Paper proves convex domains have one maximum for semi-stable solutions.
problem Analyzing critical points of semi-stable solutions on convex domains.
method Relating critical points to an auxiliary function and using topological degree.
result Positive, semi-stable solutions have exactly one non-degenerate critical point.
Classifies domains critical for heat content and exit-time moments.
problem Understanding critical domains for heat content and exit-time moments.
method First variation of heat content, constant flow property, isoparametric foliation.
result Domains critical for heat content at all times have constant flow property and isoparametric foliation.
Hot spots conjecture proven for small eigenvalue domains.
problem Hot spots conjecture for hyperbolic planar domains with small eigenvalues.
method Proved a variant of Rauch's hot spots conjecture.
result Second Neumann Laplace eigenfunctions have no interior critical points on large convex domains.
Simply connected surfaces with large constant mean curvature and free boundaries concentrate at critical points of the boundary's mean curvature.
problem Surfaces with large constant mean curvature and free boundaries.
method Proving concentration at critical points of the boundary's mean curvature.
result Simply connected H-surfaces concentrate at critical points of the boundary's mean curvature.
Study extends eigenvalue formulas to weighted manifolds and proves global rigidity theorems.
problem Eigenvalue formulas and rigidity theorems for weighted manifolds.
method Extends variational formulae to weighted manifolds, proving global rigidity theorems.
result Global rigidity theorems for critical domains in Gaussian half-space.
Study critical points of Laplace eigenfunctions in polygons.
problem Characterize critical points of Laplace eigenfunctions in polygonal domains.
method Analyze components of the critical set with codimension 1.
result For simply connected polygons, if a second Neumann eigenfunction has infinitely many critical points, the polygon must be a rectangle.
Bound critical points for minimal Radó functions.
problem Counting interior critical points for minimal Radó functions.
method Bounding critical points in terms of boundary data and domain Euler characteristic.
result Bound the number of interior critical points.
DL models for MTS regression are vulnerable to adversarial attacks, posing risks in safety-critical applications.
problem Vulnerability of DL models to adversarial examples in MTS regression.
method Adversarial attack generation techniques from image classification were adapted for MTS.
result All state-of-the-art DL regression models (CNN, LSTM, GRU) are vulnerable to adversarial attacks.
CSAC enables cooperative reinforcement learning for multi-stage tasks.
problem Coordinating consecutive reinforcement learning agents for long-term multi-stage tasks.
method CSAC modifies each agent's policy to maximize both current and next agent's critic.
result CSAC outperforms uncooperative policies and single-agent training in multi-room maze domain.
Abstract Neural Networks (ANNs) improve DNN verification efficiency.
problem Efficiently verify safety-critical DNNs without slowing exponentially.
method Introduces ANNs that use abstract domains and activation functions to overapproximate DNNs.
result ANNs can soundly overapproximate DNNs with fewer nodes, improving verification efficiency.
The paper examines critical points of solutions to a surface equation in 3D spacelike spaces.
problem Analyzing critical points of solutions to the HR=HL surface equation. method Geometrical conditions, uniqueness results, and bounds for inradius.
result Improved bounds for inradius of domains of solutions to the HR=HL surface equation. Paper proposes a dataset quality process for ML systems.
problem Inadequate standards for ML datasets in safety-critical systems.
method Proposes a dataset specification and verification process.
result Demonstrates the process on a railway signal recognition system.
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 (M,g). More precisely, we analyze locally extremal domains for the first nontrivial eigenvalue μ2(Ω) with respect …
AACC improves RL performance in changing environments.
problem Deterioration of RL performance in real-world tasks.
method Formalizes CMDPs, proposes AACC for contextual RL.
result AACC outperforms baselines in various simulated environments.
Two-dimensional domains with Kähler-Einstein Bergman metrics are biholomorphic to the unit ball.
problem Characterizing domains with Kähler-Einstein Bergman metrics.
method Asymptotics of derivatives of the Bergman kernel along critically tangent paths.
result Two-dimensional pseudoconvex 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 L2-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.
problem Constructing Morse homology for functionals involving the p-Laplacian in Banach spaces.
method The approach involves constructing critical points and ensuring injectivity of the second differential.
result Provides a positive answer to Smale's suggestion for injectivity of the second differential.
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.
problem Limited evaluation benchmarks for low-resource domains, especially Korean.
method Developed KorFinMTEB, a tailored benchmark for Korean financial texts.
result Models perform better on translated benchmarks than on domain-specific ones.
