arXiv research

A new method makes adversarial domain adaptation aware of class relationships.

Clusters asset classes to identify lead-lag relationships in market regimes.

Study the relationship between orbit braid group and equivariant mapping class group on surfaces.

New assumptions help identify causal relationships in data.

The paper proposes new strategies to exploit relationships between meta-tasks for better few-shot learning.

Mining relationships between treatment(s) and medical problem(s) is vital in the biomedical domain. This helps in various applications, such as decision support system, safety surveillance, and new treatment discovery. We propose a deep learning approach that utilizes both word level and sentence-level representations …

Nodes in real world networks often have class labels, or underlying attributes, that are related to the way in which they connect to other nodes. Sometimes this relationship is simple, for instance nodes of the same class are may be more likely to be connected. In other cases, however, this is not true, and the way tha…

We study the relative modular classes of Lie algebroids, and we determine their relationship with the modular classes of Lie algebroids with a twisted Poisson structure.

We obtain a coarse relationship between geometric intersection numbers of curves and the sum of their subsurface projection distances with explicit quasi-constants. By using this relationship, we give applications in the studies of the curve graphs and the mapping class groups.

Extends Euler class result to symplectic group.

Class selectivity affects robustness to corruptions but not to adversarial attacks.

We discuss locally simply transitive affine actions of Lie groups G on finite-dimensional vector spaces such that the commutator subgroup [G,G] is acting by translations. In other words, we consider left-symmetric algebras satisfying the identity [x,y].z=0. We derive some basic characterizations of such left-symmetric …

Estimates class posterior probabilities without using scores from classifiers.

Study improves recognition of long-tail visual relationships.

This paper studies the relationship between the sections and the Chern or Pontrjagin classes of a vector bundle by the theory of connection. Our results are natural generalizations of the Gauss-Bonnet Theorem.

One-hot encoding is a labelling system that embeds classes as standard basis vectors in a label space. Despite seeing near-universal use in supervised categorical classification tasks, the scheme is problematic in its geometric implication that, as all classes are equally distant, all classes are equally different. Thi…

Causal inference concerns the identification of cause-effect relationships between variables. However, often only linear combinations of variables constitute meaningful causal variables. For example, recovering the signal of a cortical source from electroencephalography requires a well-tuned combination of signals reco…

Multiple conventions have been adopted for denoting Interval Exchange Transformations (IETs). The "non-labeled" convention was the original, while the "labeled" convention has proven convenient when investigating Flat Surfaces as described by IETs. We establish the relationship between Extended Rauzy Classes, an equiva…

In this paper we study the modular classes of Dirac manifolds and of Dirac maps, and we discuss their basic properties. We apply these results to explain the relationship between the modular classes of the various structures involved in the reduction of a Poisson manifold under the action by of a Poisson Lie group.

We propose simple conditions equivalent to the discreteness of the spectrum of the Laplace-Beltrami operator on a class of Riemannian manifolds close to warped products. For this class of manifolds we establish a relationship between discreteness of the spectrum and stochastic incompleteness.

This work is an endeavor to develop a deep learning methodology for automated anatomical labeling of a given region of interest (ROI) in brain computed tomography (CT) scans. We combine both local and global context to obtain a representation of the ROI. We then use Relation Networks (RNs) to predict the corresponding …

The Lamarle Formula, given by Kruppa in \cite{Kr}, is known as a relationship between the Gaussian curvature and the distribution parameter of a ruled surface in the surface theory. The ruled surfaces were investigated in 3 different classes with respect to the character of base curves and rulings, \cite{Tu1},\cite{Tu2…

We introduce differentiable stacks and explain the relationship with Lie groupoids. Then we study $S^1$-bundles and $S^1$-gerbes over differentiable stacks. In particular, we establish the relationship between $S^1$-gerbes and groupoid $S^1$-central extensions. We define connections and curvings for groupoid $S^1$-cent…

Introduces new types of homogeneous spaces and their properties.

