Proves a weighted Nachbin theorem establishing universal approximation of differentiable maps from weighted infinite-dimensional manifolds to Banach spaces, including derivatives, with applications to non-anticipative path functionals and signature methods.
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A branched signature kernel method with count-sampling turns single-trajectory rough signals into hierarchical paths for kernel-collocation ODE solving, supported by a universal approximation theorem and streaming updates.
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Weighted universal approximation of differentiable maps on infinite-dimensional manifolds
Proves a weighted Nachbin theorem establishing universal approximation of differentiable maps from weighted infinite-dimensional manifolds to Banach spaces, including derivatives, with applications to non-anticipative path functionals and signature methods.
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Branched Signature Kernel Solvers for ODEs with rough Single-Trajectory signals
A branched signature kernel method with count-sampling turns single-trajectory rough signals into hierarchical paths for kernel-collocation ODE solving, supported by a universal approximation theorem and streaming updates.