Paper reduces neural network complexity for image classification.
problem High computational complexity in deep neural networks.
method Proposes a two-step classification process: coarse-grain and fine-grain.
result Achieves similar accuracy with less computational complexity.
Complex-valued neural networks perform similarly to real-valued models for real-valued classification tasks.
problem Comparing real-valued and complex-valued neural networks for real-valued classification tasks.
method Comparison of neural networks with similar capacity sizes, using various activation functions and weight initialisation strategies.
result Complex-valued neural networks perform equal to or slightly worse than real-valued models for real-valued classification tasks.
This paper surveys measures of classification complexity.
problem Estimating the difficulty of separating data points into classes.
method Analysis of descriptors from training datasets.
result Characterization of classification problem complexity.
Classifies complex hyperbolic triangle groups by types.
problem Classifying complex hyperbolic triangle groups.
method By types defined by the ellipticity of two short words.
result Improves Schwartz conjecture.
Text classification on drug SMILES strings yields competitive drug type classification results.
problem Classifying drug types using conventional text classification methods.
method Treated drug SMILES as sentences and applied basic NLP methods for classification.
result Competitive drug type classification results achieved.
Proofs Lie's classification of certain vector field subalgebras.
problem Classifying finite dimensional subalgebras of vector fields on the complex plane.
method Representation theory of sl(2, C) and previous classifications.
result Completes the classification of vector field subalgebras.
Simple proof for special surface classification.
problem Classifying surfaces with specific curvature properties.
method Elementary proof for parallel mean curvature surfaces.
result A lemma is proven for surfaces in complex space forms.
Classifies real trivectors in 9D, following complex classification methods.
problem Classifying real trivectors in 9D space.
method Used Galois cohomology to divide trivectors into nilpotent, semisimple, and mixed groups.
result Classification of real trivectors in 9D space follows the same pattern as complex classification.
Estimates neural network errors for classification problems.
problem Binary and multi-class classification problems.
method Rademacher complexity estimates and direct approximation theorems.
result A priori error estimates for regularized loss functionals.
Classifies very stable Higgs bundles for complex groups.
problem Classifying Higgs bundles for arbitrary complex groups.
method Classification based on stability and Higgs field properties.
result Extends previous classification for GLn to arbitrary groups.
This research classifies invariant complex structures and Kähler metrics on principal bundles.
problem Classifying invariant complex structures and Kähler metrics on principal bundles.
method Using Wang's theory of invariant connections and the Levi-Civita connection, the study provides direct geometric proofs and extends the classification from Hermitian to general symmetric spaces.
result The invariant integrable complex structures are unique in the reduced frame bundles of the upper half-plane and complex projective spaces.
We give a classification of compact solitons for the pluriclosed flow on complex surfaces. First, by exploiting results from the Kodaira classification of surfaces, we show that the complex surface underlying a soliton must be Kähler except for the possibility of steady solitons on minimal Hopf surfaces. Then, we const…
In this article, we give a geometric proof of the classification of complex vector cross product due to Lee-Leung.
A new algorithm reduces time complexity for binary time series classification.
problem High time complexity of ensemble shapelet transform limits its application.
method Introduces short isometric shapelet transform with two strategies: fixed shapelet length and single linear classifier.
result Demonstrates superior performance and reduced time complexity.
Unified proof of Nielsen-Thurston classification via Teichmüller's theorem.
problem Classifying mapping class groups and rational maps.
method Unified proof following Bers' approach.
result Unified proof of Nielsen-Thurston classification.
New research determines the optimal sample complexity for multiclass and list learning.
problem Determining the optimal sample complexity for multiclass classification.
method Algebraic characterization of multiclass hypothesis classes in terms of their DS dimension.
result Proves a longstanding conjecture and determines the optimal dependence of sample complexity on DS dimension.
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.
