New methods for scalable inference in modular models with misspecified sub-models.
problem Model misspecification in multi-modular models complicates evidence combination.
method Variational methods for approximating Cut and SMI posteriors, and Variational Meta-Posterior.
result Feasibility of analysis with multiple cuts using a single set of variational parameters.
NeVI-Cut uses neural networks to efficiently propagate uncertainty without feedback.
problem Efficiently propagating uncertainty in downstream Bayesian analysis without feedback.
method NeVI-Cut combines neural networks and normalizing flows for variational inference.
result NeVI-Cut achieves significant computational gains and higher accuracy than traditional methods.
Enhances multi-modular models by directing information flow between components.
problem Improving predictive performance in multi-modular models with misspecification.
method Introduces Semi-Modular Inference (SMI) with an influence parameter to control information flow between modules.
result SMI allows for tunable and directed information flow, improving prediction in some settings.
New Karger-like algorithms solve graph cuts, useful for image segmentation.
problem Finding minimum cuts in graphs and graph-based semi-supervised learning.
method Extensions of Karger's contraction algorithm for s-t-mincut and normalized cut problems. result Simple new algorithm based on Karger's original, yields linear runtime and interpretable potential.
The paper proposes a method to improve Bayesian inference for periodic data using data-driven priors.
problem Efficiency in approximating posterior distribution in models with periodicity.
method Construct a prior distribution from data using a Gaussian process with a periodic kernel, approximated using adaptive importance sampling.
result The proposed method improves the marginal posterior distribution of the period parameter.
We give polynomial-time algorithms for the exact computation of lowest-energy (ground) states, worst margin violators, log partition functions, and marginal edge probabilities in certain binary undirected graphical models. Our approach provides an interesting alternative to the well-known graph cut paradigm in that it …
New normalizing flows in hyperbolic space improve posterior modeling for hierarchical data.
problem Limited flexibility of existing normalizing flows in Euclidean space for hierarchical data.
method Elevated normalizing flows to hyperbolic spaces using coupling transforms and Wrapped Hyperboloid Coupling.
result Improved performance on density estimation and hierarchical graph data.
A method is given for calculating the strict minimum message length (SMML) estimator for 1-dimensional exponential families with continuous sufficient statistics. A set of n equations are found that the n cut-points of the SMML estimator must satisfy. These equations can be solved using Newton's method and this app…
NeuralCut learns to select cutting planes by looking ahead, outperforming traditional methods.
problem Selecting effective cutting planes for MILP optimization.
method Imitation learning on a lookahead expert to train a neural network for cut selection.
result NeuralCut outperforms standard baselines in cut selection for MILP benchmarks.
Differentiable cutting-plane layers solve parametric mixed-integer linear optimization problems.
problem Solving parametric mixed-integer linear optimization problems with changing data.
method Introducing cutting-plane layers (CPLs) for differentiable cutting-plane generation.
result The algorithm computes solutions with low integrality gaps and generalizes to unseen instances.
The paper optimizes LLM accuracy by stopping early based on consistent answers.
problem Improving LLM accuracy in math and reasoning problems.
method Bayesian stopping policy to save on sampling costs, tracking only the L-1 most frequent answer counts.
result The L=3 stopping policy is sufficient for asymptotic optimality and significantly reduces inference costs.
Paper connects probability density cuts to graph theory eigenfunctions.
problem Developing sparse cuts for probability densities.
method Defines sparse cuts and principal eigenfunctions for probability densities, proving Cheeger and Buser inequalities.
result No such inequalities hold for prior definitions, proving new inequalities for probability densities.
Study Riemannian metrics on lens spaces, find cut loci and diameters.
problem Understanding Riemannian metrics on lens spaces and their geometric properties.
method Geometric control theory methods applied to axisymmetric metrics.
result Cut loci and cut times converge to sub-Riemannian structure's values.
Study Riemannian metrics on lens spaces, find cut loci and diameters.
problem Analyzing Riemannian metrics on lens spaces.
method Geometric control theory methods.
result Cut loci and cut times converge to sub-Riemannian structure's cut locus and time.
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.
problem Stability of cut locus under C2-perturbations of the metric. method Proving stability with respect to the Hausdorff metric of the cut locus under C2 perturbation of the metric. result The Hausdorff distance between cut loci converges to zero as the metrics converge.
New equivalence relation for links using cut-diagrams.
problem Classical link concordance.
method Cut-diagrams and cut-concordance.
result Nilpotent peripheral system invariant of cut-concordance.
