arXiv:2608. 15982v1 Announce Type: new Abstract: 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.
By Mahdi Mohammadigohari, Thomas Borsani, Giuseppe Di Fatta
arXiv:2609.21422v1 Announce Type: cross
Abstract: Deep representation learning often selects hidden features and fits the final predictor on the same sample, so fixed-feature analysis performed after...
By Mahdi Mohammadigohari, Nicole M\"ucke
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. 01244v2 Announce Type: replace-cross Abstract: Inspired by the function-space theory of neural networks, we formulate and analyze a variation space for nonlinear operators between Hilbert spaces, defined through vector-valued Borel measures of bounded variation.
By Jia-Qi Yang, Lei Shi
The paper studies operator learning on function spaces using encoder–decoder architectures. It shows that as input and output resolutions grow, the induced kernels converge to a limiting kernel, enabling regularity assumptions independent of resolution. The authors derive upper and lower bounds for regularized stochastic gradient descent, extend the analysis to neural networks via the limiting neural tangent kernel, and provide error bounds and complexity guarantees for various kernel and encoding constructions.
By Lei Shi, Jia-Qi Yang, Ding-Xuan Zhou
arXiv:2609. 21693v1 Announce Type: new Abstract: Equivalent finite parameterizations can represent the same functions and intrinsic norm yet induce different optimization algorithms.
By Mahdi Mohammadigohari, Gustau Camps-Valls