arXiv:2512.19199v2 Announce Type: replace-cross
Abstract: The paper establishes generalization bounds for multitask deep neural networks using operator-theoretic techniques. The authors propose a tighter bound than those derived from conventional norm based methods by leveraging small condition numbers in the weight matrices and introducing a tailored Sobolev space as an expanded hypothesis space. This enhanced bound remains valid even in single output settings, outperforming existing Koopman based bounds. The resulting framework maintains key advantages such as flexibility and independence from network width, offering a more precise theoretical understanding of multitask deep learning in the context of kernel methods.
Portable automated rapid testing for auditory assessment: repeated at-home testing in older adults
IntroductionHearing challenges are prevalent in older adults and are associated with age-related cognitive decline. However, measuring age-related changes in hearing faces critical barriers related to