arXiv research

Paper solves curvature equations in Minkowski space for non-convex domains.

Paper shows non-convexity in solutions to Hessian equations.

Solves equality case in isoperimetric inequality for non-convex domains.

Study finds eigenvalue bounds for non-convex domains using cohomology.

This tutorial introduces the CMA Evolution Strategy (ES), where CMA stands for Covariance Matrix Adaptation. The CMA-ES is a stochastic, or randomized, method for real-parameter (continuous domain) optimization of non-linear, non-convex functions. We try to motivate and derive the algorithm from intuitive concepts and …

The paper derives new inequalities for non-convex domains and flows.

Proposes r2SGLD for efficient constrained exploration in non-convex learning.

We give a simple proof of the insoperimetric inequality for quermassintegrals of non-convex starshaped domains, using a reslut of Gerhardt \cite{G} and Urbas \cite{U} on an expanding geometric curvature flow.

The Blaschke rolling disk theorem is extended to non-convex domains.

We study the boundary and lens rigidity problems on domains without assuming the convexity of the boundary. We show that such rigidities hold when the domain is a simply connected compact Riemannian surface without conjugate points. For the more general class of non-trapping compact Riemannian surfaces with no conjugat…

Ada-BKB optimizes black-box functions on continuous domains with adaptive discretization.

Paper tackles constrained learning with non-convex losses, overcoming challenges with new approach.

This thesis explores how submodularity aids in optimizing non-convex functions and validating algorithms.

The paper constructs $λ$-hypersurfaces for $λ>0$ and $λ<0$.

Neural nets solve electric field in non-convex microfluidic devices.

In this work, we study the problem of learning a single model for multiple domains. Unlike the conventional machine learning scenario where each domain can have the corresponding model, multiple domains (i.e., applications/users) may share the same machine learning model due to maintenance loads in cloud computing serv…

New algorithms identify invariant features for domain generalization.

This paper tackles non-convex phase retrieval with structured assumptions.

New method ISR improves domain generalization with provable guarantees.

This paper tackles the computational complexity of finding approximate stationary points in non-convex optimization.

A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low rank are frequently imposed or else the objective itself is designed to be a non-c…

Algorithm optimizes non-convex functions using dueling comparisons.

The paper tackles MAP inference over non-convex constraints in safety-critical settings.

A new method solves diagonally constrained SDPs quickly and accurately.

Unified analysis for graph learning from multi-attribute Gaussian time series.

Solves a challenging problem in imaging and communication.

We find all extremal Lagrangian tori in symplectic unit balls and some toric domains.

One of the most effective algorithms for differentially private learning and optimization is objective perturbation. This technique augments a given optimization problem (e.g. deriving from an ERM problem) with a random linear term, and then exactly solves it. However, to date, analyses of this approach crucially rely …

Self-training avoids spurious features in domain adaptation.

A new algorithm estimates output ranges for deep neural networks efficiently.

This paper examines how optimization methods affect the reliability of detecting inputs outside a model's training distribution.

Consider a surface $S$ immersed in the Lorentz-Minkowski 3-space $\boldsymbol R^3_1$. A complete light-like line in $\boldsymbol R^3_1$ is called an entire null line on the surface $S$ in $\boldsymbol R^3_1$ if it lies on $S$ and consists of only null points with respect to the induced metric. In this paper, we show th…

The paper studies continuous submodular functions and their optimization.

Two private algorithms improve domain adaptation with privacy guarantees.

ProGO optimizes non-convex functions without gradients, outperforming existing methods.

Compact, non-convex curve flows are created.

Finding minima of a real valued non-convex function over a high dimensional space is a major challenge in science. We provide evidence that some such functions that are defined on high dimensional domains have a narrow band of values whose pre-image contains the bulk of its critical points. This is in contrast with the…

Paper uses integer programming for non-convex boosting in classification.

Many applications in signal processing benefit from the sparsity of signals in a certain transform domain or dictionary. Synthesis sparsifying dictionaries that are directly adapted to data have been popular in applications such as image denoising, inpainting, and medical image reconstruction. In this work, we focus in…

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

New algorithm improves convergence for non-convex problems with boundaries.

New insights into how data transformations affect self-supervised clustering.

This paper explores optimising acquisition functions in Bayesian optimisation.

A neural network approach to learn Cusp Catastrophe dynamics.

We study the minimal surface equation in the Heisenberg space, Nil_3. A geometric proof of non existence of minimal graphs over non convex, bounded and unbounded domains is achieved (our proof holds in the Euclidean space as well). We solve the Dirichlet problem for the minimal surface equation over bounded and unbound…

Machine learning techniques based on neural networks are achieving remarkable results in a wide variety of domains. Often, the training of models requires large, representative datasets, which may be crowdsourced and contain sensitive information. The models should not expose private information in these datasets. Addr…

This paper puts forth a novel bi-linear modeling framework for data recovery via manifold-learning and sparse-approximation arguments and considers its application to dynamic magnetic-resonance imaging (dMRI). Each temporal-domain MR image is viewed as a point that lies onto or close to a smooth manifold, and landmark …

Clustering consists of grouping together samples giving their similar properties. The problem of modeling simultaneously groups of samples and features is known as Co-Clustering. This paper introduces ROCCO - a Robust Continuous Co-Clustering algorithm. ROCCO is a scalable, hyperparameter-free, easy and ready to use al…