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When artificial neural networks have demonstrated exceptional practicalsuccess in a variety of domains, investigations into their theoreticalcharacteristics, such as their approximation power, statistical properties, andgeneralization performance, have concurrently made significant strides. In thispaper, we construct a novel theory for understanding the effectiveness ofneural networks, which offers a perspective distinct from prior research.Specifically, we explore the rationale underlying a common practice during theconstruction of neural network models: sample splitting. Our findings indicatethat the optimal hyperparameters derived from sample splitting can enable aneural network model that asymptotically minimizes the prediction risk. Weconduct extensive experiments across different application scenarios andnetwork architectures, and the results manifest our theory's effectiveness.

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