14 papers
Adaptive Restart under Unknown KL Geometry in Stochastic Weakly-Convex Optimization
Binh T. Nguyen, Khoa D. Nguyen, Bao Thai Huynh
KL geometry accelerates restart schedules in stochastic weakly-convex optimization, but the schedule depends jointly on an unknown and potentially nonunique geometric description.…
Curvature, Scaling, and Complexity in Riemannian Projection-Free Optimization
Binh T. Nguyen
Projection-free methods replace projections by linear minimization oracles, making their convergence fundamentally sensitive to the geometry of the feasible region. We develop a ge…
Certificate-Coupled DCA for the Trust-Region Subproblem: Early Structural Escape and Progressive Global Certification
Binh T. Nguyen
We study the nonconvex trust-region subproblem by a certificate-coupled difference-of-convex algorithm that incorporates spectral information before exact first-order stationarity…
Uniform High-Frequency Localization on Quantum Graphs
Binh T. Nguyen
We study uniform high-frequency localization for the Laplacian on compact metric graphs through the least -mass that eigenfunctions must place in a prescribed measurable obser…
Uniform Eigenfunction Observability under Mixed Reflection Monodromy
Binh T. Nguyen
We study uniform observability for Laplace eigenfunctions with mixed boundary conditions whose reflection signs do not define a scalar character. For the DDN/NND sectors of the equ…
Arithmetic Scar Accessibility and Generic Schrodinger Control on Metric Graphs
Binh T. Nguyen
We study internal exact controllability of the free Schrödinger equation on finite compact metric graphs with Kirchhoff conditions at interior vertices and a fixed Dirichlet-Neuman…
Uniform Non-Localization under Robin Boundary Perturbations: Spectral Splitting and Bounded Eigenspace Complexity
Binh T. Nguyen
We study the high-energy spectral effect of Robin boundary perturbations on complete Laplace eigenspaces and its consequences for eigenfunction non-localization. Highly degenerate…
Logarithmic-Free Moment and Generalization Bounds for Uniformly Stable Algorithms
Thanh Nguyen-Cung, Binh T. Nguyen
Uniform stability is a classical tool for controlling the generalization error of a learning algorithm. Bousquet, Klochkov, and Zhivotovskiy (2020) showed that the problem can be r…
Inertia-Sensitive Kreiss Bounds for -Selfadjoint Matrices
Thanh Nguyen-Cung, Binh T. Nguyen
Let have spectrum in the closed unit disk. Its maximal power growth measures transient…
Quantitative and Uniform Non-Localization on Integrable Polygons
Binh T. Nguyen
We study uniform non-localization of Dirichlet Laplacian eigenfunctions on planar integrable polygons, with particular emphasis on spectral degeneracy and quantitative depend…
Quadratically Regularized Optimal Transport: Localization Bounds and Affine Case Analysis
Long Nguyen-Chi, Nam Nguyen, Binh Nguyen
Quadratic regularization has emerged as a potential alternative to the popular entropic regularization in computational optimal transport, offering the theoretical advantage of pro…
Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity
Hoang Anh Tran, Binh Tuan Nguyen, Yong Sheng Soh
The Gromov-Wasserstein (GW) problem is an extension of the classical optimal transport problem to settings where the source and target distributions reside in incomparable spaces,…
Sum-of-Squares Hierarchy for the Gromov Wasserstein Problem
Hoang Anh Tran, Binh Tuan Nguyen, Yong Sheng Soh
The Gromov-Wasserstein (GW) problem is a variant of the classical optimal transport problem that allows one to compute meaningful transportation plans between incomparable spaces.…
Semidefinite Relaxations of the Gromov-Wasserstein Distance
Junyu Chen, Binh T. Nguyen, Shang Hui Koh +1
The Gromov-Wasserstein (GW) distance is an extension of the optimal transport problem that allows one to match objects between incomparable spaces. At its core, the GW distance is…