Definable nonconvex parametric optimization problems admit an adjoint state formula under a qualification condition, selecting a conservative field for the value function without smoothness or uniqueness assumptions.
Lee.Introduction to Smooth Manifolds, volume 218 ofGraduate Texts in Mathe- matics
21 Pith papers cite this work, alongside 523 external citations. Polarity classification is still indexing.
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Uncorrected Gaussian residual penalties in full-space sampling converge after marginalization to the graph-lifted reduced posterior multiplied by the inverse absolute determinant of the state Jacobian, requiring explicit determinant corrections for equivalence.
Generalized Wasserstein barycenters on Riemannian manifolds are absolutely continuous when all input measures are absolutely continuous, for strictly convex cost profiles h with singularity at zero, via a geometric approximation approach.
The rational characteristic class ring for oriented S^n x S^n-fibrations injects into smooth bundle cohomology, producing non-trivial classes in all degrees detected by bundles from cyclic subgroups of a finite-index subgroup of SL_2(Z).
Develops Hamilton-Jacobi theory for non-conservative classical field theories in the k-contact framework, with z-independent and z-dependent approaches, affine/quadratic Hamiltonian cases, and recovery of the k=1 contact theory.
GL-LowPopArt is a Catoni-style two-stage estimator for generalized low-rank trace regression that attains state-of-the-art bounds and nearly instance-wise minimax optimality up to the Hessian condition number.
Stationary MMD points show super-convergence in integration error over MMD for RKHS integrands, and MMD gradient flows compute them with a new non-asymptotic finite-particle error bound.
Introduces BRIDGE and SKFM algorithms that detect latent confounders via non-closing Lie brackets in interventional vector fields derived from density ratios.
Blended Chart Surfaces create a compact explicit globally smooth surface by optimizing per-vertex polynomial maps on a proxy mesh and blending them via one-ring coordinates.
LieEDNN embeds general Lie groups into neural dynamics using adjoint actions and metric projections to achieve stable learnable trajectories on manifolds like SE(3) for manipulator planning.
EDRBO uses ensemble surrogates and Wasserstein ambiguity sets to robustify BO acquisition functions against context distribution mismatch, with sublinear regret O(γ_T √T) and SOTA empirical results on continuous contexts.
A machine-checked Lean 4 formalization of Stokes' theorem on smooth singular cubes with true Fréchet pullback, chain-level extensions, and comparison to prior HOL Light work.
A sum-of-squares framework combined with LaSalle's principle verifies almost global asymptotic stability for spacecraft attitude control systems on non-contractible manifolds, applied to aerodynamic and gravity-gradient examples.
DPA provides closed-form relation from level-set geometry to data score and proves extra latent components are conditionally independent, revealing intrinsic dimension.
A fully discrete strain-based model for continuum robot dynamics via Lie group variational integrators, combined with an EKF-based observer for states and disturbances, validated on hardware.
Determines the GL(n,R)-invariant and Isom-invariant statistical connections on the centered Gaussian model and describes the corresponding moduli spaces under two categorical equivalence relations.
Computes perturbation amplitudes in general effective multi-field inflation without sub-horizon limit and bounds higher-derivative corrections via ε for finite-cutoff models.
A generalized zeroth-order method samples random directions on the sphere to optimize quotients of quadratics, estimates Riemannian derivatives with surrogates, and yields an accelerated algorithm outperforming prior work.
Blend-to-zero operators are formalized for smooth transitions, with polynomial interpolants represented via the regularized incomplete Beta function and explicit trigonometric smooth step functions linked to higher-order boundary value problems.
Necessary and sufficient conditions for controllability of generic reconfigurable EM devices are derived as a function of geometry and mutual coupling between elements.
TabGRAA applies group-relative advantage alignment in an iterative reward-guided post-training loop to improve tabular language model generators on fidelity, utility, and privacy trade-offs across five benchmarks.
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The adjoint state method for parametric definable optimization without smoothness or uniqueness
Definable nonconvex parametric optimization problems admit an adjoint state formula under a qualification condition, selecting a conservative field for the value function without smoothness or uniqueness assumptions.
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Constraint residuals, graph posteriors, and determinant-corrected full-space targets in Bayesian inverse problems
Uncorrected Gaussian residual penalties in full-space sampling converge after marginalization to the graph-lifted reduced posterior multiplied by the inverse absolute determinant of the state Jacobian, requiring explicit determinant corrections for equivalence.
