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Norm-Based Capacity Control in Neural Networks

arXiv 1503.00036 ↗First posted 27 Feb 2015cs.LG cs.AI cs.NEcited by 299

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Abstract (arXiv)

We investigate the capacity, convexity and characterization of a general family of norm-constrained feed-forward networks.

Key facts. Cited by 299 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Feb 2015.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 64; 2022: 60; 2023: 47; 2024: 35; 2025: 48; 2026: 45.

299 papers.

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  1. 2021What Makes Multi-modal Learning Better than Single (Provably)cited by 151
  2. 2021Inductive Biases and Variable Creation in Self-Attention Mechanismscited by 144
  3. 2022Leveraging Unlabeled Data to Predict Out-of-Distribution Performancecited by 141
  4. 2021Statistically Meaningful Approximation: a Case Study on Approximating Turing Machines with Transformerscited by 101
  5. 2022Benign Overfitting in Two-layer Convolutional Neural Networkscited by 90
  6. 2022More Than a Toy: Random Matrix Models Predict How Real-World Neural Representations Generalizecited by 87
  7. 2021Information-Theoretic Generalization Bounds for Stochastic Gradient Descentcited by 84
  8. 2021GBK-GNN: Gated Bi-Kernel Graph Neural Networks for Modeling Both Homophily and Heterophilycited by 84
  9. 2022On the Implicit Bias in Deep-Learning Algorithmscited by 84
  10. 2021Model Complexity of Deep Learning: A Surveycited by 64
  11. 2021What Kinds of Functions do Deep Neural Networks Learn? Insights from Variational Spline Theorycited by 60
  12. 2021When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?cited by 57
38 more
  1. 2021Exploring Memorization in Adversarial Trainingcited by 55
  2. 2021Analytic Insights into Structure and Rank of Neural Network Hessian Mapscited by 52
  3. 2021Heavy Tails in SGD and Compressibility of Overparametrized Neural Networkscited by 44
  4. 2023The Implicit Regularization of Dynamical Stability in Stochastic Gradient Descentcited by 44
  5. 2021On the Generalization of Models Trained with SGD: Information-Theoretic Bounds and Implicationscited by 31
  6. 2022Pruning's Effect on Generalization Through the Lens of Training and Regularizationcited by 31
  7. 2021On the statistical complexity of quantum circuitscited by 25
  8. 2021Block Contextual MDPs for Continual Learningcited by 25
  9. 2023Explaining Generalization Power of a DNN Using Interactive Conceptscited by 25
  10. 2021Measuring Generalization with Optimal Transportcited by 24
  11. 2023To grok or not to grok: Disentangling generalization and memorization on corrupted algorithmic datasetscited by 24
  12. 2022Learning sparse features can lead to overfitting in neural networkscited by 23
  13. 2021Formalizing Generalization and Robustness of Neural Networks to Weight Perturbationscited by 22
  14. 2022Non-Vacuous Generalisation Bounds for Shallow Neural Networkscited by 22
  15. 2023Reducing Communication for Split Learning by Randomized Top-k Sparsificationcited by 22
  16. 2024What Do Learning Dynamics Reveal About Generalization in LLM Reasoning?cited by 22
  17. 2021Uniform Generalization Bounds for Overparameterized Neural Networkscited by 21
  18. 2022Approximation bounds for norm constrained neural networks with applications to regression and GANscited by 21
  19. 2023Generalization and Stability of Interpolating Neural Networks with Minimal Widthcited by 21
  20. 2023Generalization bounds for neural ordinary differential equations and deep residual networkscited by 21
  21. 2024The Empirical Impact of Neural Parameter Symmetries, or Lack Thereofcited by 21
  22. 2021RATT: Leveraging Unlabeled Data to Guarantee Generalizationcited by 20
  23. 2021An Embedding of ReLU Networks and an Analysis of their Identifiabilitycited by 20
  24. 2021The Impact of Reinitialization on Generalization in Convolutional Neural Networkscited by 20
  25. 2021Noether: The More Things Change, the More Stay the Samecited by 19
  26. 2021Post-mortem on a deep learning contest: a Simpson's paradox and the complementary roles of scale metrics versus shape metricscited by 19
  27. 2021On Margins and Derandomisation in PAC-Bayescited by 19
  28. 2022Integral Probability Metrics PAC-Bayes Boundscited by 19
  29. 2022Quantifying the Knowledge in a DNN to Explain Knowledge Distillation for Classificationcited by 19
  30. 2023Fantastic Generalization Measures are Nowhere to be Foundcited by 19
  31. 2025FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modelingcited by 19
  32. 2021Inductive Bias of Multi-Channel Linear Convolutional Networks with Bounded Weight Normcited by 18
  33. 2022Evaluating natural language processing models with generalization metrics that do not need access to any training or testing datacited by 18
  34. 2022Adversarial Rademacher Complexity of Deep Neural Networkscited by 18
  35. 2024How Uniform Random Weights Induce Non-uniform Bias: Typical Interpolating Neural Networks Generalize with Narrow Teacherscited by 18
  36. 2025Scaling Laws and Spectra of Shallow Neural Networks in the Feature Learning Regimecited by 18
  37. 2021Generalization bounds for graph convolutional neural networks via Rademacher complexitycited by 17
  38. 2022Bridging Mean-Field Games and Normalizing Flows with Trajectory Regularizationcited by 17

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