An abstract framework for neural flows with composition and separation structures is proven to universally approximate any operator, recovering ResNet and plain architectures via discretization.
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18 Pith papers cite this work. Polarity classification is still indexing.
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Richardson and a new Krylov method MINBERR achieve universal (condition-free) backward-error rates 1/k and O(1/k^{2}) for PSD linear systems, with a near-universal O(log n / k) extension to general systems.
SparseModesNet uses linear POD encoding plus LassoNet-enforced sparse nonlinear neural decoding to select informative modes and cut reconstruction error on advection-dominated and turbulent flows.
UA-NEB and UA-Dimer embed covariance into oblique projections and weighted rotations within NEB and Dimer frameworks, yielding 21-56% error reductions on analytic and tungsten-vacancy benchmarks under a local Lyapunov stability hypothesis.
A single-network implicit neural optimal transport method that solves the c-transform via proximal fixed-point iteration for stable, non-adversarial training.
The circumcentric direction d of a cone has an exact polyhedral admissible perturbation set larger than the inscribed ball of radius ||d||^2 in the polar cone, with closed-form ||d||^2 from the inverse Gram matrix and specific values like 1/r for symmetric cones.
The authors introduce predicted-weighted balanced accuracy (pBA), a utility-weighted evaluation metric that uses predicted subconcept posteriors to reduce bias from within-class heterogeneity in imbalanced data.
TSN-Affinity enables continual offline RL via similarity-guided parameter reuse in sparse subnetworks, showing better retention than replay baselines on Atari and robotic arm tasks.
A new edge-multiscale homogenization method for high-wavenumber Maxwell equations in heterogeneous media achieves near-linear mesh-size scaling with wavenumber via a nonstandard variational formulation.
A theoretical framework combining Toeplitz limiting spectra and modal decomposition is used to analyze weak scalability and wave-number robustness of one-level Schwarz methods for Maxwell's equations in strip-wise decomposed waveguides under impedance and PML transmission conditions.
A single numerical Jacobian, under a log-linear monomial assumption, recovers global identifiable parameter combinations and supports likelihood-based uncertainty quantification.
A unifying framework constructs spectral approximations for fractional integrals via transplanted Chebyshev polynomials from algebraic or exponential transforms.
A hybrid mixed domain decomposition method with stabilization achieves optimal q+1 convergence for primal and hybrid variables and uniform error bounds in the stabilization parameter tau using Raviart-Thomas elements.
Existence of optimal solutions together with first-order and necessary/sufficient second-order optimality conditions are established for pointwise tracking optimal control of a fractional semilinear elliptic PDE.
Randomized subspace iteration improves low-rank approximation quality over randomized SVD for pretrained models by using power iterations to enhance spectral separation, preserving predictive accuracy better under aggressive compression.
Von Neumann analysis shows that Lie-Trotter and Strang splittings yield identical stability conditions for DtP and PtD on hyperbolic problems while Strang enlarges the region, and that Crank-Nicolson or hybrid Euler schemes restore unconditional stability for parabolic problems despite a negative S-
Lipschitz stability holds for low-rank unknowns in the fully nonlinear inverse medium scattering problem, with an ensemble Kalman filter proposed for iterative reconstruction whose dimension is set by the wave number.
Gives a minimal compact description of the diversity index polytope arising from phylogenetic diversity indices on trees.
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Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations
An abstract framework for neural flows with composition and separation structures is proven to universally approximate any operator, recovering ResNet and plain architectures via discretization.
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Towards Universal Convergence of Backward Error in Linear System Solvers
Richardson and a new Krylov method MINBERR achieve universal (condition-free) backward-error rates 1/k and O(1/k^{2}) for PSD linear systems, with a near-universal O(log n / k) extension to general systems.
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Sparse POD Mode Selection and Manifold Dimensionality Reduction with Neural Networks
SparseModesNet uses linear POD encoding plus LassoNet-enforced sparse nonlinear neural decoding to select informative modes and cut reconstruction error on advection-dominated and turbulent flows.
