Asymptotic convexity of wide and shallow neural networks
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Abstract (arXiv)
For a simple model of shallow and wide neural networks, we show that the epigraph of its input-output map as a function of the network parameters approximates epigraph of a. convex function in a precise sense. This leads to a plausible explanation of their observed good performance.
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 10 of its 17 references that are in the map. First posted on arXiv 23 Jun 2025.
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References · 10
- 2019Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descentcited by 732
- 2017The Expressive Power of Neural Networks: A View from the Widthcited by 318
- 2020Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networkscited by 166
- 2019Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivationcited by 146
- 2020Neural Networks are Convex Regularizers: Exact Polynomial-time Convex Optimization Formulations for Two-layer Networkscited by 96
- 2020Do Wider Neural Networks Really Help Adversarial Robustness?cited by 79
- 2017The loss surface of deep and wide neural networkscited by 74
- 2021Wide Neural Networks Forget Less Catastrophicallycited by 64
- 2022What Can Be Learnt With Wide Convolutional Neural Networks?cited by 16
- 2022Wide and Deep Neural Networks Achieve Optimality for Classificationcited by 12
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