Global EQG sums boundary states over manifold diffeomorphism classes.
problem Summing boundary states over manifold diffeomorphism classes.
method Formulated as classical statistical physics, weights determined by general principles.
result Hartle-Hawking state as a probability measure.
FedReLa: A novel data-level approach for imbalanced federated learning
problem Improving accuracy of federated learning models under class imbalance and data heterogeneity
method Re-labeling samples with a feature-dependent label re-allocator
result Significant improvements in accuracy for minority classes and overall accuracy on stepwise-imbalanced and long-tailed datasets
Globally hyperbolic spacetimes admitting infinitely many causal (and timelike) homotopy classes of curves joining two prescribed points, are exhibited and discussed.
Global fixed points in low-dimensional surface group space correspond to trivial representations.
problem Understanding global fixed points in surface group deformation spaces.
method Direct analysis of the deformation space, focusing on the trivial representation.
result Global fixed points in low-dimensional surface group deformation spaces correspond to the trivial representation of the pure mapping class group.
We introduce a special class of knots, called global knots, in F^2 x R and we construct new isotopy invariants, called T-invariants, for global knots. Some T-invariants are of finite type but they cannot be extracted from the generalized Kontsevitch integral (which is consequently not the universal invariant of finite …
The possibility of the global Lagrangian reduction of a mechanical system with symmetry is shown to be connected with the characteristic class of a principal fiber bundle of the configuration space over the factor manifold. It is proved that the reduced system is globally Lagrangian if and only if the product of the mo…
The local-to-global property is proven for Morse quasi-geodesics in various groups.
problem Proving local-to-global properties for Morse quasi-geodesics in different groups.
method Developing a theory of deep points for local quasi-geodesics in relatively hyperbolic spaces.
result Generalization of combination theorems for stable subgroups of various groups.
Graph-based framework for generalized few-shot learning.
problem Transferring learned models to novel tasks with few labeled examples.
method Graph-based framework that models relationships between seen and novel classes.
result Demonstrates benefits on benchmark datasets.
Paper proves a quantitative estimate for transforming almost complex structures into standard ones.
problem Transforming almost complex structures into standard ones on bounded domains.
method Proves existence of global diffeomorphisms under Hölder-Zygmund conditions.
result Existence of a global diffeomorphism in a specified Hölder-Zygmund class.
Study explores embedding signature-changing manifolds into higher-dimensional spaces.
problem Smooth metric signature changes in spacetimes.
method Global isometric embeddings into higher-dimensional pseudo-Euclidean spaces.
result Explicit constructions of global embeddings into Minkowski and Misner spaces.
Constructs classifiers for neural networks with specific data configurations.
problem Finding global minima of deep ReLU neural networks on sequentially separable data.
method Explicitly constructs zero loss neural network classifiers using cumulative parameters and truncation maps.
result Global minimizers can be described with a limited number of parameters based on the data structure.
S-VQ-VAE learns interpretable class-specific representations.
problem Learning interpretable representations of data.
method Supervised Vector Quantized Variational AutoEncoder (S-VQ-VAE).
result S-VQ-VAE learns interpretable class-specific representations.
The paper proves weaker conditions for global smoothings of special Lagrangian submanifolds with conical singularities.
problem Conditions for global smoothings of special Lagrangian submanifolds with isolated conical singularities.
method Proof of weaker conditions for global smoothings.
result Global smoothings are possible under weaker hypotheses than previously known.
Generalizes global hyperbolicity to higher signatures and proves compactness.
problem Global hyperbolicity in higher pseudo-Riemannian signatures.
method Generalization and proof of compactness of causal diamonds.
result Existence of solutions to a Plateau problem and characterization of holonomies.
Local and global classifications of Einstein submanifolds in Euclidean space.
problem Classifying Einstein submanifolds in Euclidean space.
method Local and global parametric classifications with emphasis on intrinsic assumptions.
result Local and global classifications of Einstein submanifolds of codimension two.
Wave maps from circle to manifold controllable if homotopy classes match.
problem Global controllability of wave maps from circle to Riemannian manifolds.
method Characterization of controllability via homotopy classes, uniform-time global controllability between steady states, quantitative exponential stability.
result Global controllability is equivalent to homotopy class of data.
The chapter explores globally hyperbolic spacetimes using topology and functional analysis.
problem Understanding global hyperbolicity in spacetimes.
method Foundational tools from order theory and topology, geometric analysis, and connections to physics.
result A connection between global hyperbolicity and geodesic completeness of space-like surfaces.
