We develop operator-theoretic generalization bounds for deep multi-output function classes by representing network layers as Koopman composition operators on vector-valued reproducing kernel Hilbert spaces. In vector-valued Sobolev RKHSs, we derive Rademacher complexity bounds for invertible and width-expanding injective architectures.
arXiv:2606. 17419v1 Announce Type: new Abstract: We develop approximation and generalization error estimates for multi-input neural operators, with the output error measured in Sobolev norms.
By Yahong Yang, Zecheng Zhang, Wei Zhu, Wenjing Liao, Hao Liu
arXiv:2606. 16028v1 Announce Type: new Abstract: Modern deep learning architectures are increasingly multi-task and multi-modal, using a pretrained foundation model combined with task-specific, fine-tuned models.
By Thomas Dittrich, Oliver Potocki, Philipp Grohs
arXiv:2608. 11661v1 Announce Type: cross Abstract: A multiplicative dual-encoder network computes a real-valued output for a pair of inputs as the inner product of their separate encodings.
By Zijian Zhao, Sen Li
arXiv:2606. 01244v1 Announce Type: cross Abstract: We study operator learning using encoder--decoder neural networks.
By Jia-Qi Yang, Lei Shi
arXiv:2606. 15812v1 Announce Type: new Abstract: Constructing mathematically tractable function spaces that capture hierarchical compositional representations remains a central challenge in statistical learning theory.
By Mahdi Mohammadigohari, Giuseppe Di Fatta, Giuseppe Nicosia, Panos M Pardalos