Neural networks parameterize finite-rank generators for ODEs on the orthogonal Lie group, allowing optimization of orthonormal bases in function space with a universality result that rank-2 generators suffice for density.
SIAM, 2011
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The paper introduces a data-informed subspace method with quotient-space Golub-Kahan bidiagonalization and integrated empirical Bayes for efficient posterior approximation in high-dimensional linear inverse problems.
Neural networks regress oversized subspaces for parametric problems using subspace-specific losses, with theory and experiments showing improved accuracy and smoother mappings.
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Learning Orthonormal Bases for Function Spaces
Neural networks parameterize finite-rank generators for ODEs on the orthogonal Lie group, allowing optimization of orthonormal bases in function space with a universality result that rank-2 generators suffice for density.
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Data-informed posterior approximation for Bayesian linear inverse problems
The paper introduces a data-informed subspace method with quotient-space Golub-Kahan bidiagonalization and integrated empirical Bayes for efficient posterior approximation in high-dimensional linear inverse problems.
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Deep Learning for Subspace Regression
Neural networks regress oversized subspaces for parametric problems using subspace-specific losses, with theory and experiments showing improved accuracy and smoother mappings.