arXiv research

BraidNet uses braid theory to optimize neural networks for image classification.

Machine Learning has become very famous currently which assist in identifying the patterns from the raw data. Technological advancement has led to substantial improvement in Machine Learning which, thus helping to improve prediction. Current Machine Learning models are based on Classical Theory, which can be replaced b…

Unified proof of Nielsen-Thurston classification via Teichmüller's theorem.

The paper classifies bundles over complex projective plane.

Proofs Lie's classification of certain vector field subalgebras.

This work refines Cover's theory for binary classification on low-dimensional data.

In 2005 V. Turaev introduced the theory of topology of words and phrases. Turaev defined an equivalence relation on generalized words and phrases which is called homotopy. This is suggested by the Reidemeister moves in the knot theory. Then Turaev gave the homotopy classification of generalized words with less than or …

Improved 3D LiDAR data classification using product coefficients.

Classifies prime algebraic tangles up to 14 crossings.

Theory for soft-margin classifiers on object manifolds.

Virtual knot theory, introduced by Kauffman, is a generalization of classical knot theory of interest because its finite-type invariant theory is potentially a topological interpretation of Etingof and Kazhdan's theory of quantization of Lie bi-algebras. Classical knots inject into virtual knots, and flat virtual knots…

Classifies theories with eight supercharges using pseudo-periodic maps and Riemann surfaces.

Paper presents a Bayesian-decision-theory framework for long-tailed classification.

Complete classification of links up to specific moves.

A surgery classification theory is introduced for manifolds of bounded geometry up to quasi-isometry. The Borel conjecture for this theory is proven for flat Euclidean space.

We classify elements of a cluster modular group into three types. We characterize them in terms of fixed point property of the action on the tropical compactifications associated with the corresponding cluster ensemble. The characterization gives an analogue of the Nielsen-Thurston classification theory on the mapping …

Using methods of descriptive theory it is shown that the classification problem for wild knots is strictly harder than that for countable structures.

New measure of feature influence in classification problems considering feature dependencies.

Study of ${\cal M}$-theory dual of thermal QCD-like theories at intermediate coupling.

The paper develops a statistical theory explaining overfitting in imbalanced classification.

Braid theory optimizes neural network structures.

The classification of isoparametric hypersurfaces with four principal curvatures in the sphere interplays in a deep fashion with commutative algebra, whose abstract and comprehensive nature might obscure a differential geometer's insight into the classification problem that encompasses a wide spectrum of geometry and t…

We classify compact 2-connected homogeneous spaces with the same rational cohomology as a product of spheres. This classification relies on spectral sequences, homotopy theory, and representation theory. We then apply this classification to two geometric problems. The first problem is the classification of all isoparam…

Constructs 2-vector bundles and 2K-theory for Lie groupoids and 2-equivariant settings.

Motivated by social balance theory, we develop a theory of link classification in signed networks using the correlation clustering index as measure of label regularity. We derive learning bounds in terms of correlation clustering within three fundamental transductive learning settings: online, batch and active. Our mai…

We review the remarkable progress that has been made the last 15 years towards the classification of supersymmetric solutions with emphasis on the description of the bilinears and spinorial geometry methods. We describe in detail the geometry of backgrounds of key supergravity theories, which have applications in the c…

New classification of nonorientable 4-manifolds with specific fundamental groups.

This text is about geometric structures imposed by robust dynamical behaviour. We explain recent results towards the classification of partially hyperbolic systems in dimension 3 using the theory of foliations and its interaction with topology. We also present recent examples which introduce a challenge in the classifi…

Neural NCD reveals LLMs don't compress well for classification.

The paper analyzes the dynamics of a simple neural network using a mean-field approach.

Theory extends optimal learning rates without realizability assumption.

In current paper we refer to the geometrical classification of the Einstein equations which has been developed by one of the authors of this paper. This classification was based on the classical theory for decomposition of the tensor product of representations into irreducible components, which is studied in the elemen…

Perceptual manifolds arise when a neural population responds to an ensemble of sensory signals associated with different physical features (e.g., orientation, pose, scale, location, and intensity) of the same perceptual object. Object recognition and discrimination requires classifying the manifolds in a manner that is…

The problem of equivariant rigidity is the $Γ$-homeomorphism classification of $Γ$-actions on manifolds with compact quotient and with contractible fixed sets for all finite subgroups of $Γ$. In other words, this is the classification of cocompact $E_{fin}Γ$-manifolds. We use surgery theory, algebraic $K$-theory, and t…

New approach for classification using trigonometric polynomial kernels from signal processing.

Unified classification of equivariant principal bundles using higher homotopy theory.

In this paper, we develop the theory for classifying all the geometric fibrations of compact, connected, flat $n$-orbifolds, over a 1-orbifold, up to affine equivalence. We apply our classification theory to classify all the geometric fibrations of compact, connected, flat $2$-orbifolds, over a 1-orbifold, up to affine…

The subgroups of GL(n,R) that act irreducibly on R^n and that can occur as the holonomy of a torsion-free affine connection on an n-manifold are classified, thus completing the work on this subject begun by M. Berger in the 1950s. The methods employed include representation theory, the theory of hermitian symmetric spa…

New classification for some unorientable 4-manifolds using modified surgery theory.

Multi-label classification (MLC) is a supervised learning problem in which, contrary to standard multiclass classification, an instance can be associated with several class labels simultaneously. In this chapter, we advocate a rule-based approach to multi-label classification. Rule learning algorithms are often employe…

AdaBoost improves binary classification in robust one-bit compressed sensing with adversarial errors.

New theory improves understanding of ensemble learning systems.

New algebraic theory classifies symplectic curves in complex projective space.

Study on error probabilities of machine learning classification techniques using large deviations theory.

Classification tasks usually assume that all possible classes are present during the training phase. This is restrictive if the algorithm is used over a long time and possibly encounters samples from unknown classes. The recently introduced extreme value machine, a classifier motivated by extreme value theory, addresse…

We review the basic elements of the geometrical formalism for description of gauge fields and the theory of invariant connections, and their applications to the coset space dimensional reduction of Yang-Mills theories. We also discuss the problem of classification of principal fibre bundles, which is important for the …

This study connects prevalence and machine learning for diagnostic testing.

New K-theory approach classifies anyonic topological phases in 2D semimetals.