A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Unified framework for differentiable graph partitioning with probabilistic cuts.
This paper presents a new probabilistic generative model for image segmentation, i.e. the task of partitioning an image into homogeneous regions. Our model is grounded on a mid-level image representation, called a region tree, in which regions are recursively split into subregions until superpixels are reached. Given t…
We study the small time asymptotics of the gradient and Hessian of the logarithm of the heat kernel at the cut locus, giving, in principle, complete expansions for both quantities. We relate the leading terms of the expansions to the structure of the cut locus, especially to conjugacy, and we provide a probabilistic in…
We present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. Moments of a…
In this paper we prove a short time asymptotic expansion of a hypoelliptic heat kernel on an Euclidean space and a compact manifold. We study the "cut locus" case, namely, the case where energy-minimizing paths which join the two points under consideration form not a finite set, but a compact manifold. Under mild assum…
New method for probabilistic modeling of integer submodular functions.
Off-policy reinforcement learning with eligibility traces is challenging because of the discrepancy between target policy and behavior policy. One common approach is to measure the difference between two policies in a probabilistic way, such as importance sampling and tree-backup. However, existing off-policy learning …
Transforms distance-based outlier scores into interpretable probabilistic estimates.
NeuralCut learns to select cutting planes by looking ahead, outperforming traditional methods.
Differentiable cutting-plane layers solve parametric mixed-integer linear optimization problems.
NeVI-Cut uses neural networks to efficiently propagate uncertainty without feedback.
Paper connects probability density cuts to graph theory eigenfunctions.
Study Riemannian metrics on lens spaces, find cut loci and diameters.
Study Riemannian metrics on lens spaces, find cut loci and diameters.
We consider a left invariant Riemannian metric on SO(3) with two equal eigenvalues. We find the cut locus and the equation for the cut time. We find the diameter of such metric and describe the set of all most distant points from the identity. Also we prove that the cut locus and the cut time converge to the cut locus …
Stability of cut locus under metric perturbations in compact Riemannian manifolds.
In recent studies on model-based reinforcement learning (MBRL), incorporating uncertainty in forward dynamics is a state-of-the-art strategy to enhance learning performance, making MBRLs competitive to cutting-edge model free methods, especially in simulated robotics tasks. Probabilistic ensembles with trajectory sampl…
New equivalence relation for links using cut-diagrams.
Study shows convergence rates for Cheeger cuts on data clouds.
Stochastic cutting planes improve data-driven optimization speed.
Study of Randers metrics on spheres with simple cut loci.
We define spin-c prequantization of a symplectic manifold to be a spin-c structure and a connection which are compatible with the symplectic form. We describe the cutting of an S^1-equivariant spin-c prequantization. The cutting process involves a choice of a spin-c prequantization for the complex plane. We prove that …
A symplectic cut of a manifold M with a Hamiltonian circle action is a symplectic quotient of M x C. If M is Kaehler then, since C is Kaehler, the cut space is Kaehler as well. The symplectic structure on the cut is well understood. In this paper we describe the complex structure (and hence the metric) on the cut. We t…
In this note, we study the cut locus of the free, step two Carnot groups with generators, equipped with their left-invariant Carnot-Carathéodory metric. In particular, we disprove the conjectures on the shape of the cut loci proposed in [Myasnichenko - 2002] and [Montanari, Morbidelli - 2016], by exh…
Max flow/min cut theorem extended to currents and topology.
Spectral Clustering as a relaxation of the normalized/ratio cut has become one of the standard graph-based clustering methods. Existing methods for the computation of multiple clusters, corresponding to a balanced -cut of the graph, are either based on greedy techniques or heuristics which have weak connection to th…
Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data since they tend to emphasize cut sizes over cut values. We propose a graph partit…
This paper establishes the consistency of a family of graph-cut-based algorithms for clustering of data clouds. We consider point clouds obtained as samples of a ground-truth measure. We investigate approaches to clustering based on minimizing objective functionals defined on proximity graphs of the given sample. Our f…
New upper bound for geodesic complexity derived from cut locus decompositions.
New 2-spheres of revolution with simple cut locus structures.
We consider the Lie group PSL(2) (the group of orientation preserving isometries of the hyperbolic plane) and a left-invariant Riemannian metric on this group with two equal eigenvalues that correspond to space-like eigenvectors (with respect to the Killing form). For such metrics we find a parametrization of geodesics…
In this article we extend cutting and blowing up to the nonrational symplectic toric setting. This entails the possibility of cutting and blowing up for symplectic toric manifolds and orbifolds in nonrational directions.
Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced cluster sizes sin…
Functor connects symplectic and contact structures via cutting and blowups.
In this paper we investigate the small time heat kernel asymptotics on the cut locus on a class of surfaces of revolution, which are the simplest 2-dimensional Riemannian manifolds different from the sphere with non trivial cut-conjugate locus. We determine the degeneracy of the exponential map near a cut-conjugate poi…
Proves a generalized Whitehead cut vertex lemma for tree groups.
Extends Milnor invariants to surface-links using cut-diagrams.
We show how to associate an R-tree to the set of cut points of a continuum. If X is a continuum without cut points we show how to associate an R-tree to the set of cut pairs of X.
Surgeons normally need surgical scissors and tissue grippers to cut through a deformable surgical tissue. The cutting accuracy depends on the skills to manipulate these two tools. Such skills are part of basic surgical skills training as in the Fundamentals of Laparoscopic Surgery. The gripper is used to pinch a point …
A new spectrum recovers cobordism cut and paste groups of manifolds with boundary.
We study the relationship between two concepts: cut limits and hyperbolic extensions.
Study of longest arcs and cut loci in deformed anti de-Sitter spaces.
We consider the structured-output prediction problem through probabilistic approaches and generalize the "perturb-and-MAP" framework to more challenging weighted Hamming losses, which are crucial in applications. While in principle our approach is a straightforward marginalization, it requires solving many related MAP …
The paper extends spacetime topology results using codimension 2 null cut locus properties.
New method calculates cut locus on surfaces without boundary.
The paper explores new phenomena in boundaries of relatively hyperbolic groups.
Generalizes neural network verification by adding arbitrary cutting planes.
We showed in another paper [arXiv:1103.1759] that every connected graph can be realized as the cut locus of some point on some riemannian surface . Here, criteria for the orientability of are given, and are applied to classify the distinct, orientable, cut locus structures on graphs with four generating cycles.