New framework infers multiple classes per image for one-shot learning.

Capsule networks improve temporal data understanding, achieving 96.21% ECG accuracy.

We consider commensurability of quadratic differentials on surfaces. Each commensurability class has a natural order by the covering relation. We show that each commensurability class contains a unique (orbifold) element. We also discuss the relationship between commensurability of quadratic differentials and fibered c…

We study the Birman exact sequence for compact $3$--manifolds, obtaining a complete picture of the relationship between the mapping class group of the manifold and the mapping class group of the submanifold obtained by deleting an interior point. This covers both orientable manifolds and non-orientable ones.

Class-conditional extensions of generative adversarial networks (GANs), such as auxiliary classifier GAN (AC-GAN) and conditional GAN (cGAN), have garnered attention owing to their ability to decompose representations into class labels and other factors and to boost the training stability. However, a limitation is that…

The paper studies curvature tensors and hypersurfaces in Kenmotsu type manifolds.

We compute the genus one family Gromov-Witten invariants of K3 surfaces for non-primitive classes. These calculations verify Gottsche-Yau-Zaslow formula for non-primitive classes with index two. Our approach is to use the genus two topological recursion formula and the symplectic sum formula to establish relationships …

In classification problems, especially those that categorize data into a large number of classes, the classes often naturally follow a hierarchical structure. That is, some classes are likely to share similar structures and features. Those characteristics can be captured by considering a hierarchical relationship among…

In this paper we classify the homotopy classes of proper maps $E\rightarrow \mathbb R^k$, where $E$ is a vector bundle over a compact Hausdorff space. As a corollary we compute the homotopy classes of proper maps $\mathbb R^n\rightarrow \mathbb R^k$. We find a stability range of such maps. We conclude with some remarks…

We consider various equivalence relations on the set of homotopy classes of curves on a hyperbolic surface based on topological, algebraic, and geometric structures. The purpose of this work is to determine the relationship between these equivalences.

In many domains, there is significant interest in capturing novel relationships between time series that represent activities recorded at different nodes of a highly complex system. In this paper, we introduce multipoles, a novel class of linear relationships between more than two time series. A multipole is a set of t…

Semi-supervised learning (SSL) has become important in current data analysis applications, where the amount of unlabeled data is growing exponentially and user input remains limited by logistics and expense. Constrained clustering, as a subclass of SSL, makes use of user input in the form of relationships between data …

Introduces positivity for $(1,1)$ classes in foliated manifolds.

New model captures complex relationships from experimental data.

This work improves metric learning models by incorporating class hierarchies.

We introduce a class of Higgs bundles called cyclic which lie in the Hitchin component of representations of a compact Riemann surface into the split real form of a simple Lie group. We then prove that such a Higgs bundle is equivalent to a certain class of solutions to the affine Toda equations. We further explain thi…

Study on generalization in reparameterizable RL, deriving new guarantees.

Stacked Capsule Autoencoders reconstruct objects from images using part relationships.

This paper refines MMD for domain adaptation by balancing intra-class and inter-class distances.

For each holomorphic vector bundle we construct a holomorphic bundle 2-gerbe that geometrically represents its second Beilinson-Chern class. Applied to the cotangent bundle, this may be regarded as a higher analogue of the canonical line bundle in complex geometry. Moreover, we exhibit the precise relationship between …

A new algorithm reduces imbalanced data classification errors in multi-class settings.

The well-known fact that any genus $g$ symplectic Lefschetz fibration $X^{4}\to S^{2}$ is given by a word that is equal to the identity element in the mapping class group and each of whose elements is given by a positive Dehn twist, provides an intimate relationship between words in the mapping class group and 4-manif…

We study the existence of $S^1$-equivariant characteristic classes on certain natural infinite rank bundles over the loop space $LM$ of a manifold $M$. We discuss the different $S^1$-equivariant cohomology theories in the literature and clarify their relationships. We attempt to use $S^1$-equivariant Chern-Weil techniq…

New classifiers account for context-specific independences.