The paper classifies bundles over complex projective plane.
problem Classifying S3-bundles over CP2. method Two-step approach: PL-homeomorphism classification via Kreck-Stolz invariants, followed by homotopy equivalence classification using surgery theory.
result Established the homotopy equivalence classification of S3-bundles over CP2. We give a local classification of generalized complex structures. About a point, a generalized complex structure is equivalent to a product of a symplectic manifold with a holomorphic Poisson manifold. We use a Nash-Moser type argument in the style of Conn's linearization theorem.
We study a number of local and global classification problems in generalized complex geometry. In the first topic, we characterize the local structure of generalized complex manifolds by proving that a generalized complex structure near a complex point arises from a holomorphic Poisson structure. In the proof we use a …
The paper presents a new framework for complex Support Vector Regression as well as Support Vector Machines for quaternary classification. The method exploits the notion of widely linear estimation to model the input-out relation for complex-valued data and considers two cases: a) the complex data are split into their …
In this article we obtain a classification of special Lagrangian submanifolds in complex space forms subject to an SO(2)⋊S3-symmetry on the second fundamental form. The algebraic structure of this form has been obtained by Marianty Ionel. However, the classification of special Lagrangian submanifolds in $\mat…
New algorithms for hierarchical classification using conformal prediction.
problem Valid prediction sets in hierarchical classification tasks.
method Extended split conformal prediction framework with two inference algorithms.
result Empirical evaluations show effectiveness in achieving nominal coverage.
Almost complex structures found on many homotopy complex projective spaces.
problem Finding almost complex structures on homotopy complex projective spaces.
method New proof using Chern classes and homotopy properties.
result Classification of almost complex structures on homotopy CPn for 3≤n≤6. Survey of text classification algorithms for complex documents.
problem Understanding and classifying complex texts using machine learning.
method Discusses various text feature extractions, dimensionality reduction methods, and classification algorithms.
result Overview of text classification techniques and their limitations.
In this paper we consider three deeply connected classificational problems on four-dimensional manifolds. First we consider and describe locally regular distributions. Second we give a classification of almost complex structures of general position in terms of distributions. Finally we classify nondegenerate Monge-Ampe…
We present a new proof of the classification of complex simple Lie algebras via the projective geometry of homogeneous varieties. Our proof proceeds by constructing homogeneous varieties using the ideals of the secant and tangential varieties of homogeneous varieties already constructed. Our algorithms make no referenc…
Local probabilistic models simplify Bayesian classification for complex data.
problem Complex real-world data requires simpler models than global ones.
method Establish local probabilistic models for local regions, relaxing global assumptions.
result Local probabilistic models improve classification accuracy on real-world datasets.
We use Bott-Chern cohomology to measure the non-Kählerianity of 6-dimensional nilmanifolds endowed with the invariant complex structures in M. Ceballos, A. Otal, L. Ugarte, and R. Villacampa's classification, [Invariant Complex Structures on 6-Nilmanifolds: Classification, Frölicher Spectral Sequence and Special Hermit…
It is well known that the classification of the Weyl tensor in Lorentzian manifolds of dimension four, the so called Petrov classification, was a great tool to the development of general relativity. Using the bivector approach it is shown in this article a classification for the Weyl tensor in all four-dimensional mani…
New method builds complex networks from attribute interactions without normalization.
problem Improving high-level classification algorithms by capturing hidden attribute interactions.
method Proposes a new complex network building methodology based on attribute-attribute interactions, avoiding normalization.
result Demonstrates improved performance in high-level classification techniques.
Classifies fake surfaces up to complexity 5.
problem Classifying fake surfaces for low-dimensional topology.
method Derived properties of fake surfaces, classified up to complexity 5.
result Proved conjectures about fake surfaces up to complexity 5.
The paper classifies real hypersurfaces with a specific Jacobi operator in complex Grassmannians.
problem Classifying real hypersurfaces with a particular Jacobi operator.
method Introducing and classifying real hypersurfaces with a quadratic Killing structure Jacobi operator.
result A classification theorem for Hopf real hypersurfaces with quadratic Killing structure Jacobi operator.
Improved private sample complexity for answering classification queries.
problem Designing an algorithm to accurately answer classification queries while maintaining differential privacy.
method Formally studied in agnostic PAC model, derived new upper bound on private sample complexity.
result Improved private sample complexity bound for answering classification queries.
