On the limit set of Neural Network functions trainable by Machine Learning
Abstract
We define a functional space together with a convenient norm for the set of functions generated by modern Neural Network structures [4] which can be trained by Machine Learning algorithms. The key is to concentrate on an effective version of the chain rule for functions which are slightly more regular than Lipschitz continuous. Two applications are detailed with one numerical illustration in Pytorch.
Fields of Study & Subjects
Neural Networks and Applications
Stochastic Gradient Optimization Techniques
Advanced Banach Space Theory
Publication details
- Journal / source
- HAL
- Publication date
- 6 February 2026
- Language
- EN
- Document type
- Preprint