arXiv research

IMPaCT improves node classification in chronological split temporal graphs.

In the current article our primary objects of study are compact complex submanifolds of quotient manifolds of irreducible bounded symmetric domains by torsion free discrete lattices of automorphisms. We are interested in the characterization of the totally geodesic submanifolds among compact splitting complex submanifo…

By Cheeger-Colding's almost splitting theorem, if a domain in a Ricci flat manifold is pointed-Gromov-Hausdorff close to a lower dimensional Euclidean domain, then there is a harmonic almost splitting map. We show that any eigenfunction of the Laplace operator is almost constant along the fibers of the almost splitting…

SBAMDT uses adaptive soft splits to model complex decision boundaries.

Paper establishes a new formula for Atiyah-Patodi-Singer index using eta invariants.

Recent work has shown that using unlabeled data in semi-supervised learning is not always beneficial and can even hurt generalization, especially when there is a class mismatch between the unlabeled and labeled examples. We investigate this phenomenon for image classification on the CIFAR-10 and the ImageNet datasets, …

Study evaluates when splitting classifiers can improve performance despite disparate treatment.

The paper explores how splitting data samples influences optimal neural network hyperparameters.

We provide monotonicity formulas for solutions to the p-Laplace equation defined in the exterior of a convex domain. A number of analytic and geometric consequences are derived, including the classical Minkowski inequality as well as new characterizations of rotationally symmetric solutions and domains. The proofs rely…

A novel variational inference based resampling framework is proposed to evaluate the robustness and generalization capability of deep learning models with respect to distribution shift. We use Auto Encoding Variational Bayes to find a latent representation of the data, on which a Variational Gaussian Mixture Model is a…

New method embeds phylogenetic trees for clustering, recovering evolutionary relationships.

Improved guarantees for misspecified kernelized bandit optimization.

The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range constraints. Split feasibility generalizes important inverse problems including con…

Let $Γ$ be a one-ended, torsion-free hyperbolic group and let $G$ be a semisimple Lie group with finite center. Using the canonical JSJ splitting due to Sela, we define amalgam Anosov representations of $Γ$ into $G$ and prove that they form a domain of discontinuity for the action of $\mathrm{Out}(Γ)$. In the appendix,…

The paper classifies capillary graphs on manifolds with Ricci lower bounds.

The energy of any $C^1$ representative of a homotopy class of maps from a compact and connected Riemannian manifold with nonnegative Ricci curvature into a complete Riemannian manifold with no conjugate points is bounded below by a constant determined by the asymptotic geometry of the target, with equality if and only …

Gradient bounds and Liouville theorems for quasi-linear equations on manifolds with nonnegative Ricci curvature.

Study classifies graphs in Euclidean and non-Euclidean spaces with specific curvature conditions.

New method estimates individual treatment effects using domain generalization.

The paper introduces a method to control false splits in tree-based data aggregation.

A new method for predicting insurance claims with statistical guarantees.

Quantized-TinyLLaVA reduces communication costs in split learning for multimodal models.

Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When the entropy regularization is added to the problem, the transportation plan can be…

We introduce O-systems (Definition \ref{DO}) of orthogonal transformations of ${\Bbb R}^{m}$, and establish $1-1$ correspondences both between equivalence classes of Clifford systems and that of O-systems, and between O-systems and orthogonal multiplications of the form $μ:{\Bbb R}^{n} \times {\Bbb R}^{m} \longrightarr…

Enhances Random Forest for imbalanced functional data classification.

Learning knowledge representation is an increasingly important technology applicable in many domain-specific machine learning problems. We discuss the effectiveness of traditional Link Prediction or Knowledge Graph Completion evaluation protocol when embedding knowledge representation for categorised multi-relational d…

New invariant defined for Weinstein domains, related to Kirby-Thompson's invariant.

We derive some consequences of the Liouville theorem for plurisubharmonic functions of L.-F. Tam and the author. The first result provides a nonlinear version of the complex splitting theorem (which splits off a factor of $\mathbb{C}$ isometrically from the simply-connected Kähler manifold with nonnegative bisectional …

FLBench automates federated learning benchmarking.

Tree-based algorithm for functional data analysis reduces generalization error.

Proposes a framework for semi-supervised continual learning from sequentially arriving data.

In this paper, we present Russian language datasets in the digital humanities domain for the evaluation of word embedding techniques or similar language modeling and feature learning algorithms. The datasets are split into two task types, word intrusion and word analogy, and contain 31362 task units in total. The chara…

We consider a curve of Fredholm pairs of Lagrangian subspaces in a fixed Banach space with continuously varying (weak) symplectic structures. Assuming vanishing index, we obtain intrinsically a continuously varying splitting of the total Banach space into pairs of symplectic subspaces. Using such decompositions we defi…

CMCO provides robust uncertainty estimates for neural operators without retraining.

This paper computes fixed point Floer cohomology for Dehn twists on surfaces.

FastForest boosts Random Forest speed by 24%.

We prove that a compact $RCD^*(0,N)$ (or equivalently $RCD(0,N)$) metric measure space, $\left(X, d, m \right)$, with $\diam X \le d$ and its first (nonzero) eigenvalue of the Laplacian (in the sense of Ambrosio-Gigli-Savaré) , $λ_1 = \frac{π^2}{d^2}$, has to be a circle or a line segment with diameter, $π$. This compl…

Transfer learning is a popular practice in deep neural networks, but fine-tuning of large number of parameters is a hard task due to the complex wiring of neurons between splitting layers and imbalance distributions of data in pretrained and transferred domains. The reconstruction of the original wiring for the target …

Data representations that contain all the information about target variables but are invariant to nuisance factors benefit supervised learning algorithms by preventing them from learning associations between these factors and the targets, thus reducing overfitting. We present a novel unsupervised invariance induction f…

Myocardial infarction is the leading cause of death worldwide. In this paper, we design domain-inspired neural network models to detect myocardial infarction. First, we study the contribution of various leads. This systematic analysis, first of its kind in the literature, indicates that out of 15 ECG leads, data from t…

SPlit optimizes dataset splitting for better model performance.

The paper extends keenness concept to bridge splittings and finds conditions for existence.

Non-split almost complex supermanifolds and non-split Riemannian supermanifolds are studied. The first obstacle for a splitting is parametrized by group orbits on an infinite dimensional vector space. Further it is shown that non-split structures appear in the first case as deformations of a split reduction and in the …

Study flippable Heegaard splittings in Seifert fibered spaces.

We study the self-dual Yang-Mills equations in split signature. We give a special solution, called the basic split instanton, and describe the ADHM construction in the split signature. Moreover a split version of t'Hooft ansatz is described.

BERT models can classify multilingual party manifestos across different dimensions.

Paper proposes a novel SVM method for creating survival trees.

In this paper we provide a new method for establishing the rotational symmetry of the solutions to a couple of very classical overdetermined problems arising in potential theory, in both the exterior and the interior punctured domain. Thanks to a conformal reformulation of the problems, we obtain Riemannian manifolds w…