arXiv research

Single knot crossings can transform one torus knot into its mirror image.

Smooth Schrödinger Bridges improve trajectory inference by smoothing Gaussian processes.

NESS improves neighbor embedding for smooth cell-state transitions in single-cell data.

New example of non-smooth isotopy after stabilization in 4-manifolds.

TKFT models computation via smooth vector fields, simulating functions in a single dynamical step.

Improved SGD learning for single index models reduces sample complexity.

By studying the example of smooth structures on CP^2#3(-CP^2) we illustrate how surgery on a single embedded nullhomologous torus can be utilized to change the symplectic structure, the Seiberg-Witten invariant, and hence the smooth structure on a 4-manifold.

New algorithms improve convergence of minimax optimization.

We shall give useful criteria of lips, beaks and swallowtail singularities of smooth map from the plane into the plane. As an application of criteria, we will discuss the singularities of Cauchy problem of single conservation law.

Two single-timescale algorithms improve TD learning with nonlinear approximations.

New method improves adversarial training efficiency and robustness.

For each composite number $n\ne 2^k$, there does not exist a single connected closed $(n+1)$-manifold such that any smooth, simply-connected, closed $n$-manifold can be topologically flat embedded into it. There is a single connected closed 5-manifold $W$ such that any simply-connected, 4-manifold $M$ can be topologica…

Many problems on signal processing reduce to nonparametric function estimation. We propose a new methodology, piecewise convex fitting (PCF), and give a two-stage adaptive estimate. In the first stage, the number and location of the change points is estimated using strong smoothing. In the second stage, a constrained s…

The paper explores the identifiability and interpretability of Gaussian process models using different kernel structures.

New algorithms reduce complexity for solving nonconvex optimization problems with stochastic objectives and constraints.

Orbits of families of vector fields on a subcartesian space are shown to be smooth manifolds. This allows for a global description of a smooth geometric structure on a family of manifolds in terms of a single object defined on the corresponding family of vector fields. Stratified spaces, Poisson spaces and almost compl…

Modified perturbation method removes non-smoothness in solving Black-Scholes equations.

Proposes PSCs for UQ in deep nets without retraining.

The study analyzes convergence rates for sparse pivotal estimators in high-dimensional regression.

Single-timescale analysis improves convergence in multi-sequence stochastic approximation.

ES-Single uses ES to estimate gradients in unrolled graphs, reducing variance and improving performance.

Proves invertibility of layer potentials for generalized Stokes operators on smooth domains.

Label smoothing improves generalization by controlling generalization loss.

VIND infers smooth nonlinear dynamics from electrophysiology data.

New method creates indistinguishable but misclassified ECG signals.

This paper improves convergence guarantees for SGD algorithms in non-convex smooth functions.

Paper proposes a new method for sparse spectral clustering on Stiefel manifold.

New algorithm solves complex minimax problems efficiently.

New algorithm tackles stochastic bilevel optimization under relaxed smoothness conditions.

SWEEN improves certified robustness via weighted ensembling of smoothed classifiers.

In this paper we study the singular set of Dirichlet-minimizing $Q$-valued maps from $\mathbb{R}^m$ into a smooth compact manifold $\mathcal{N}$ without boundary. Similarly to what happens in the case of single valued minimizing harmonic maps, we show that this set is always $(m-3)$-rectifiable with uniform Minkowski b…

Single gradient step finds adversarial examples in random neural networks.

Study on lens spaces bounding 4-manifolds with specific Betti numbers.

Study shows how any group can be fundamental of a non-orientable 4-manifold with exotic structure.

Defines smooth actions of a group on manifolds and vector spaces.

For a smoothing Y of a 2-dimensional cyclic quotient singularity X, we construct a simple handle decomposition of Y by using a particular birational map from Y to the projective plane. The manifold Y is built up from the product of an annulus with a disk by attaching 2-handles in a manner which can be described by mean…

New method improves robustness of large models without sacrificing accuracy.

We propose a new proximal, path-following framework for a class of constrained convex problems. We consider settings where the nonlinear---and possibly non-smooth---objective part is endowed with a proximity operator, and the constraint set is equipped with a self-concordant barrier. Our approach relies on the followin…

Consider a smooth effective action of a torus $\mathbb{T}^n$ on a connected $C^{\infty}$-manifold $M$ of dimension $m$. Then $n\leq m$. In this work we show that if $n<m$, then there exist a complete vector field $X$ on $M$ such that the automorphism group of $X$ equals $\mathbb T^n \otimes \mathbb{R}$, where the facto…

New insights into simple kernel smoothing reveal surprising asymptotics.

For 5 <= k <= 8 we show that the infinite family of exotic smooth structures on CP^2# k(-CP^2) can be achieved by 1/n - surgeries on a single embedded nullhomologous torus in a manifold R_k which is homeomorphic to CP^2# k(-CP^2).

Time series analysis is used to understand and predict dynamic processes, including evolving demands in business, weather, markets, and biological rhythms. Exponential smoothing is used in all these domains to obtain simple interpretable models of time series and to forecast future values. Despite its popularity, expon…

MARINA-P improves non-smooth federated optimization with adaptive stepsizes.

The study finds a special type of smooth function on connected sums of manifolds.

Single-stage neural architecture improves text-to-image synthesis.

We consider in this paper the regularity problem for time-optimal trajectories of a single-input control-affine system on a n-dimensional manifold. We prove that, under generic conditions on the drift and the controlled vector field, any control u associated with an optimal trajectory is smooth out of a countable set o…

New algorithm for differentially private distributed optimization of smooth, non-convex problems.

Generative models improved with smoothed score functions for better sample quality.