arXiv:2512.19184v2 Announce Type: replace Abstract: This paper presents novel generalization bounds for vector-valued neural networks and deep kernel methods, focusing on multi-task learning through an operator-theoretic framework. Our key development lies in strategically combining a Koopman based approach with existing techniques, achieving tighter generalization guarantees compared to traditional norm-based bounds. To mitigate computational challenges associated with Koopman-based methods, we introduce sketching techniques applicable to vector valued neural networks. These techniques yield
This research addresses fundamental challenges in deep learning generalization, a critical bottleneck for its deployment in complex, multi-task environments.
Improved generalization bounds directly enhance the reliability and efficiency of AI systems, particularly for emergent multi-task AI agents.
The theoretical understanding and practical implementation of robust deep learning models for diverse applications are advanced, potentially accelerating multi-task AI development.
- · AI developers
- · Deep learning researchers
- · AI-driven industries
- · Academic institutions
- · Companies relying on less efficient deep learning models
- · Traditional theoretical approaches
Tighter generalization guarantees allow for the development of more robust and less data-hungry multi-task AI models.
This could lead to faster and more reliable deployment of complex AI systems across various industries, including robotics and autonomous agents.
The enhanced theoretical foundation might democratize advanced AI development by reducing the need for massive, highly curated datasets under certain conditions.
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Read at arXiv cs.LG