Global calculus for manifolds with boundary, solving evolution problems.
problem Global solvability of evolution problems on manifolds with boundary.
method Established global functional calculus and Gårding inequality for pseudo-differential operators without local coordinates.
result Global solvability for a class of evolution problems.
Global Chern currents and Baum Bott currents defined on arbitrary complex manifolds.
problem Defining Chern classes and Baum Bott residues on complex manifolds without global resolutions.
method Combining Green's techniques with previous constructions to yield representatives of Chern classes and Baum Bott residues, using local resolutions and metrics.
result Transgression formula for the representatives, showing they differ by a current of the form dN. Khovanov homology shows (4,5) torus knot is a summand in its concordance class.
problem Understanding the global ribbon minima in knot concordance classes.
method Application of Khovanov homology to ribbon concordance.
result Khovanov homology of (4,5) torus knot is a summand in any knot's homology.
Unified Newton-type methods for convex optimization using generalized self-concordant functions.
problem Designing efficient Newton-type methods for convex optimization.
method Introducing generalized self-concordant functions and developing Newton-type methods.
result Unified framework for global and local convergence of Newton-type methods.
NormLIME improves feature importance explanations for deep neural networks.
problem Improving local feature explanations for deep learning models.
method NormLIME aggregates local models into global and class-specific interpretations.
result NormLIME outperforms other feature importance metrics in human user studies and numerical experiments.
The paper proves that certain geodesics pass through timelike poles on specific Lorentzian 2-tori.
problem Existence of closed timelike geodesics through timelike poles on class A Lorentzian 2-tori.
method Study of isometries on globally hyperbolic planes to prove the existence of geodesics.
result Existence of closed timelike geodesics through timelike poles in the interior of the stable time cone.
Characterizes and analyzes the large scale geometry of big mapping class groups of surfaces.
problem Analyzing the large scale geometry of big mapping class groups of surfaces with a unique maximal end.
method Building on previous work, the paper characterizes and analyzes the large scale geometry of big mapping class groups of surfaces with a unique maximal end.
result Proves that any locally CB big mapping class group is CB generated and gives an explicit criterion for determining which big mapping class groups are CB generated.
In this paper we study the global behavior of the Ricci flow equation for two classes of homogeneous manifolds with two isotropy summands. Using methods of the qualitative theory of differential equations, we present the global phase portrait of such systems and derive some geometrical consequences on the structure of …
Chernov-Nemirovski observed that the existence of a globally hyperbolic Lorentzian metric on a (3 + 1)-spacetime pins down a smooth structure on the underlying 4-manifold. In this paper, we point out that the diffeomorphism type of a globally hyperbolic (n + 1)-spacetime is determined by the h-cobordism class of its Ca…
The paper explores global index formulas for one-dimensional holomorphic foliations.
problem Global index formulas for one-dimensional holomorphic foliations.
method Microlocal point of view and short proofs for existing index formulas.
result Generalizations of existing index formulas.
Following the lines of the celebrated Riemannian result of Gromoll and Meyer, we use infinite dimensional equivariant Morse theory to establish the existence of infinitely many geometrically distinct closed geodesics in a class of globally hyperbolic stationary Lorentzian manifolds.
This paper explores the limits of Transformers in learning new patterns from scratch.
problem Understanding when Transformers can learn new patterns from scratch.
method Introducing the 'globality degree' to measure learnability and developing scratchpad techniques.
result Distributions with high globality cannot be learned efficiently by Transformers.
Classifies pure mapping class groups based on surface properties.
problem Classifying pure mapping class groups based on surface properties.
method Complete classification without additional assumptions.
result PMap(Σ) is globally CB if and only if Σ is the Loch Ness monster surface.
Study of spacetimes with timelike boundaries, proving their orthogonal product structure.
problem Understanding spacetimes with boundaries and their properties.
method Proving spacetimes can be split orthogonally and embedding them in higher dimensions.
result Globally hyperbolic spacetimes with timelike boundaries can be split orthogonally and embedded in higher dimensions.
Bayesian optimization improves multi-start global optimization.
problem Global optimization challenges in real-world applications.
method Bayesian optimization framework to determine local search starting points.
result Bayesian optimization enhances the efficiency of multi-start local searches.
