# Asymptotic convexity of wide and shallow neural networks

arXiv: https://arxiv.org/abs/2507.01044 · HTML: https://mlsanity.com/paper/2507.01044/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 17 references that are in the map.
- First posted on arXiv 23 Jun 2025.

## Builds on (most cited first, 10 of 10)

- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networks](https://mlsanity.com/paper/2006.13198/) (2020)
- [Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivation](https://mlsanity.com/paper/1902.04760/) (2019)
- [Neural Networks are Convex Regularizers: Exact Polynomial-time Convex Optimization Formulations for Two-layer Networks](https://mlsanity.com/paper/2002.10553/) (2020)
- [Do Wider Neural Networks Really Help Adversarial Robustness?](https://mlsanity.com/paper/2010.01279/) (2020)
- [The loss surface of deep and wide neural networks](https://mlsanity.com/paper/1704.08045/) (2017)
- [Wide Neural Networks Forget Less Catastrophically](https://mlsanity.com/paper/2110.11526/) (2021)
- [What Can Be Learnt With Wide Convolutional Neural Networks?](https://mlsanity.com/paper/2208.01003/) (2022)
- [Wide and Deep Neural Networks Achieve Optimality for Classification](https://mlsanity.com/paper/2204.14126/) (2022)

## 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.