Explicit function classes are constructed where compositional approximation strictly outperforms superpositional approximation with arbitrarily large gaps.
Properties of the Set of Functions Generated by Neural Networks of Fixed Size
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Tropical differential algebraic geometry restricts PINN hypothesis spaces to valid formal power series supports, improving convergence on Van der Pol and Burgers equations.
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Compositional Approximation Can Strictly Outperform Superpositional Approximation
Explicit function classes are constructed where compositional approximation strictly outperforms superpositional approximation with arbitrarily large gaps.
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Tropical Geometry as a Restricted Architecture for Physics-Informed Neural Networks: Applications in Nonlinear Fluid-Structure Examples
Tropical differential algebraic geometry restricts PINN hypothesis spaces to valid formal power series supports, improving convergence on Van der Pol and Burgers equations.