New SSL methods reduce sample complexity for nonparametric multiclass classification.
problem Sample complexity in nonparametric semi-supervised learning.
method Assumptions on mixture models and permutation learning.
result Near-optimal classifier with few labeled samples possible.
The classification problem for holonomy of pseudo-Riemannian manifolds is actual and open. In the present paper, holonomy algebras of Lorentz-Kähler manifolds are classified. A simple construction of a metric for each holonomy algebra is given. Complex Walker coordinates are introduced and described using the potential…
A methodology for binary classification of EEG records which correspond to different mental states is proposed. This model-free methodology is based on our theory of the ε-complexity of continuous functions which is extended here (see Appendix) to the case of vector functions. This extension permits us to handle mult…
The existence of some complex geometrical structures on a compact manifold such as complex structures, Kaehler (pseudo-Kaehler) structures often impose certain restrictions on its underling topological or differentiable manifold. In this article we survey recent developments in the study of the existence, classificatio…
Complete classification of homogeneous real hypersurfaces in complex 3-space.
problem Classifying locally homogeneous real hypersurfaces in C3. method Classification of abstract 5-dimensional real Lie algebras and their representations by algebras of holomorphic vector fields in complex 3-space.
result 47 types of homogeneous hypersurfaces, including 1- or 2-parametric families and single hypersurfaces/families.
DOC3 learns from contradictions to improve deep one class classification.
problem Deep one class classification problems.
method Formalizes learning from contradictions for one class large-margin loss, proposes DOC3 algorithm.
result DOC3 incurs lower generalization error compared to traditional inductive learning.
Simple classifiers can't be robust to adversarial perturbations, but more complex ones can.
problem The gap between standard accuracy and robustness to adversarial attacks.
method Theoretical examples and quantitative analysis of classification tasks.
result There is a trade-off between robustness and standard accuracy among simple classifiers.
Survey on rational curves on complex surfaces, highlighting different approaches.
problem Existence of rational curves on complex surfaces.
method Classification of complex surfaces and systematic study of rational curves in each class.
result Highlighting the different approaches to study rational curves on complex surfaces.
QGNN uses Quaternion space for better graph and node classification.
problem Existing GNN methods struggle with Euclidean vector space limitations.
method Proposes QGNN to learn graph representations in Quaternion space.
result Obtains state-of-the-art results on graph and node classification benchmarks.
Study Hodge-de Rham numbers for almost complex 4-manifolds, extending properties from complex surfaces.
problem Understanding Hodge-de Rham numbers for almost complex 4-manifolds.
method Introduced and studied Hodge-de Rham numbers, extending properties from complex surfaces.
result All Hodge-de Rham numbers for compact almost complex 4-manifolds are determined by the cohomology, except for one (the irregularity).
A hybrid model reduces graph complexity for improved classification accuracy.
problem High computational complexity and large number of parameters in higher-order graph convolutional networks.
method Weight sharing mechanism and novel fusion pooling layer to reduce parameters and complexity.
result The proposed model achieves highest classification accuracy with fewer trainable parameters.
An isometric immersion f:Mn→M~n from a Riemannian n-manifold Mn into a Kähler n-manifold M~n is called {\it Lagrangian} if the complex structure J of the ambient manifold M~n interchanges each tangent space of Mn with the corresponding normal space. In this paper, we completel…
Classifies symplectic torus actions up to equivariant symplectomorphism.
problem Classifying symplectic torus actions up to equivariant symplectomorphism.
method Classification theorems based on Duistermaat and Pelayo's work on symplectic torus actions with coisotropic orbits.
result Every almost isotropy-maximal symplectic torus action is equivariantly diffeomorphic to a product of a symplectic toric manifold and a torus.
Simple algorithm outperforms complex methods in graph classification.
problem Efficient graph classification methods with comparable performance to state-of-the-art algorithms.
method Spectral decomposition of graph Laplacian.
result Simple algorithm achieves competitive results.