Transformers and generalized neural integral operators are shown to universally approximate operators between Hölder and Banach spaces.
Neural integral equations.arXiv preprint arXiv:2209.15190, 2022
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Deep neural networks are framed as discrete dynamical systems, and PINNs are shown to approximate the same PDE dynamics as classical discretization but through dense parameter representations rather than structured stencils.
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Universal Approximation of Operators with Transformers and Neural Integral Operators
Transformers and generalized neural integral operators are shown to universally approximate operators between Hölder and Banach spaces.
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Deep Neural Networks as Discrete Dynamical Systems: Implications for Physics-Informed Learning
Deep neural networks are framed as discrete dynamical systems, and PINNs are shown to approximate the same PDE dynamics as classical discretization but through dense parameter representations rather than structured stencils.