{"ID":2879657,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.15198","arxiv_id":"2508.15198","title":"Frequency-adaptive tensor neural networks for high-dimensional multi-scale problems","abstract":"Tensor neural networks (TNNs) have demonstrated their superiority in solving high-dimensional problems. However, similar to conventional neural networks, TNNs are also influenced by the Frequency Principle, which limits their ability to accurately capture high-frequency features of the solution. In this work, we analyze the training dynamics of TNNs by Fourier analysis and enhance their expressivity for high-dimensional multi-scale problems by incorporating random Fourier features. Leveraging the inherent tensor structure of TNNs, we further propose a novel approach to extract frequency features of high-dimensional functions by performing the Discrete Fourier Transform to one-dimensional component functions. This strategy effectively mitigates the curse of dimensionality. Building on this idea, we propose a frequency-adaptive TNNs algorithm, which significantly improves the ability of TNNs in solving complex multi-scale problems. Extensive numerical experiments are performed to validate the effectiveness and robustness of the proposed frequency-adaptive TNNs algorithm.","short_abstract":"Tensor neural networks (TNNs) have demonstrated their superiority in solving high-dimensional problems. However, similar to conventional neural networks, TNNs are also influenced by the Frequency Principle, which limits their ability to accurately capture high-frequency features of the solution. In this work, we analyz...","url_abs":"https://arxiv.org/abs/2508.15198","url_pdf":"https://arxiv.org/pdf/2508.15198v2","authors":"[\"Jizu Huang\",\"Yue Qiu\",\"Rukang You\"]","published":"2025-08-21T03:16:52Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math-ph\"]","methods":"[]","has_code":false}