Classifies minimal submanifolds in complex hyperbolic spaces.
problem Identifying minimal submanifolds in complex hyperbolic spaces.
method Classification based on extrinsic homogeneity.
result Classification of minimal extrinsically homogeneous submanifolds.
The paper classifies invariant generalized complex structures on specific flag manifolds.
problem Classifying invariant generalized complex structures on partial flag manifolds.
method Proved that invariant generalized almost complex structures are constant in each component of the isotropy representation.
result All invariant generalized complex structures on partial flag manifolds with at most four isotropy summands are classified.
Classifies complex structures on specific nilpotent Lie algebras.
problem Classifying complex structures on nilpotent Lie algebras with minimal center.
method Classification through algebraic and geometric methods.
result Space of complex structures on specific Lie algebras up to isomorphism.
This paper studies the generalization error of invariant classifiers. In particular, we consider the common scenario where the classification task is invariant to certain transformations of the input, and that the classifier is constructed (or learned) to be invariant to these transformations. Our approach relies on fa…
The paper classifies Hopf hypersurfaces with constant curvatures on complex quadrics.
problem Classifying Hopf hypersurfaces with specific curvature properties.
method Analyzing hypersurfaces on complex quadrics with at most five distinct constant principal curvatures.
result All classified hypersurfaces are open parts of homogeneous examples.
Paper classifies special slant surfaces with varying curvature.
problem Classifying surfaces with non-constant mean curvature.
method Analyzing special slant surfaces in complex space forms.
result Complete classification of surfaces with non-constant mean curvature.
Classifies actions on complex space forms with Lagrangian orbits.
problem Classifying actions on complex space forms with Lagrangian orbits.
method Classifies holomorphic isometric actions on complex space forms.
result Only examples are Lagrangian affine subspace foliations of complex Euclidean spaces and Lagrangian horocycle foliations of complex hyperbolic spaces.
Classifies CR submanifolds in complex hyperbolic spaces.
problem Understanding CR submanifolds in complex hyperbolic spaces.
method Classifying orbits of a subgroup of the solvable part of the Iwasawa decomposition.
result Classification of homogeneous CR submanifolds.
Classified spaces in low dimensions.
problem Irreducible homogeneous almost Hermite-Lorentz spaces in low dimensions.
method Classification through complex dimension 3.
result Classification of spaces in low dimensions.
Classifies degenerations of complex projective plane with rational singularities.
problem Classifying singularities of complex projective plane.
method Assuming Wahl's conjecture, classifies degenerations using rational homology disk smoothing.
result Classifies surfaces with rational singularities, including new degenerations with non-log canonical singularities.
We propose a novel combination of optimization tools with learning theory bounds in order to analyze the sample complexity of optimal kernel sum classifiers. This contrasts the typical learning theoretic results which hold for all (potentially suboptimal) classifiers. Our work also justifies assumptions made in prior w…
Algorithm estimates bounds of updated classifier coefficients efficiently.
problem Determining sensitivity of updated classifiers without retraining.
method Proposes an algorithm to estimate upper and lower bounds of updated classifier coefficients.
result Estimates bounds with low computational complexity and tightness.
Current techniques in machine learning are so far are unable to learn classifiers that are robust to adversarial perturbations. However, they are able to learn non-robust classifiers with very high accuracy, even in the presence of random perturbations. Towards explaining this gap, we highlight the hypothesis that $\te…
Classifies GL(2,R)-invariant subvarieties in complex geometry.
problem Classifying GL(2,R)-invariant subvarieties.
method Classification of natural subvarieties including double covers and Teichmüller space.
result Classification of high rank invariant subvarieties and new examples.
C-SURE improves complex-valued deep learning models by shrinking estimates, outperforming MLE and SurReal.
problem Improving accuracy and robustness of complex-valued deep learning models.
method Proposes a Stein's unbiased risk estimate (SURE) for complex-valued data and integrates it into a prototype CNN classifier.
result C-SURE outperforms SurReal and MLE in accuracy and robustness on complex-valued datasets.