Global solutions found for certain reaction-diffusion equations on specific manifolds.
problem Understanding reaction-diffusion equations on various manifolds.
method Analyzing the bottom of the L2 spectrum of −Δ and using time-independent nonlinearities. result Global existence of solutions for certain power nonlinearities on specific manifolds.
Study finds multiple periodic solutions to ODEs related to curvature problems.
problem Finding multiple positive periodic solutions to quasilinear ODEs.
method Global bifurcation techniques applied to second order quasilinear ODEs.
result Bifurcation-theoretic proof of nonuniqueness for conformal metrics with constant scalar curvature.
SGD methods fail to converge to global minimizers in deep neural networks with ReLU activation.
problem Failure of SGD methods to converge to global minimizers in deep neural networks.
method Stochastic Gradient Descent (SGD) and its variants like Adam, RMSProp, etc.
result SGD methods fail to converge to global minimizers with high probability in deep neural networks with ReLU activation.
Study proves global existence and decay for complex wave equations.
problem Global existence and decay for quasilinear wave equations with weak-null condition.
method Novel decoupling of higher order energy estimates, focusing on tangential components.
result Established global existence and decay for solutions with small data.
Paper proves global optimality of a simple optimization scheme for learning DAG models.
problem Learning acyclic directed graphical models from data.
method Path-following optimization scheme for bivariate setting.
result Simple optimization scheme globally converges to global minimum.
New global adversarial attacks improve DNN robustness assessment.
problem Vulnerability of deep neural networks to adversarial attacks.
method Proposed global adversarial example pairs and attack methods.
result DNNs hardened with local adversarial training are vulnerable to global attacks.
Paper introduces hierarchical softmax for global hierarchical classification tasks.
problem Improving classification accuracy in tasks with class hierarchies.
method Global hierarchical neural networks using hierarchical softmax.
result Hierarchical softmax outperforms regular softmax in multiple datasets.
We consider the global symplectic classification problem of plane curves. First we give the exact classification result under symplectomorphisms, for the case of generic plane curves, namely immersions with transverse self-intersections. Then the set of symplectic classes form the symplectic moduli space which we compl…
Generalizes Álvarez class vanishing to singular Riemannian foliations.
problem Characterize geometric tautness in singular Riemannian foliations.
method Glue Álvarez classes of strata into a global class.
result Geometric tautness of singular foliations can be characterized by a global Álvarez class.
The paper constructs Levi flat structures using structure sheaves and differential complexes.
problem Global solvability and regularity of Levi flat structures.
method Employing formal integrability and differential complexes, the paper constructs a resolution for the structure sheaf.
result Global exactness and Sobolev regularity of the differential complex for Levi flat structures.
Boundary Dehn twist on K3 surfaces becomes trivial after abelianization.
problem Understanding the boundary Dehn twist on K3 surfaces. method Obstruction from Baraglia-Konno and global Torelli theorem of K3 surfaces. result Boundary Dehn twist becomes trivial after abelianization.
Study on manifolds with higher-rank lattice actions in projective and conformal classes.
problem Global properties of manifolds with higher-rank lattice actions.
method Analysis of actions of cocompact lattices in higher-rank Lie groups on manifolds with projective or conformal structures.
result Manifolds with maximal real-rank are globally equivalent to their model spaces or their double covers.
We give a description of local and global moves on a class of locally planar trivalent graphs and we show that it contains λ-Scale calculus, therefore in particular untyped lambda calculus. Surprisingly, the beta reduction rule comes from a local "sewing" transformation of trivalent locally planar graphs.
Global solutions and smoothing effects for reaction-diffusion equations on manifolds.
problem Global existence and smoothing effects for reaction-diffusion equations on Riemannian manifolds.
method Functional analytic methods, Sobolev and Poincaré inequalities.
result Existence of global solutions under certain conditions on the manifold.
Study shows global oscillatory solutions for Yang-Mills heat flow in 4D space.
problem Investigating long-time dynamics of Yang-Mills heat flow with specific initial data.
method Analysis of SO(4)-equivariant Yang-Mills heat flow with SU(2) group in 4D space. result Global solutions can exhibit oscillatory behavior at time infinity.
The paper proves a smooth Birman-Hilden theorem for hyperkähler manifolds.
problem Understanding the smooth mapping class groups of certain 4-manifolds.
method Geometric and Teichmüller-theoretic methods.
result Proves a global Torelli theorem for generalized Enriques manifolds.