arXiv research

The paper introduces new metrics for evaluating generative models of behavior.

Study precise asymptotic behavior of functions in singular metric spaces.

No radial balanced metrics found on Kepler manifold unit ball with mild boundary conditions.

The paper studies the curvature behavior near the boundary of certain domains.

Introduces LoCA regret to evaluate model-based RL methods.

We propose Turing Learning, a novel system identification method for inferring the behavior of natural or artificial systems. Turing Learning simultaneously optimizes two populations of computer programs, one representing models of the behavior of the system under investigation, and the other representing classifiers. …

Study asymptotic behaviors of solutions near singular boundaries for the Yamabe problem.

In this paper, we study the boundary behavior of the negatively curved Kähler-Einstein metric attached to a log canonical pair $(X,D)$ such that $K_X+D$ is ample. In the case where $X$ is smooth and $D$ has simple normal crossings support (but possibly negative coefficients), we provide a very precise estimate on the p…

Study low energy resolvent behavior on fibred boundary metrics.

Study shows quantum behavior near infinity in metric asymptotics.

Study on asymptotic behavior of Taub-NUT type solitons and construction of new ALF Calabi-Yau metrics.

We use a generalization of the Gibbons-Hawking ansatz to study the behavior of certain non-compact Calabi-Yau manifolds in the large complex structure limit. This analysis provides an intermediate step toward proving the metric collapse conjecture for toric hypersurfaces and complete intersections.

Study confirms asymptotic behavior of logarithmic balanced metric near infinity.

Study asymptotic behavior of second Chern forms on degenerating Kähler-Einstein surfaces.

Despite the growing importance of multilingual aspect of web search, no appropriate offline metrics to evaluate its quality are proposed so far. At the same time, personal language preferences can be regarded as intents of a query. This approach translates the multilingual search problem into a particular task of searc…

Unique Poincaré type cscK metric with singularity at smooth divisor is unique up to holomorphic transformations.

For one-parameter degenerations of compact Kähler manifolds, we determine the asymptotic behavior of the first Chern form of the direct image of a Nakano semi-positive vector bundle twisted by the relative canonical bundle, when the direct image is equipped with the L2-metric.

This is a continuation of paper \cite{Li}. On any toric Fano manifold, we discuss the behavior of limit metric of a sequence of metrics, which are solutions to a continuity family of complex Monge-Ampere equations in Kahler-Einstein problem. We show that the limit metric satisfies a singular complex Monge-Ampere equati…

In this work, we describe the asymptotic behavior of complete metrics with prescribed Ricci curvature on open Kahler manifolds that can be compactified by the addition of a smooth and ample divisor. First, we construct a explicit sequence of Kahler metrics with special approximating properties. Using those metrics as s…

New metric MADD assesses fairness of predictive student models.

Let X be a quasiprojective manifold given by the complement of a divisor $\bD$ with normal crossings in a smooth projective manifold $\bX$. Using a natural compactification of $X$ by a manifold with corners $\tX$, we describe the full asymptotic behavior at infinity of certain complete Kahler metrics of finite volume o…

Paper uses DBSCAN variation to detect ship anomalies.

We study the complete Kahler-Einstein metric in tube domains. We obtain estimates of this metric and its holomorphic bisectional curvatures near the weakly pseudoconvex boundary points.

The paper analyzes systoles of complex projective spaces under various metrics.

Study shows asymptotic behavior of metric near singular points of a Monge-Ampère equation.

A simpler metric for latent space geometry.

We investigate the metric behavior of the Kahler-Ricci flow on the Hirzebruch surfaces, assuming the initial metric is invariant under a maximal compact subgroup of the automorphism group. We show that, in the sense of Gromov-Hausdorff, the flow either shrinks to a point, collapses to $\mathbb{P}^1$ or contracts an exc…

The study calculates Weyl entropy in spacetime regions and shows its monotonic behavior.

A new framework for mobile authentication using deep metric learning.

Study describes how conformal metrics behave as Q-curvature changes, forming spherical bubbles.

The paper examines torsions in Minkowskian product of Finsler metrics.

We study Yamabe metrics, and the moduli space of Yamabe metrics, on an arbitrary closed 3-manifold M. The main focus is on the boundary behavior of the moduli space, i.e. the behavior of degenerating sequences of unit volume Yamabe metrics on M. It is proved that such degenerations, when non-trivial in a certain sense,…

For a complete Riemannian metric, a pointwise conformal transformation may lead to a complete or incomplete transformed Riemannian metric, depending on the behavior of the conformal factor. We establish conditions on the growth of the conformal factor towards the infinity of the Riemannian metric, such that the conform…

Study on solutions near isolated singularities in 6D Yamabe equation.

The vulnerability to slight input perturbations is a worrying yet intriguing property of deep neural networks (DNNs). Despite many previous works studying the reason behind such adversarial behavior, the relationship between the generalization performance and adversarial behavior of DNNs is still little understood. In …

FOCAL tackles offline meta-reinforcement learning with efficient task inference and behavior regularization.

This work studies the entity-wise topical behavior from massive network logs. Both the temporal and the spatial relationships of the behavior are explored with the learning architectures combing the recurrent neural network (RNN) and the convolutional neural network (CNN). To make the behavioral data appropriate for th…

Study evaluates five LLMs for financial report analysis, revealing performance differences and variability.

This paper begins to study the limiting behavior of a family of Hermitian Yang-Mills (HYM for brevity) metrics on a class of rank two slope stable vector bundles over a product of two elliptic curves with Kähler metrics $ω_ε$ when $ε\to 0$. Here $ω_ε$ are flat and have areas $ε$ and $ε^{-1}$ on the two elliptic curves …

In this paper, we study the large time behavior of the heat kernel on complete Riemannian manifolds with nonnegative Ricci curvature, which was studied by P. Li with additional maximum volume growth assumption. Following Y. Ding's original strategy, by blowing down the metric, using Cheeger and Colding's theory about l…

Study small eigenvalues of Riemann surfaces degenerating with Kähler metrics.

We present new algorithms for computing and approximating bisimulation metrics in Markov Decision Processes (MDPs). Bisimulation metrics are an elegant formalism that capture behavioral equivalence between states and provide strong theoretical guarantees on differences in optimal behaviour. Unfortunately, their computa…

A new method detects fraud transactions by analyzing user behavior over time.

Curved metrics on Wallach spaces bounded by curves under flow.

Estimates for complex Monge-Ampère equations lead to insights on moduli spaces and singular metrics.

Under the assumption of asymptotic relative Chow-stability for polarized algebraic manifolds $(M, L)$, a series of weighted balanced metrics $ω_m$, $m \gg 1$, called polybalanced metrics, are obtained from complete linear systems $|L^m|$ on $M$. Then the asymptotic behavior of the weights as $m \to \infty$ will be stud…

In this note, we obtain existence results for complete Ricci-flat Kahler metrics on crepant resolutions of singularities of Calabi-Yau varieties. Furthermore, for certain asymptotically flat Calabi-Yau varieties, we show that the Ricci-flat metric on the resolved manifold has the same asymptotic behavior as the initial…

The study finds arbitrarily small spectral gaps for random hyperbolic surfaces with many cusps.