arXiv research

Paper proves convex domains have one maximum for semi-stable solutions.

Classifies domains critical for heat content and exit-time moments.

Hot spots conjecture proven for small eigenvalue domains.

Simply connected surfaces with large constant mean curvature and free boundaries concentrate at critical points of the boundary's mean curvature.

Study extends eigenvalue formulas to weighted manifolds and proves global rigidity theorems.

Study critical points of Laplace eigenfunctions in polygons.

Bound critical points for minimal Radó functions.

DL models for MTS regression are vulnerable to adversarial attacks, posing risks in safety-critical applications.

CSAC enables cooperative reinforcement learning for multi-stage tasks.

Abstract Neural Networks (ANNs) improve DNN verification efficiency.

The paper examines critical points of solutions to a surface equation in 3D spacelike spaces.

Paper proposes a dataset quality process for ML systems.

Resource scheduling and coordination is an NP-hard optimization requiring an efficient allocation of agents to a set of tasks with upper- and lower bound temporal and resource constraints. Due to the large-scale and dynamic nature of resource coordination in hospitals and factories, human domain experts manually plan a…

The present paper is devoted to geometric optimization problems related to the Neumann eigenvalue problem for the Laplace-Beltrami operator on bounded subdomains $Ω$ of a Riemannian manifold $(\mathcal{M},g)$. More precisely, we analyze locally extremal domains for the first nontrivial eigenvalue $μ_2(Ω)$ with respect …

AACC improves RL performance in changing environments.

Two-dimensional domains with Kähler-Einstein Bergman metrics are biholomorphic to the unit ball.

We study several quantities associated to the Green's function of a multiply connected domain in the complex plane. Among them are some intrinsic properties such as geodesics, curvature, and $L^2$-cohomology of the capacity metric and critical points of the Green's function. The principal idea used is an affine scaling…

The paper constructs Morse homology for functionals involving the p-Laplacian in Banach spaces.

We build new examples of extremal domains with small prescribed volume for the first eigenvalue of the Laplace-Beltrami operator in some Riemannian manifold with boundary. These domains are close to half balls of small radius centered at a nondegenerate critical point of the mean curvature function of the boundary of t…

Study introduces KorFinMTEB for Korean financial texts, revealing model limitations.

We propose a new algorithm, Mean Actor-Critic (MAC), for discrete-action continuous-state reinforcement learning. MAC is a policy gradient algorithm that uses the agent's explicit representation of all action values to estimate the gradient of the policy, rather than using only the actions that were actually executed. …

Characterizes infinite harmonic maps using 1-currents.

We prove the existence of extremal domains with small prescribed volume for the first eigenvalue of the Laplace-Beltrami operator in any compact Riemannian manifold. This result generalizes a results of F. Pacard and the second author where the existence of a nondegenerate critical point of the scalar curvature of the …

We show that an embedded minimal annulus $Σ^2 \subset B^3$ which intersects $\partial B^3$ orthogonally and is invariant under reflection through the coordinate planes is the critical catenoid. The proof uses nodal domain arguments and a characterization, due to Fraser and Schoen, of the critical catenoid as the unique…

New algorithm constructs PAC prediction sets for meta-learning.

TAROT enhances robustness and domain adaptability with domain-invariant features.

In conventional domain adaptation, a critical assumption is that there exists a fully labeled domain (source) that contains the same label space as another unlabeled or scarcely labeled domain (target). However, in the real world, there often exist application scenarios in which both domains are partially labeled and n…

Multiple marginal matching problem aims at learning mappings to match a source domain to multiple target domains and it has attracted great attention in many applications, such as multi-domain image translation. However, addressing this problem has two critical challenges: (i) Measuring the multi-marginal distance amon…

Many real world tasks require multiple agents to work together. Multi-agent reinforcement learning (RL) methods have been proposed in recent years to solve these tasks, but current methods often fail to efficiently learn policies. We thus investigate the presence of a common weakness in single-agent RL, namely value fu…

New mathematical surfaces without boundaries found.

The well known domain shift issue causes model performance to degrade when deployed to a new target domain with different statistics to training. Domain adaptation techniques alleviate this, but need some instances from the target domain to drive adaptation. Domain generalisation is the recently topical problem of lear…

A new generative adversarial network is developed for joint distribution matching. Distinct from most existing approaches, that only learn conditional distributions, the proposed model aims to learn a joint distribution of multiple random variables (domains). This is achieved by learning to sample from conditional dist…

The study proves nearly Frobenius algebras over certain domains are Frobenius.

Reinforcement learning algorithms are known to be sample inefficient, and often performance on one task can be substantially improved by leveraging information (e.g., via pre-training) on other related tasks. In this work, we propose a technique to achieve such knowledge transfer in cases where agent trajectories conta…

Text analytics based on supervised machine learning classifiers has shown great promise in a multitude of domains, but has yet to be applied to Seismology. We test various standard models (Naive Bayes, k-Nearest Neighbors, Support Vector Machines, and Random Forests) on a seismological corpus of 100 articles related to…

New meta-learning method improves domain generalization by balancing parameters closer to domain centroids.

Domain adaptation aims at generalizing a high-performance learner on a target domain via utilizing the knowledge distilled from a source domain which has a different but related data distribution. One solution to domain adaptation is to learn domain invariant feature representations while the learned representations sh…

Network alignment is a critical task to a wide variety of fields. Many existing works leverage on representation learning to accomplish this task without eliminating domain representation bias induced by domain-dependent features, which yield inferior alignment performance. This paper proposes a unified deep architectu…

Riemannian gradient descent escapes some spurious critical points on low-rank matrix manifold.

Multi-domain dialogue state tracking (DST) is a critical component for conversational AI systems. The domain ontology (i.e., specification of domains, slots, and values) of a conversational AI system is generally incomplete, making the capability for DST models to generalize to new slots, values, and domains during inf…

We analyze critical points of the Sliced Wasserstein Distance for optimization stability.

The paper proves a disk's energy minimizer is holomorphic and calculates its Morse index.

DET unifies geometric and functional alignment for high-dimensional scientific data.

Semantic Embeddings are a popular way to represent knowledge in the field of zero-shot learning. We observe their interpretability and discuss their potential utility in a safety-critical context. Concretely, we propose to use them to add introspection and error detection capabilities to neural network classifiers. Fir…

DCASE 2022 Task 2 tackles domain shifts in ASD for machine condition monitoring.

SCTL scales causal domain adaptation without prior knowledge.

Study on the Euler-Plateau energy with elastic modulus, focusing on minimizers and critical surfaces.

Domain adaptation framework identifies latent variables for target distribution identifiability.