arXiv research

SGD converges exponentially fast in non-convex over-parametrized learning.

New inequalities for convex curves with multiple geometric factors.

Study real projective structures on a specific Coxeter orbifold.

Study examines surfaces with bounded fractional mean curvature, proving control over local parametrization.

Estimates risk in finance using Wasserstein distance and parametric models.

New proofs given for space curves with totally positive torsion.

Study on the optimization of neural networks with ReLU activation and the degeneracy of their parametrizations.

Differentiable layers for convex optimization problems.

Study contact structures on lens spaces, classifying rational knots.

Over-parametrized networks with quadratic activations can find globally optimal solutions for convex losses.

New guarantees for MRLEs in prediction accuracy.

Method identifies shifts leading to large model performance differences.

Derives exact formula for Minkowski sum of ellipsoids in N-space.

Study shows surfaces in Lorentz manifold evolve by translation.

New parametrization handles sextactic points on closed curves.

We present a novel and comprehensive approach to the study of the parametric Plateau problem for locally strictly convex (LSC) hypersurfaces of prescribed curvature for general convex curvature functions inside general Riemannian manifolds. We prove existence of solutions to the Plateau problem with outer barrier for L…

Proposes a convex model for mixed logit to handle individual heterogeneity.

We characterization hyperbolic metrics on compact surfaces with boundary using a variational principle. As a consequence, a new parametrization of the Teichmuller space of compact surface with boundary is produced. In the new parametrization, the Teichmuller space becomes an open convex polytope. It is conjectured that…

We consider strictly convex hypersurfaces which are evolving by the non-parametric logarithmic Gauss curvature flow subject to a Neumann boundary condition. Solutions are shown to converge smoothly to hypersurfaces moving by translation. In particular, for bounded domains we prove that convex functions with prescribed …

Convex iso-Delaunay regions found in flat surface strata.

New method reduces over-parametrization in neural networks, ensuring sparsity and finite network size.

The theory of convex risk functions has now been well established as the basis for identifying the families of risk functions that should be used in risk averse optimization problems. Despite its theoretical appeal, the implementation of a convex risk function remains difficult, as there is little guidance regarding ho…

Large deviations theory applied to policy gradient methods.

Explains solution space of Toda equations using Lie theory.

Deep neural networks with multiple branches are less non-convex, improving performance.

Upper bound found for convex hull volume of 4-vertex curve.

Paper relaxes assumptions for non-parametric estimation in pairwise learning.

The study describes the geometry of surfaces and their representations in SL(3,R).

This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g. sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of…

First order methods can take extremely long to find global minima of non-convex functions.

The study connects polygon areas and projective structures in 3D space.

Convex program for estimating nonlinear recurrent models with stability conditions.

Unified analysis for nonlinear parametric models in Bayesian optimization.

We show that parametric models trained by a stochastic gradient method (SGM) with few iterations have vanishing generalization error. We prove our results by arguing that SGM is algorithmically stable in the sense of Bousquet and Elisseeff. Our analysis only employs elementary tools from convex and continuous optimizat…

EGL optimizes complex functions without fitting them, achieving state-of-the-art results.

Convex learning for diverse invariances in semi-inner-product space.

New estimator robust to adversarial noise and data heterogeneity.

Let P(S) be the space of convex projective structures on a surface S with negative Euler characteristic. Goldman and Bonahon-Dreyer constructed two different sets of global coordinates for P(S), both associated to a pair of pants decomposition of the surface S. The article explicitly describes the coordinate change bet…

Unified parametric assumption improves convergence guarantees for nonconvex optimization.

We demonstrate that almost all non-parametric dimensionality reduction methods can be expressed by a simple procedure: regularized loss minimization plus singular value truncation. By distinguishing the role of the loss and regularizer in such a process, we recover a factored perspective that reveals some gaps in the c…

Study finds optimal loops in hyperbolic space with Finsler structure.

Develops coresets for scalable multivariate distribution estimation.

This paper deals with non-Archimedean representations of punctured surface groups in PGL(3), associated actions on Euclidean buildings (of type A2), and degenerations of real convex projective structures on surfaces. The main result is that, under good conditions on Fock-Goncharov generalized shear parameters, non-Arch…

Improved complexity for machine learning optimization methods.

The paper provides approximation guarantees for neural networks trained with gradient flow.

The study explores isoptic curves of cycloids and their applications.

New neural network models extreme value distributions with preserved shape constraints.

The paper develops a convex parameterization for robust RNNs ensuring stability and robustness.