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.
problem Defines critical points of a non-differentiable functional.
method Uses subdifferential and geometric condition in terms of 1-currents.
result Geometric condition equivalent to criticality in terms of 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 Σ2⊂B3 which intersects ∂B3 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.
problem Uncertainty quantification in safety-critical systems.
method Proposes a novel algorithm to construct PAC prediction sets.
result Prediction sets satisfy a PAC guarantee with high probability over future tasks.
TAROT enhances robustness and domain adaptability with domain-invariant features.
problem Developing models robust to adversarial attacks across diverse domains.
method Derives a new generalization bound and proposes TAROT algorithm.
result TAROT outperforms state-of-the-art methods in accuracy and robustness.
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…
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.
problem Existence of nonlocal free boundary minimal surfaces.
method Fractional perimeter critical points with invariant boundary.
result Existence of nonlocal free boundary minimal surfaces without boundaries.
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.
problem Understanding nearly Frobenius algebras and their properties.
method Analyzing nearly Frobenius algebras over principal ideal domains with specific algebraic properties.
result Any nearly Frobenius algebra with surjective multiplication and injective comultiplication is a Frobenius algebra.
MWGAN tackles multi-marginal matching problem with Wasserstein GAN.
problem Learning mappings to match a source domain to multiple target domains with cross-domain correlations.
method Develops a novel Multi-marginal Wasserstein GAN (MWGAN) with inner- and inter-domain constraints to minimize Wasserstein distance.
result Theoretical and empirical evaluations show MWGAN's effectiveness on balanced and imbalanced translation tasks.
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.
problem Improving domain generalization by reducing overfitting to specific domains.
method Arithmetic meta-learning with arithmetic-weighted gradients to balance parameters closer to domain centroids.
result Experimental validation of improved domain generalization performance.
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.
problem Spurious critical points on the boundary of low-rank matrix manifold.
method Riemannian gradient descent with dynamical low-rank approximation and rescaled gradient flow.
result Riemannian gradient descent escapes some spurious critical points on the boundary of the manifold.
We analyze critical points of the Sliced Wasserstein Distance for optimization stability.
problem Understanding the behavior of optimization algorithms for models trained with the Sliced Wasserstein Distance.
method Explicit perturbations and critical point analysis of the SW objective.
result Stable critical points of SW cannot concentrate on segments, providing optimization stability.
The paper proves a disk's energy minimizer is holomorphic and calculates its Morse index.
problem Analyzing the Morse index of a non-holomorphic disk in pseudoconvex domains.
method Proof of holomorphic minimizers and Morse index calculation.
result Non-holomorphic critical disks have a Morse index of at least n-1.
DET unifies geometric and functional alignment for high-dimensional scientific data.
problem Challenges in nonrigid registration for high-dimensional, irregular data.
method Domain Elastic Transform (DET) treats data as functions on irregular domains, using a Bayesian framework for elastic motion registration.
result DET achieves 92% topological preservation on MERFISH data and successfully registers whole-embryo Stereo-seq atlases.
Improves dialogue state tracking across multiple domains.
problem Incomplete domain ontology limits DST models' adaptability.
method Model DST as Q&A, using evolving knowledge graph.
result 5.80% and 12.21% relative improvement on datasets.
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.
problem Domain shifts change acoustic characteristics, affecting ASD performance.
method Domain generalization techniques to detect anomalies across unknown domains.
result Two types of domain generalization techniques were identified and analyzed.
SCTL scales causal domain adaptation without prior knowledge.
problem Domain adaptation with covariate shift and invariances across domains.
method SCTL: scalable causal discovery algorithm based on Markov blanket.
result SCTL achieves scalable and robust domain adaptation.
Study on the Euler-Plateau energy with elastic modulus, focusing on minimizers and critical surfaces.
problem Minimizing the Euler-Plateau energy with elastic modulus.
method Analyzing the energy functional and its minimizers, considering different boundary conditions and topological constraints.
result Potential minimizers are highly dependent on physical rigidity parameters, and the area of critical surfaces can be computed from boundary data.
Domain adaptation framework identifies latent variables for target distribution identifiability.
problem Unsupervised domain adaptation without identifiable joint distribution of features and labels.
method Formulated latent variable model with invariant and changing components, constrained domain shift to influence only changing components.
result Joint distribution of data and labels in target domain is identifiable under mild conditions.