{"ID":2858431,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.08780","arxiv_id":"2510.08780","title":"Weights initialization of neural networks for function approximation","abstract":"Neural network-based function approximation plays a pivotal role in the advancement of scientific computing and machine learning. Yet, training such models faces several challenges: (i) each target function often requires training a new model from scratch; (ii) performance is highly sensitive to architectural and hyperparameter choices; and (iii) models frequently generalize poorly beyond the training domain. To overcome these challenges, we propose a reusable initialization framework based on basis function pretraining. In this approach, basis neural networks are first trained to approximate families of polynomials on a reference domain. Their learned parameters are then used to initialize networks for more complex target functions. To enhance adaptability across arbitrary domains, we further introduce a domain mapping mechanism that transforms inputs into the reference domain, thereby preserving structural correspondence with the pretrained models. Extensive numerical experiments in one- and two-dimensional settings demonstrate substantial improvements in training efficiency, generalization, and model transferability, highlighting the promise of initialization-based strategies for scalable and modular neural function approximation. The full code is made publicly available on Gitee.","short_abstract":"Neural network-based function approximation plays a pivotal role in the advancement of scientific computing and machine learning. Yet, training such models faces several challenges: (i) each target function often requires training a new model from scratch; (ii) performance is highly sensitive to architectural and hyper...","url_abs":"https://arxiv.org/abs/2510.08780","url_pdf":"https://arxiv.org/pdf/2510.08780v1","authors":"[\"Xinwen Hu\",\"Yunqing Huang\",\"Nianyu Yi\",\"Peimeng Yin\"]","published":"2025-10-09T19:56:26Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.NA\"]","methods":"[]","has_code":false}