# Towards Optimal Neural Networks: the Role of Sample Splitting in Hyperparameter Selection

arXiv: https://arxiv.org/abs/2307.07726 · HTML: https://mlsanity.com/paper/2307.07726/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 45 references that are in the map.
- First posted on arXiv 15 Jul 2023.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [Learning Overparameterized Neural Networks via Stochastic Gradient Descent on Structured Data](https://mlsanity.com/paper/1808.01204/) (2018)
- [On Hyperparameter Optimization of Machine Learning Algorithms: Theory and Practice](https://mlsanity.com/paper/2007.15745/) (2020)
- [ResNet with one-neuron hidden layers is a Universal Approximator](https://mlsanity.com/paper/1806.10909/) (2018)
- [Globally Optimal Gradient Descent for a ConvNet with Gaussian Inputs](https://mlsanity.com/paper/1702.07966/) (2017)
- [Gradient Descent Learns One-hidden-layer CNN: Don't be Afraid of Spurious Local Minima](https://mlsanity.com/paper/1712.00779/) (2017)

## Abstract (arXiv)

When artificial neural networks have demonstrated exceptional practical success in a variety of domains, investigations into their theoretical characteristics, such as their approximation power, statistical properties, and generalization performance, have concurrently made significant strides. In this paper, we construct a novel theory for understanding the effectiveness of neural networks, which offers a perspective distinct from prior research. Specifically, we explore the rationale underlying a common practice during the construction of neural network models: sample splitting. Our findings indicate that the optimal hyperparameters derived from sample splitting can enable a neural network model that asymptotically minimizes the prediction risk. We conduct extensive experiments across different application scenarios and network architectures, and the results manifest our theory's effectiveness.