This paper introduces a novel framework for analyzing operator learning within encoder-decoder architectures. It formulates operator learning on function spaces, addressing the challenge of finite-dimensional training data representations. The research establishes that as input and output resolutions increase, the induced kernels converge to a limiting kernel, enabling resolution-independent regularity assumptions. The work also provides theoretical bounds for regularized stochastic gradient descent and extends the analysis to encoder-decoder neural networks using the limiting neural tangent kernel. AI
IMPACT Provides a theoretical foundation for understanding and improving operator learning in complex neural network architectures.
RANK_REASON The item is an academic paper detailing a new theoretical framework and analysis for operator learning in encoder-decoder architectures. [lever_c_demoted from research: ic=1 ai=1.0]
- arXiv
- Fourier
- Legendre polynomial
- Limiting Kernels
- Neural tangent kernel
- Operator Learning
- principal component analysis
- Regularized Stochastic Gradient Descent
- Reproducing Kernel Hilbert Spaces
- wavelet
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