  13. 2022How deep convolutional neural networks lose spatial information with trainingcited by 5
  14. 2023Fairness in Machine Learning meets with Equity in Healthcarecited by 5
  15. 2022GENEOnet: A new machine learning paradigm based on Group Equivariant Non-Expansive Operators. An application to protein pocket detectioncited by 4
  16. 2023Riesz feature representation: scale equivariant scattering network for classification taskscited by 4
  17. 2024Spectral Norm of Convolutional Layers with Circular and Zero Paddingscited by 4
  18. 2024Approximation properties relative to continuous scale space for hybrid discretizations of Gaussian derivative operatorscited by 4
  19. 2024A novel approach to graph distinction through GENEOs and permutantscited by 4
  20. 2021On the geometric and Riemannian structure of the spaces of group equivariant non-expansive operatorscited by 3
  21. 2021Co-domain Symmetry for Complex-Valued Deep Learningcited by 3
  22. 2022Taking ROCKET on an Efficiency Mission: Multivariate Time Series Classification with LightWaveScited by 3
  23. 2022On Non-Linear operators for Geometric Deep Learningcited by 3
  24. 2022Asymptotic Analysis of Deep Residual Networkscited by 3
  25. 2024Reimagining Linear Probing: Kolmogorov-Arnold Networks in Transfer Learningcited by 3
  26. 2022A Note on the Regularity of Images Generated by Convolutional Neural Networkscited by 2
  27. 2022On the Shift Invariance of Max Pooling Feature Maps in Convolutional Neural Networkscited by 2
  28. 2023Bigger is not Always Better: The Effect of Context Size on Speech Pre-Trainingcited by 2
  29. 2024Bayesian identification of nonseparable Hamiltonians with multiplicative noise using deep learning and reduced-order modelingcited by 2
  30. 2025The Riemannian Geometry Associated to Gradient Flows of Linear Convolutional Networkscited by 2
  31. 2021Towards glass-box CNNscited by 1
  32. 2021Maximal function pooling with applicationscited by 1
  33. 2021Mitigating severe over-parameterization in deep convolutional neural networks through forced feature abstraction and compression with an entropy-based heuristiccited by 1
  34. 2022Multi-Resolution Online Deterministic Annealing: A Hierarchical and Progressive Learning Architecturecited by 1
  35. 2022VC dimensions of group convolutional neural networkscited by 1
  36. 2023SSN: Stockwell Scattering Network for SAR Image Change Detectioncited by 1
  37. 2024Symmetry group based domain decomposition to enhance physics-informed neural networks for solving partial differential equationscited by 1
  38. 2024Energy Propagation in Scattering Convolution Networks Can Be Arbitrarily Slowcited by 1

50 most cited of 76 All 76 (JSON)