We study a recent model of collaborative PAC learning where k players with k different tasks collaborate to learn a single classifier that works for all tasks. Previous work showed that when there is a classifier that has very small error on all tasks, there is a collaborative algorithm that finds a single classifi…
We classify the transitive, effective, holomorphic actions of connected complex Lie groups on complex surfaces.
Classifies meromorphic affine connections on complex surfaces.
problem Investigating uniformization in higher dimensions with singularities.
method Extending work on holomorphic connections, classifying meromorphic connections on compact surfaces.
result Classification of meromorphic affine connections on compact complex surfaces.
Classifies toric dually flat manifolds into complex space forms.
problem Classifying 1D toric dually flat manifolds.
method Using complex space forms and exponential families.
result Toric dually flat manifolds are complex space forms.
The paper classifies complex Dirac structures on flag manifolds.
problem Classifying invariant complex Dirac structures on flag manifolds.
method Described using roots of the Lie algebra and classified under B-transformations. result All invariant complex Dirac structures with constant real index on a maximal flag manifold are described.
In this article we study minimal flat Lorentzian surfaces in Lorentzian complex space forms. First we prove that, for minimal flat Lorentzian surfaces in a Lorentzian complex form, the equation of Ricci is a consequence of the equations of Gauss and Codazzi. Then we classify minimal flat Lorentzian surfaces in the Lore…
This paper classifies planar-Rips complexes and their unit disk graphs up to homotopy.
problem Classifying planar-Rips complexes and their unit disk graphs.
method Simplicial classification, homotopy equivalence, and hereditary properties.
result Classification of planar-Rips complexes and unit disk graphs up to homotopy.
Classifies complex structures on SL(2,C), finding new non-regular ones.
problem Classifying complex structures on SL(2,C) up to automorphisms.
method Classification via Lie group automorphisms and topological analysis.
result Found one new, non-regular complex structure.
The study classifies complex symplectic structures on 4D Lie algebras and constructs hypersymplectic structures.
problem Classifying and constructing complex symplectic structures on 4D Lie algebras.
method Interpreting complex symplectic and pseudo-Kähler structures, developing a method for constructing hypersymplectic structures.
result Obtained an example of a hypersymplectic structure on a 4-step nilmanifold.
Enhances mixture models with classifier-defined weights.
problem Density evaluation and sampling in mixture models.
method Introduces Classifier Weighted Mixtures (CWM) with functional weights.
result Improves expressivity in variational estimation without increasing complexity.
The study provides a sample complexity estimate for multi-category classifiers with bounded variation.
problem Controlling the deviation between empirical and generalization performances of multi-category classifiers.
method Using the empirical L1-norm covering number and fat-shattering dimension, the study derives a sample size estimate for classifiers of bounded variation.
result The sample size estimate is sufficient for the performances to be close with high probability, improving the dependency on the number of classes.
We classify isoparametric hypersurfaces in complex hyperbolic spaces.
Classifies complex symplectic structures on Lie algebras with large abelian ideals.
problem Classifying complex symplectic structures on Lie algebras with large abelian ideals.
method Two constructions of complex symplectic structures on Lie algebras with large abelian ideals, considering compact quotients of Lie groups.
result Complete classification of complex symplectic structures on almost abelian Lie algebras.
Classifies curves up to symplectic isotopy.
problem Classifying rational cuspidal curves up to symplectic isotopy.
method Topological tools, pseudoholomorphic techniques, and birational transformations.
result Classifies rational cuspidal curves of degrees 6 and 7 up to symplectic isotopy.
Classifies 3-manifolds from cube identifications.
problem Classifying non-orientable 3-manifolds.
method Identifying cube faces to form manifolds, classifying based on surface-complexity.
result Identifies four flat non-orientable 3-manifolds with surface-complexity one.
New method counts boundary pieces in ReLU classifiers for better complexity measure.
problem Current classification complexity measures are misleading and ineffective.
method Developed a novel method using tropical geometry to count exact boundary pieces.
result Boundary piece count is negatively correlated with robustness.
Researchers classify special curved spheres in a complex space.
problem Classifying special holomorphic two-spheres in a complex Grassmannian.
method Completely classified noncongruent spheres with constant curvature and second fundamental form.
result Found all homogeneous spheres with constant curvature and second fundamental form.
