arXiv:2410.00357v2 Announce Type: replace Abstract: Neural scaling laws play a pivotal role in the performance of deep neural networks and have been observed in a wide range of tasks. However, a complete theoretical framework for understanding these scaling laws remains underdeveloped. In this paper, we explore the neural scaling laws for deep operator networks, which involve learning mappings between function spaces, with a focus on the Chen and Chen style architecture. These approaches, which include the popular Deep Operator Network (DeepONet), approximate the output functions using a linea
The paper was just published, representing continued academic progress in understanding the foundational mechanisms of deep learning, particularly scaling laws.
Understanding neural scaling laws is critical for optimizing the design and training of large AI models, directly impacting performance and resource efficiency.
This theoretical study refines the understanding of how DeepONets scale, providing a blueprint for more predictable and efficient development of AI systems capable of learning functional mappings.
- · AI researchers
- · DeepONet developers
- · Engineering simulation platforms
- · Developers relying solely on brute-force scaling without theoretical guidance
Improved theoretical understanding of deep neural network scaling, particularly for operator networks.
More efficient and predictable development of large-scale AI models for scientific computing and complex function approximation.
Accelerated discovery and deployment of AI in fields requiring sophisticated functional mappings, such as materials science or climate modeling.
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Read at arXiv cs.LG