Proposes a global model from local sparsity assumptions in inverse problems.
problem Inability of traditional sparse modeling to model entire global signals optimally.
method Constructs a global model from local sparsity assumptions using constrained underdetermined systems and ADMM optimization.
result Shows unique and stable recovery conditions for global signal representation.
SEARNN improves RNN training by incorporating global-local losses.
problem RNNs trained with MLE fail to exploit structured losses and suffer from exposure bias.
method SEARNN introduces global-local losses through test-alike search space exploration.
result SEARNN outperforms MLE on OCR, spelling correction, and machine translation tasks.
We derive a new radial link for binary classification under shared elliptical distributions.
problem Binary classification under shared-generator elliptical class-conditional distributions.
method We derive the Bayes radial-link family from the within-class radius law and estimate it by a finite fractional-power stochastic-polynomial projection.
result The derived link is asymptotically Bayes-optimal and significantly better than QDA on various benchmarks.
Study on curvature decay in steady Ricci solitons, proving dichotomy.
problem Curvature decay in steady Ricci solitons.
method Established a dichotomy for curvature decay in specific types of solitons.
result Proved a dichotomy on curvature decay for certain steady Ricci solitons.
Every locally compact local group is locally isomorphic to a topological group.
Extends Hopf-Tsuji-Sullivan dichotomy to higher rank groups and applies to Anosov subgroups.
problem Understanding discrete subgroups of semisimple real algebraic groups.
method Establishes an extension of the Hopf-Tsuji-Sullivan dichotomy and applies it to Anosov subgroups.
result Anosov subgroups exhibit different phenomena depending on the rank of the group.
A new TwinGP framework for efficient large-scale GP modeling.
problem Efficiently modeling large-scale Gaussian processes with computational constraints.
method Combines global and local approximations using a subset-of-data approach.
result TwinGP framework performs on par or better than state-of-the-art methods at a fraction of the computational cost.
Discusses the tight versus overtwisted dichotomy in 3D contact geometry.
problem Understanding the tight versus overtwisted dichotomy in 3D contact geometry.
method Reviews Eliashberg's seminal work and contributions to the theory.
result Explains the genesis and importance of the tight versus overtwisted dichotomy.
Proposes a new method to control FDR using frequentist-assisted horseshoe for high-dimensional testing.
problem Designing tests with frequentist false discovery rate control using horseshoe prior.
method Frequentist-assisted horseshoe procedure for high-dimensional normal means testing.
result Consistently achieves robust finite-sample FDR control in various sparse cases.
Improves classification accuracy with random-pair selection in nested dichotomies.
problem Improving classification accuracy with nested dichotomies.
method Random-pair selection for class subset selection in ensembles of nested dichotomies.
result Random-pair selection outperforms other methods in many cases.
Improves predictive performance of nested dichotomies.
problem Improving the performance of multi-class classification problems.
method A simple, general method for improving nested dichotomies produced by random subset selection techniques.
result Improves root mean squared error of nested dichotomies.
Nested dichotomies for multiclass tasks often fail to calibrate probabilities.
problem Poor probability calibration in nested dichotomies for multiclass classification.
method Transforming multiclass problems into binary ones using a tree structure, and applying various calibration strategies.
result Improving accuracy and log-loss by calibrating both internal base models and the nested dichotomy structure.
Optimizes edge coloring in graph bundling for better edge differentiation.
problem Difficulty in identifying origins and destinations of individual edges in strongly bundled graphs.
method Optimizes edge coloring based on pairwise edge strength and origin-destination dissimilarity, solving a nonlinear optimization problem.
result Peacock bundles enhance graph layout comprehensibility with edge differentiation.
Study of Matsumoto maps on foliated bundles over hyperbolic manifolds.
problem Characterizing ergodic harmonic measures on foliated bundles.
method Analysis of actions of hyperbolic manifold groups on the circle.
result Suspension of actions with non-discrete images cannot admit Matsumoto maps of type I.
The paper revisits and improves on a Bayesian relevance vector machine method for small sample sizes.
problem Statistical modeling with small sample sizes relative to the number of covariates.
method Introduces a new class of global-local priors and provides theoretical properties.
result Results on posterior consistency and contraction rates are provided.
Uniform boundedness of Riesz transforms on Riemannian manifolds is established with a dichotomy.
problem Establishing uniform boundedness of Riesz transforms on Riemannian manifolds.
method Constructing a complete Riemannian manifold M to demonstrate the dichotomy. result A dichotomy concerning uniform boundedness of Riesz transforms on Riemannian manifolds.