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Absolute continuity of generalized Wasserstein barycenters of finitely many measures
Generalized Wasserstein barycenters on Riemannian manifolds are absolutely continuous when all input measures are absolutely continuous, for strictly convex cost profiles h with singularity at zero, via a geometric approximation approach.
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Rational characteristic classes of bundles with fibre a product of spheres
The rational characteristic class ring for oriented S^n x S^n-fibrations injects into smooth bundle cohomology, producing non-trivial classes in all degrees detected by bundles from cyclic subgroups of a finite-index subgroup of SL_2(Z).
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Hamilton--Jacobi theory for non-conservative field theories in the $k$-contact framework
Develops Hamilton-Jacobi theory for non-conservative classical field theories in the k-contact framework, with z-independent and z-dependent approaches, affine/quadratic Hamiltonian cases, and recovery of the k=1 contact theory.
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GL-LowPopArt: A Nearly Instance-Wise Minimax-Optimal Estimator for Generalized Low-Rank Trace Regression
GL-LowPopArt is a Catoni-style two-stage estimator for generalized low-rank trace regression that attains state-of-the-art bounds and nearly instance-wise minimax optimality up to the Hessian condition number.
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Stationary MMD Points
Stationary MMD points show super-convergence in integration error over MMD for RKHS integrands, and MMD gradient flows compute them with a new non-asymptotic finite-particle error bound.
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Latent Confounded Causal Discovery via Lie Bracket Geometry
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Blended Chart Surfaces: A Seamless Explicit Representation for Smooth Surface Fitting
Blended Chart Surfaces create a compact explicit globally smooth surface by optimizing per-vertex polynomial maps on a proxy mesh and blending them via one-ring coordinates.
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Planning Neural Dynamics with Lie Group Embedding through Supervised Projective Manifold Learning
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Ensemble Distributionally Robust Bayesian Optimisation with Continuous Context
EDRBO uses ensemble surrogates and Wasserstein ambiguity sets to robustify BO acquisition functions against context distribution mismatch, with sublinear regret O(γ_T √T) and SOTA empirical results on continuous contexts.
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Stokes' Theorem for Smooth Singular Cubes in Lean 4: True Pullback, Bridges to mathlib4, and Chain-Level d^2=0
A machine-checked Lean 4 formalization of Stokes' theorem on smooth singular cubes with true Fréchet pullback, chain-level extensions, and comparison to prior HOL Light work.
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Sum-of-Squares Stability Verification on Manifolds with Applications in Spacecraft Attitude Control
A sum-of-squares framework combined with LaSalle's principle verifies almost global asymptotic stability for spacecraft attitude control systems on non-contractible manifolds, applied to aerodynamic and gravity-gradient examples.
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Distributional Autoencoders Know the Score
DPA provides closed-form relation from level-set geometry to data score and proves extra latent components are conditionally independent, revealing intrinsic dimension.
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Discrete Geometric Modeling and Extended State Estimation of Continuum Robots
A fully discrete strain-based model for continuum robot dynamics via Lie group variational integrators, combined with an EKF-based observer for states and disturbances, validated on hardware.
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Invariant statistical connections on the multivariate centered Gaussian model and their moduli spaces
Determines the GL(n,R)-invariant and Isom-invariant statistical connections on the centered Gaussian model and describes the corresponding moduli spaces under two categorical equivalence relations.
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Generalization of Zeroth-Order Method for Quotients of Quadratic Functions
A generalized zeroth-order method samples random directions on the sphere to optimize quotients of quadratics, estimates Riemannian derivatives with surrogates, and yields an accelerated algorithm outperforming prior work.
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Blend-to-zero operators for smooth transition functions
Blend-to-zero operators are formalized for smooth transitions, with polynomial interpolants represented via the regularized incomplete Beta function and explicit trigonometric smooth step functions linked to higher-order boundary value problems.
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Fundamental Theorems on Controllability in Wave-domain Processing for Holographic MIMO
Necessary and sufficient conditions for controllability of generic reconfigurable EM devices are derived as a function of geometry and mutual coupling between elements.
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Self-Improving Tabular Language Models via Iterative Reward-Guided Post-Training
TabGRAA applies group-relative advantage alignment in an iterative reward-guided post-training loop to improve tabular language model generators on fidelity, utility, and privacy trade-offs across five benchmarks.