Defines polyslot pslot[C] and srep[C] constructions on symmetric monoidal categories that reconstruct unitary supermaps and forbid time-loops in composition, with equivalence shown on path-contraction groupoids.
Automatic Backward Filtering Forward Guiding for Markov processes and graphical models
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A deep BSDE neural network method approximates unnormalized filtering densities for nonlinear Bayesian filtering, trained offline and applied online, with a hybrid a priori-a posteriori error bound proved under the parabolic Hörmander condition.
A convergent deep splitting scheme approximates the nonlinear filtering density via Fokker-Planck prediction and exact Bayesian update, with sampling to address high dimensions.
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Polycategorical Constructions for Unitary Supermaps of Arbitrary Dimension
Defines polyslot pslot[C] and srep[C] constructions on symmetric monoidal categories that reconstruct unitary supermaps and forbid time-loops in composition, with equivalence shown on path-contraction groupoids.
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Nonlinear filtering based on density approximation and deep BSDE prediction
A deep BSDE neural network method approximates unnormalized filtering densities for nonlinear Bayesian filtering, trained offline and applied online, with a hybrid a priori-a posteriori error bound proved under the parabolic Hörmander condition.
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A convergent scheme for the Bayesian filtering problem based on the Fokker--Planck equation and deep splitting
A convergent deep splitting scheme approximates the nonlinear filtering density via Fokker-Planck prediction and exact Bayesian update, with sampling to address high dimensions.