New framework optimizes complex systems decisions via simulation.
problem Optimizing strategic, tactical, and operational decisions in complex systems.
method Global-local metamodel assisted two-stage optimization via simulation.
result Framework efficiently searches for optimal decisions with unknown objective.
Bayesian method clusters data and selects variables with shrinkage priors.
problem Sparse convex clustering with limited data accuracy issues.
method Bayesian approach using global-local shrinkage priors and Gibbs sampling.
result Improved estimation accuracy in sparse convex clustering.
ETC improves Transformer models for long and structured inputs.
problem Scaling input length and encoding structured inputs in Transformers.
method Introduces global-local attention, relative position encodings, and CPC pre-training.
result Achieves state-of-the-art results on four natural language datasets.
We offer the following explanation of the statement of the Kuratowski graph planarity criterion and of 6/7 of the statement of the Robertson-Seymour-Thomas intrinsic linking criterion. Let us call a cell complex 'dichotomial' if to every cell there corresponds a unique cell with the complementary set of vertices. Then …
The paper studies contact topology submanifolds and their rigidity.
problem Contact topology submanifolds rigidity and degeneracy.
method Contact coisotropic submanifolds, pseudo-metric, Chekanov type pseudo-metric.
result A contact topology analogue to Chekanov's dichotomy of degeneracy.
The study proves a dichotomy for minimal hypersurfaces in certain thick manifolds.
problem Characterizing minimal hypersurfaces in thick manifolds.
method Generalizes Yau's conjecture using bounded geometry or thick at infinity conditions.
result Either infinitely many saddle points or no minimal hypersurfaces exist.
Anosov groups' measures on limit sets are uniquely determined by their dimension.
problem Characterizing measures on limit sets of Anosov groups.
method Higher rank Hopf-Tsuji-Sullivan dichotomy for maximal diagonal actions.
result Uniqueness of Γ-conformal measures for critical dimensions. We prove a global local rigidity result for character varieties of 3-manifolds into SL2. Given a 3-manifold with toric boundary M satisfying some technical hypotheses, we prove that all but a finite number of its Dehn fillings Mp/q are globally locally rigid in the following sense: every irreducible repr…
TQFT invariants are either easy or hard to compute, depending on the TQFT type.
problem Computing TQFT invariants on closed 3-manifolds.
method Application of a dichotomy result for weighted constraint satisfaction problems over C.
result TQFT invariants are either solvable in polynomial time or #P-hard. The paper explores actions on metric spaces similar to 3D manifolds, proving rigidity results.
problem Rigidity of actions on metric spaces similar to 3D manifolds.
method Reexamined isometry groups of geometric 3-manifolds, considered homomorphisms to them, established a dichotomy.
result Established a dichotomy between finite image or infinite volume of quotient spaces.
The paper studies ergodicity of flows on subspaces, generalizing earlier work.
problem Ergodicity of flows on subspaces of higher rank groups.
method Analyzes one-parameter diagonalizable subgroups of connected semisimple groups acting on homogeneous spaces.
result Obtains an ergodicity criterion similar to Hopf-Tsuji-Sullivan for general Anosov subgroups.
The paper explores Anosov flows on torus bundles and provides new insights.
problem Investigating Anosov flows on affine torus bundles and their properties.
method Surgery type construction of Anosov flows and dichotomy result for fiberwise Anosov flows.
result New insights into Anosov flows, including non-transitive flows in odd dimensions.
Study zippers in hyperbolic 3-manifolds, proving fixed point dichotomy.
problem Existence and behavior of elements in hyperbolic 3-manifold groups.
method Action analysis on minimal zippers, proving fixed point dichotomy.
result Every nontrivial element either fixes a unique point in each tree or acts freely on both.
TopoGeoScore selects robust checkpoints using only source-domain representations.
problem Selecting robust checkpoints without target-domain labels or samples.
method Constructs class-conditional mutual k-nearest-neighbour graphs and extracts three interpretable signals.
result Source representations contain measurable global-local-topological evidence of robustness.
New theory shows perishable goods markets are more stable and efficient.
problem Lower stability and efficiency of markets for re-tradable assets compared to perishable goods.
method Reformulation of no-trade and no-arbitrage theorems in neoclassical finance.
result Perishable goods markets exhibit higher stability and efficiency.
The study quantifies how many objects can be linearly classified under all views.
problem Understanding the expressivity of group-equivariant representations.
method Generalization of Cover's Function Counting Theorem to quantify separable dichotomies.
result The fraction of separable dichotomies is determined by the fixed space dimension of the group action.
Model for dynamic relational data with regime changes.
problem Handling abrupt changes in dynamic relational data.
method Factorized fusion shrinkage model with global-local shrinkage priors.
result Posterior distribution attains minimax optimal rate up to logarithmic factors.