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Geometry-Preserving Nudged Elastic Band and Dimer Methods under Anisotropic Force Uncertainty
UA-NEB and UA-Dimer embed covariance into oblique projections and weighted rotations within NEB and Dimer frameworks, yielding 21-56% error reductions on analytic and tungsten-vacancy benchmarks under a local Lyapunov stability hypothesis.
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Implicit Neural Optimal Transport via Fixed-Point Optimization
A single-network implicit neural optimal transport method that solves the c-transform via proximal fixed-point iteration for stable, non-adversarial training.
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On the geometry of circumcentric directions of cones
The circumcentric direction d of a cone has an exact polyhedral admissible perturbation set larger than the inscribed ball of radius ||d||^2 in the polar cone, with closed-form ||d||^2 from the inverse Gram matrix and specific values like 1/r for symmetric cones.
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Correcting Performance Estimation Bias in Imbalanced Classification with Minority Subconcepts
The authors introduce predicted-weighted balanced accuracy (pBA), a utility-weighted evaluation metric that uses predicted subconcept posteriors to reduce bias from within-class heterogeneity in imbalanced data.
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TSN-Affinity: Similarity-Driven Parameter Reuse for Continual Offline Reinforcement Learning
TSN-Affinity enables continual offline RL via similarity-guided parameter reuse in sparse subnetworks, showing better retention than replay baselines on Atari and robotic arm tasks.
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Numerical homogenization for indefinite time-harmonic Maxwell equations
A new edge-multiscale homogenization method for high-wavenumber Maxwell equations in heterogeneous media achieves near-linear mesh-size scaling with wavenumber via a nonstandard variational formulation.
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Modal analysis of a domain decomposition method for Maxwell's equations in a waveguide
A theoretical framework combining Toeplitz limiting spectra and modal decomposition is used to analyze weak scalability and wave-number robustness of one-level Schwarz methods for Maxwell's equations in strip-wise decomposed waveguides under impedance and PML transmission conditions.
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Invariant Image Reparameterisation: Bridging Symbolic and Numerical Methods for Identifiability Analysis, Model Reduction, and Prediction
A single numerical Jacobian, under a log-linear monomial assumption, recovers global identifiable parameter combinations and supports likelihood-based uncertainty quantification.
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Fractional calculus via variable-transform-based spectral approximations
A unifying framework constructs spectral approximations for fractional integrals via transplanted Chebyshev polynomials from algebraic or exponential transforms.
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On a Hybrid Mixed Domain Decomposition Method
A hybrid mixed domain decomposition method with stabilization achieves optimal q+1 convergence for primal and hybrid variables and uniform error bounds in the stabilization parameter tau using Raviart-Thomas elements.
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A pointwise tracking optimal control problem for a fractional, semilinear PDE
Existence of optimal solutions together with first-order and necessary/sufficient second-order optimality conditions are established for pointwise tracking optimal control of a fractional semilinear elliptic PDE.
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Low-Rank Compression of Pretrained Models via Randomized Subspace Iteration
Randomized subspace iteration improves low-rank approximation quality over randomized SVD for pretrained models by using power iterations to enhance spectral separation, preserving predictive accuracy better under aggressive compression.
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On the stability of the low-rank projector-splitting integrators for hyperbolic and parabolic equations
Von Neumann analysis shows that Lie-Trotter and Strang splittings yield identical stability conditions for DtP and PtD on hyperbolic problems while Strang enlarges the region, and that Crank-Nicolson or hybrid Euler schemes restore unconditional stability for parabolic problems despite a negative S-
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Low-rank-assisted inverse medium scattering: Lipschiz stability and ensemble Kalman filter
Lipschitz stability holds for low-rank unknowns in the fully nonlinear inverse medium scattering problem, with an ensemble Kalman filter proposed for iterative reconstruction whose dimension is set by the wave number.
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A minimal compact description of the diversity index polytope
Gives a minimal compact description of the diversity index polytope arising from phylogenetic diversity indices on trees.