We classify polar actions on complex hyperbolic spaces up to orbit equivalence.
We classify compact Kähler manifolds with semi-positive holomorphic bisectional and big tangent bundles. We also classify compact complex surfaces with semi-positive tangent bundles and compact complex 3-folds of the form P(T∗X) whose tangent bundles are nef. Moreover, we show that if X is a Fano manifold such t…
This paper classifies Ricci solitons in complex hyperbolic spaces.
problem Understanding Ricci solitons in complex hyperbolic spaces.
method Analyzing homogeneous expanding Ricci solitons as submanifolds of complex hyperbolic spaces.
result Classification and analysis of Lie subgroups with Ricci soliton induced metric in complex hyperbolic spaces.
Study and classify totally geodesic submanifolds in nearly Kaehler flag manifold.
problem Classifying totally geodesic submanifolds in nearly Kaehler flag manifold.
method Developed structural approach to nearly Kaehler flag manifold, expressed curvature tensor in terms of nearly Kaehler structure and canonical complex structures.
result Classified almost complex totally geodesic submanifolds of nearly Kaehler flag manifold and its semi-Riemannian counterpart.
Classifies and computes cohomologies of complex structures on Lie groups.
problem Classifying and computing cohomologies of complex structures on Lie groups.
method Complete classification and computation of invariant cohomologies for left invariant structures.
result Computed invariant cohomologies for various generalized complex and Kähler structures.
CBC makes CNNs robust against adversarial attacks with minimal computational overhead.
problem Making CNNs robust against adversarial attacks without increasing computational complexity.
method CBC uses a stacked encoder-convolutional model where an auto-encoder encodes the input image, and the latent representation is used for classification.
result CBC is more robust to adversarial examples and has significantly lower computational complexity.
Classifies holomorphic parabolic geometries on complex manifolds.
problem Classifying holomorphic parabolic geometries on complex manifolds.
method Bounding numerical dimension and using geometric invariants.
result Uncovering foliations and fibrations on smooth projective varieties.
Paper introduces algorithms for explaining monotonic classifiers.
problem Need for explanations of monotonic classifiers.
method Polynomial algorithms for formal explanations of monotonic classifiers.
result Efficient model-agnostic algorithm for enumerating explanations.
After a short summary of known results on surface-complexity of closed 3-manifolds, we will classify all closed orientable 3-manifolds with surface-complexity one.
We classify all real hypersurfaces with constant principal curvatures in the complex hyperbolic plane.
We complete our recent classification of compact inner symmetric spaces with weakly complex tangent bundle by filling up a case which was left open, and extend this classification to the larger category of compact homogeneous spaces with positive Euler characteristic. We show that a simply connected compact equal rank …
We classify invariant almost complex structures on homogeneous manifolds of dimension 6 with semi-simple isotropy. Those with non-degenerate Nijenhuis tensor have the automorphism group of dimension either 14 or 9. An invariant almost complex structure with semi-simple isotropy is necessarily either of specified 6 homo…
New classifiers converge under large data, simplifying complex models.
problem Complex predictive models under large datasets.
method Convergence of simultaneous and marginal classifiers under partition exchangeability.
result Asymptotic convergence of classifiers with large data reduces computational complexity.
The study classifies complex smooth Fano varieties with large pseudoindex.
problem Classifying Fano varieties with specific properties.
method Analyzing Fano varieties with large pseudoindex and Picard number greater than one.
result Classification of Fano varieties with pseudoindex at least n-2 and Picard number greater than one.
Adaptive stopping in MCMC using classifier-based dynamics
problem Sampling from complex, unnormalized probability densities
method Training state-dependent neural classifiers
result Significant reduction in average trajectory lengths
Complex Hantzsche-Wendt manifolds are flat Kähler manifolds with holonomy group Z2n−1⊂SU(n). They are important example of Calabi-Yau manifolds of abelian type. In this paper we describe them as quotients of a product of elliptic curves by a finite group G~. This will allow us to classify…