用算子理论推导多任务深度学习更紧的泛化界。
On the Koopman-Based Generalization Bounds for Multi-Task Deep Learning
- 基于算子理论，引入定制化Sobolev空间提升假设空间
- 利用权重矩阵小条件数，得到比传统方法更紧的泛化界
- 适用于单输出场景，适合研究理论机制的研究者
本文采用算子理论方法，为多任务深度神经网络建立了泛化边界。作者通过利用权重矩阵的小条件数，并引入定制化的Sobolev空间作为扩展假设空间，提出了比传统范数方法更紧的边界。该边界在单输出设置下依然有效，优于现有基于Koopman的边界。所提出的框架保持了灵活性和对网络宽度的无关性，为核方法背景下多任务深度学习提供了更精确的理论理解。
原文摘要 · Abstract (English)
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.
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