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Dimensionality reduction and width of deep neural networks based on topological degree theory
Xiao-Song Yang
https://arxiv.org/abs/2511.06821 https://arxiv.org/pdf/2511.06821 https://arxiv.org/html/2511.06821
arXiv:2511.06821v1 Announce Type: new
Abstract: In this paper we present a mathematical framework on linking of embeddings of compact topological spaces into Euclidean spaces and separability of linked embeddings under a specific class of dimension reduction maps. As applications of the established theory, we provide some fascinating insights into classification and approximation problems in deep learning theory in the setting of deep neural networks.
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Riddled basin geometry sets fundamental limits to predictability and reproducibility in deep learning
Andrew Ly, Pulin Gong
https://arxiv.org/abs/2510.05606 https://

Riddled basin geometry sets fundamental limits to predictability and reproducibility in deep learning
Fundamental limits to predictability are central to our understanding of many physical and computational systems. Here we show that, despite its remarkable capabilities, deep learning exhibits such fundamental limits rooted in the fractal, riddled geometry of its basins of attraction: any initialization that leads to one solution lies arbitrarily close to another that leads to a different one. We derive sufficient conditions for the emergence of riddled basins by analytically linking features w…

Deep Generative Model for Human Mobility Behavior
Ye Hong, Yatao Zhang, Konrad Schindler, Martin Raubal
https://arxiv.org/abs/2510.06473 https://arxiv.org/…

Deep Generative Model for Human Mobility Behavior
Understanding and modeling human mobility is central to challenges in transport planning, sustainable urban design, and public health. Despite decades of effort, simulating individual mobility remains challenging because of its complex, context-dependent, and exploratory nature. Here, we present MobilityGen, a deep generative model that produces realistic mobility trajectories spanning days to weeks at large spatial scales. By linking behavioral attributes with environmental context, MobilityGe…

Compressed Video Quality Enhancement: Classifying and Benchmarking over Standards
Xiem HoangVan, Dang BuiDinh, Sang NguyenQuang, Wen-Hsiao Peng
https://arxiv.org/abs/2509.10407 …

Compressed Video Quality Enhancement: Classifying and Benchmarking over Standards
Compressed video quality enhancement (CVQE) is crucial for improving user experience with lossy video codecs like H.264/AVC, H.265/HEVC, and H.266/VVC. While deep learning based CVQE has driven significant progress, existing surveys still suffer from limitations: lack of systematic classification linking methods to specific standards and artifacts, insufficient comparative analysis of architectural paradigms across coding types, and underdeveloped benchmarking practices. To address these gaps, …