Classifies actions of groups on hyperbolic spaces, proving dichotomy.
problem Classifying actions of groups on hyperbolic spaces.
method Formalization using Borel equivalence relations, focusing on non-elementary actions without fixed points at infinity.
result For every countable group G, either all general type actions can be classified by an explicit invariant or they are unclassifiable in a strong sense. Study dynamics of automorphisms on cubic surfaces and their connection to Painlevé 6.
problem Dynamics of holomorphic automorphisms on cubic surfaces and their relation to Painlevé 6.
method Defined Julia and Fatou sets, studied locally discrete and non-discrete dynamics, and proved existence of non-empty Fatou and Julia sets.
result Existence of non-empty Fatou and Julia sets for the group action.
The paper defines flexible domains for minimal surfaces in Euclidean spaces and explores their properties.
problem Understanding the flexibility of domains in Euclidean spaces for minimal surfaces.
method Investigates the concept of flexibility in terms of minimal surfaces contained in domains.
result Defines flexible domains and shows how they can be approximated by minimal immersions.
Study homotopy groups of open books and their pages, pages, and bindings.
problem Homotopy groups of open books and their components.
method Homotopy theoretic conditions on monodromy, integral and rational loop space decompositions.
result Integral and rational loop space decompositions for open books under specific conditions.
The paper studies proper discontinuity of actions on Weyl chamber flow spaces.
problem Properly discontinuous actions on Weyl chamber flow spaces for transverse subgroups.
method Analyzes limit sets and quotient spaces, introduces growth indicators and conformal measures.
result Establishes ergodic dichotomy for Weyl chamber flow and introduces new measures.
New geometric structures defined in contact metric geometry.
problem Introducing new geometric structures in almost contact metric geometry.
method Defining locally conformal almost generalized f-cosymplectic manifolds and deriving integrability conditions. result Dimensional dichotomy: transverse components in dimension 3, proportional to η in higher dimensions.
Given a harmonic measure of a hyperbolic lamination on a compact metric space, a positive harmonic function is defined on the universal cover of a typical leaves. We discuss some properties of this function. Especially if all the leaves are hyperbolic, ergodic harmonic measures are divided into two classes.
Minimal submanifolds either fill space or are confined with geometric restrictions.
problem Understanding the behavior of minimal submanifolds in space.
method A dichotomy principle and volume doubling theorem.
result Quantitative restrictions on confined minimal submanifolds, including volume growth and optimal density rates.
Recent work of M. Yoshinaga shows that in some instances certain higher homotopy groups of arrangements map onto non-resonant homology. This is in contrast to the usual Hurewicz map to untwisted homology, which is always the zero homomorphism in degree greater than one. In this work we examine this dichotomy, generaliz…
Study free energy in spherical spin glasses, proving universality dichotomy.
problem Analyzing free energy in spherical spin glass models with different tail exponents.
method Introduced a tail-adapted normalization and used universality dichotomy.
result Sharp universality dichotomy for free energy across different tail exponents.
This work refines Cover's theory for binary classification on low-dimensional data.
problem The challenge of analyzing how low-dimensional data structures affect classification models.
method Refines Cover's function-counting theory to account for low-dimensional data structure.
result Derives dichotomy counts and analyzes the impact of data structure on classification models.
The paper develops a theory of conformal density at infinity for groups with contracting elements.
problem Understanding conformal dynamics at infinity for groups with contracting elements.
method Introducing a class of convergence boundary and establishing the basic theory of conformal density on it.
result Unified theory of conformal density on various boundaries for different types of groups.
Horseshoe priors improve small area estimation by borrowing strength globally but locally.
problem Improving precision of small area estimators through global-local borrowing of strength.
method Developed a tail-robust horseshoe model for Fay-Herriot small area estimation, using heteroscedastic Tweedie identity and regular variation theory.
result The horseshoe model outperforms structured Gaussian smoothing on strongly spatial data, identifying exceptional areas that smoothing suppresses.
Breiman's data analysis dichotomy is outdated, offering a third approach: mechanistic models.
problem Data analysis dichotomy between data modelers and algorithmic modelers.
method Interpolating between simple interpretable models and flexible function approximations using mechanistic models.
result Flexible, interpretable, and scientifically-informed hybrids can provide accurate and robust predictions.
HS-MoE selects sparse experts using adaptive priors and data-adaptive gating.
problem Sparse expert selection in mixture-of-experts architectures.
method Combines horseshoe prior with input-dependent gating for data-adaptive sparsity.
result Data-adaptive sparsity in expert usage.