arXiv research

Improved neural framework for scaling entropic MOT with significant computational gains.

New algorithms compute robustness bounds for multiclass classification models.

TreeDSB solves mOT problems on tree-structured costs for Wasserstein barycenters.

Hybrid Bayesian MOT uses neural networks to improve model aspects, achieving state-of-the-art performance.

We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be approximated using linear programming (LP) problems which result from a discretisa…

A drone-based MOT algorithm tracks vehicles using neural network detections and TPMBM filter.

Enhances MOT with causality constraints for better option pricing.

Area-charge inequalities and local rigidity of free boundary MOTS in charged initial data sets

We prove in this paper that, under suitable coinditions on an initial data set, we can obtain Area and Curvature Estimates for simple marginally outer trapped surfaces (or MOTS). Using this estimates, we derive a Compactness Theorem for MOTS. Moreover, the Compactness Theorem will allow us to adapt the recent Degree Th…

In a recent paper, Eichmair, Galloway and Pollack have proved a Gannon-Lee-type singularity theorem based on the existence of marginally outer trapped surfaces (MOTS) on noncompact initial data sets for globally hyperbolic spacetimes. This result requires that the MOTS be generic in a suitable sense. In the same spirit…

Study shows how charged MOTS restrict spacetime configurations.

The study examines the index of MOTS in Kerr-Newman-de Sitter spacetime and its relation to mass and charge.

New method to find surfaces in null cones with constant curvature near black hole indicators.

In recent work, the notion of Double Convexity for a foliation of a conical null hypersurface was introduced to give a proof, if satisfied, of the Null Penrose Inequality. Double Convexity constrains the geometry of a Marginally Outer Trapped Surface (MOTS), called a quasi-round MOTS. In the first part of this paper, f…

The paper explains emergent phenomena in deep learning using entropic forces.

Paper proves rigidity of initial data sets with boundary and capillary MOTS.

Study of mean curvature flow on null hypersurfaces leading to MOTS.

Neural networks' optimization dynamics are confined to a single basin despite connected basins in the loss landscape.

Unified framework for optimal transport on curved spaces using neural potentials.

Proves properties of free boundary stable MOTS in spacetimes.

The aim of this paper is to collect some facts about the blowup of Jang's equation. First, we discuss how to construct solutions that blow up at an outermost MOTS. Second, we exclude the possibility that there are extra blowup surfaces in data sets with non-positive mean curvature. Then we investigate the rate of conve…

A new relaxed framework for pricing illiquid derivatives using bid-ask spreads.

Quantification of the stationary points and the associated basins of attraction of neural network loss surfaces is an important step towards a better understanding of neural network loss surfaces at large. This work proposes a novel method to visualise basins of attraction together with the associated stationary points…

MOT uses RL with OT to adapt to different market conditions for algorithmic trading.

Online Multi-Object Tracking (MOT) from videos is a challenging computer vision task which has been extensively studied for decades. Most of the existing MOT algorithms are based on the Tracking-by-Detection (TBD) paradigm combined with popular machine learning approaches which largely reduce the human effort to tune a…

We study the evolution of hypersurfaces in spacetime initial data sets by their null mean curvature. A theory of weak solutions is developed using the level-set approach. Starting from an arbitrary mean convex, outer untapped hypersurface $\partialΩ_0$, we show that there exists a weak solution to the null mean curvatu…

Method learns conditional distributions using neural entropic optimal transport.

New algorithm ATENT improves adversarial robustness in neural networks.

Study stability of surfaces in spacetimes, proving new estimates and theorems.

Study shows instability of certain MOTSs with continuous symmetry.

Small deformations of marginally outer trapped surfaces (MOTS) are studied by using the stability operator introduced by Andersson-Mars-Simon. Novel formulae for the principal eigenvalue are presented. A characterization of the many marginally outer trapped tubes (MOTT) passing through a given MOTS is given, and the po…

MOTS improves Thompson sampling to match minimax bounds for bandit problems.

MERLIN tackles multi-objective task scheduling with hierarchical DRL, outperforming existing methods.

Vacuum gravity shows black holes can form without collapse.

We prove dual attainment for multi-asset financial derivatives pricing.

The problem of Multiple Object Tracking (MOT) consists in following the trajectory of different objects in a sequence, usually a video. In recent years, with the rise of Deep Learning, the algorithms that provide a solution to this problem have benefited from the representational power of deep models. This paper provid…

Study stability and rigidity of axisymmetric marginally outer trapped surfaces.

Study examines stability of MOTS in symmetric initial data sets.

We study the complexity of approximating the multimarginal optimal transport (MOT) distance, a generalization of the classical optimal transport distance, considered here between $m$ discrete probability distributions supported each on $n$ support points. First, we show that the standard linear programming (LP) represe…

New method protects neural networks from adversarial attacks without generating adversarial examples.

Introduces entropic tribrackets and their applications in link distinguishing.

We introduce a new geometric evolution equation for hypersurfaces in asymptotically flat spacetime initial data sets, that unites the theory of marginally outer trapped surfaces (MOTS) with the study of inverse mean curvature flow in asymptotically flat Riemannian manifolds. A theory of weak solutions is developed usin…

New groupoids generalize classical motion and mapping classes.

We define link and graph invariants from entropic magmas modeling them on the Kauffman bracket and Tutte polynomial. We define the homology of entropic magmas. We also consider groups that can be assigned to the families of compatible entropic magmas.

Constructs initial data leading to apparent horizons and tests Penrose Inequality.

Batch normalization with regularization turns deterministic autoencoders into generative models.

In [5], a rigidity result was obtained for outermost marginally outer trapped surfaces (MOTSs) that do not admit metrics of positive scalar curvature. This allowed one to treat the "borderline case" in the author's work with R. Schoen concerning the topology of higher dimensional black holes [8]. The proof of this rigi…

Unified Kantorovich duality for multimarginal optimal transport on Polish spaces.