Can we make Bayesian posterior MCMC sampling more efficient when faced with very large datasets? We argue that computing the likelihood for N datapoints in the Metropolis-Hastings (MH) test to reach a single binary decision is computationally inefficient. We introduce an approximate MH rule based on a sequential hypoth…
Study shows convergence rates for Cheeger cuts on data clouds.
problem Optimizing graph cuts for clustering data sampled from a manifold.
method Analyzes statistical properties of Cheeger cuts on proximity graphs built from data.
result Obtains high probability convergence rates for Cheeger constant and cuts.
Unified framework for differentiable graph partitioning with probabilistic cuts.
problem Lack of general guarantees and principled gradients in prior probabilistic relaxations of graph cuts.
method Unified probabilistic framework covering a wide class of cuts, including Normalized Cut, with tight analytic upper bounds.
result Rigorous, numerically stable foundation for scalable, differentiable graph partitioning.
Stochastic cutting planes improve data-driven optimization speed.
problem Data-driven Mixed-Integer Nonlinear Optimization problems.
method Stochastic version of cutting-plane method.
result Stochastic algorithm converges to ε-optimal solution with high probability.
Study of Randers metrics on spheres with simple cut loci.
problem Understanding Randers metrics on spheres and their cut loci.
method Analyzing geodesics, conjugate, and cut loci of Finsler metrics of Randers type.
result Found new families of Randers metrics 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 Gk with k 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.
problem Continuous max flow/min cut theorem for complex domains.
method Continuous analogue of max flow/min cut theorem considering topology.
result Continuous max flow/min cut theorem proven for currents and laminations.
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 k-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.
problem Understanding geodesic complexity in Riemannian manifolds.
method Study of decompositions of cut loci and their tangent fibers.
result Established a new upper bound for geodesic complexity.
New 2-spheres of revolution with simple cut locus structures.
problem Determining surfaces of revolution with simple cut locus structures.
method Introducing a new family of 2-spheres of revolution.
result The new family {M_n}_n has a simple cut locus structure.
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…
Laplacian of distance function shows negative infinity at cut locus points.
problem Understanding the Laplacian of distance functions on Riemannian manifolds.
method Analyzing the Laplacian of the distance function to a point on a smooth Riemannian manifold.
result The Laplacian of the distance function is −∞ at points of the cut locus. 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.
problem Establishing a functorial relationship between symplectic and contact structures.
method Developed a cutting procedure and its inverse for manifolds with boundary and equivariant transverse maps, then applied it to non-symplectic and non-contact structures.
result Obtained an inverse functor for equivariant radial-squared 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.
problem Extending Whitehead's cut vertex lemma to tree group conjugacy classes.
method Proves a version of Whitehead's lemma for tree groups.
result Establishes a cut vertex in star graphs for tree group conjugacy classes.
Extends Milnor invariants to surface-links using cut-diagrams.
problem Tackles invariants for surface-links in 4-space.
method Introduces cut-diagrams and groups associated to them.
result Yields concordance and link-homotopy invariants for surface-links.
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.
problem Defining and studying cobordism cut and paste groups of manifolds with boundary.
method Constructing a spectrum that recovers the cobordism cut and paste groups of manifolds with boundary.
result Construction of a spectrum that recovers the cobordism cut and paste groups of manifolds with boundary.
Study of longest arcs and cut loci in deformed anti de-Sitter spaces.
problem Existence and properties of time-like cycles in deformed Lorentzian manifolds.
method Analysis of universal covering, admissible curves, and Lorentzian geodesics.
result Identification of cut time and cut locus in deformed anti de-Sitter spaces.
We study the relationship between two concepts: cut limits and hyperbolic extensions.
The paper extends spacetime topology results using codimension 2 null cut locus properties.
problem Understanding spacetime topology with and without horizons.
method Review and extension of existing literature on spacetime topology, utilizing codimension 2 null cut locus properties.
result Results for spacetimes with and without horizons, including asymptotically AdS settings.
New method calculates cut locus on surfaces without boundary.
problem Computing the cut locus on compact submanifolds.
method Variational convex problem with conic constraints.
result Proven convergence of the approximation method.
The paper explores new phenomena in boundaries of relatively hyperbolic groups.
problem Exploring new phenomena in boundaries of relatively hyperbolic groups.
method Combination theorem to create examples of relatively hyperbolic groups with parabolic cut pairs.
result All relatively hyperbolic groups with inseparable parabolic cut pairs arise via the combination theorem.
Generalizes neural network verification by adding arbitrary cutting planes.
problem Handling general cutting plane constraints in neural network verification.
method Generalized bound propagation method (GCP-CROWN) that allows arbitrary cutting plane constraints.
result GCP-CROWN significantly improves neural network verification performance.