On the Koopman-Based Generalization Bounds for Multi-Task Deep Learning
This provides a more precise theoretical understanding for researchers in multitask deep learning, though it appears incremental as it builds on existing Koopman-based methods.
The paper tackles the problem of establishing generalization bounds for multitask deep neural networks by proposing a tighter bound using operator-theoretic techniques, which outperforms existing Koopman-based bounds and remains valid even in single output settings.
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.