arXiv research

Study evaluates relevance metrics for similarity-based model explanations.

In machine learning, the choice of a learning algorithm that is suitable for the application domain is critical. The performance metric used to compare different algorithms must also reflect the concerns of users in the application domain under consideration. In this work, we propose a novel probability-based performan…

Novel metrics improve machine learning models for ICU patient care.

A large amount of data accommodated in knowledge graphs (KG) is actually metric. For example, the Wikidata KG contains a plenitude of metric facts about geographic entities like cities, chemical compounds or celestial objects. In this paper, we propose a novel approach that transfers orometric (topographic) measures to…

Generative AI reduces IR evaluation costs but introduces errors; this work provides reliable CIs.

Decision-alignment evaluates uncertainty quantification for decision-relevant UQ

New cohomological obstruction found for astheno-Kahler metrics.

Optimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether that ground metric parameter is suitably chosen. Selecting it adaptively and algorithmically from prior knowledge…

XR improves search advertising relevance predictions.

The study evaluates saliency metrics for image classifier outputs, finding inconsistencies and unreliability.

Survey of spectral, probabilistic, and deep metric learning methods.

On connected manifolds of dimension higher than three, the non-existence of $132$ Chinea and González-Dávila types of almost contact metric structures is proved. This is a consequence of some interrelations among components of the intrinsic torsion of an almost contact metric structure. Such interrelations allow to des…

We introduce and study $H$-paracontact metric manifolds, that is, paracontact metric manifolds whose Reeb vector field $ξ$ is harmonic. We prove that they are characterized by the condition that $ξ$ is a Ricci eigenvector. We then investigate how harmonicity of the Reeb vector field $ξ$ of a paracontact metric manifold…

Evaluating the style of handwriting generation is a challenging problem, since it is not well defined. It is a key component in order to develop in developing systems with more personalized experiences with humans. In this paper, we propose baseline benchmarks, in order to set anchors to estimate the relative quality o…

Choppy optimizes ranked list truncation using Transformer architecture.

GRM uses graph neural networks to score process activity relevance.

Study relates Finsler structures to Clifford bundles for flat metrics.

Study on metrics with positive scalar curvature on manifolds with singularities.

This article presents a new and more elementary proof of the main Seiberg-Witten-based obstruction to the existence of Einstein metrics on smooth compact 4-manifolds. It also introduces a new smooth manifold invariant which conveniently encapsulates those aspects of Seiberg-Witten theory most relevant to the study of R…

Study Finsler metric measure manifolds' concentration properties.

We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings, and is considerably more general than Lorentzian geometry. Our construction of geo…

We study adiabatic limits of Ricci-flat Kahler metrics on a Calabi-Yau manifold which is the total space of a holomorphic fibration when the volume of the fibers goes to zero. By establishing some new a priori estimates for the relevant complex Monge-Ampere equation, we show that the Ricci-flat metrics collapse (away f…

New TDA approach using Finsler metrics.

A mass-type invariant for smooth metric measure spaces and its relation with the fractional Yamabe problem

We propose a novel VAE-based deep auto-encoder model that can learn disentangled latent representations in a fully unsupervised manner, endowed with the ability to identify all meaningful sources of variation and their cardinality. Our model, dubbed Relevance-Factor-VAE, leverages the total correlation (TC) in the late…

String backgrounds and D-branes do not possess the structure of Lorentzian manifolds, but that of manifolds with area metric. Area metric geometry is a true generalization of metric geometry, which in particular may accommodate a B-field. While an area metric does not determine a connection, we identify the appropriate…

Paper proposes adaptive margin loss to improve few-shot learning.

Given a Kähler fiber space $p:X\to Y$ whose generic fiber is of general type, we prove that the fiberwise singular Kähler-Einstein metric induces a semipositively curved metric on the relative canonical bundle $K_{X/Y}$ of $p$. We also propose a conjectural generalization of this result for relative twisted Kähler-Eins…

Modified BP attribution methods often ignore later layers' information, leading to misleading explanations.

We analyze a class of conical G_2 metrics admitting two commuting isometries, together with a certain one-parameter family of G_2 deformations which preserves these symmetries. Upon using recent results of Calderbank and Pedersen, we write down the explicit G_2 metric for the most general member of this family and extr…

The Gromov-Hausdorff distance provides a metric on the set of isometry classes of compact metric spaces. Unfortunately, computing this metric directly is believed to be computationally intractable. Motivated by applications in shape matching and point-cloud comparison, we study a semidefinite programming relaxation of …

Following Donaldson's oppenness theorem on deforming a conical Kähler-Einstein metric, we prove a parabolic Schauder-type estimate with respect to conical metrics. As a corollary, we show that the conical Kähler-Ricci Flow exists for short time. The key is to establish the relevant heat kernel estimates, where we use t…

Classifies all flat Riemannian metrics on the plane, including complete and incomplete cases.

Classifies metric lines in Engel-type groups, a step towards solving sub-Riemannian manifold problems.

We prove that every Weil-Petersson isometry of the Teichmuller space T(g,n) is induced by an element of the extended mapping class group; here 3g-3+n > 1 and (g,n) is not (1,2). Our method follows Ivanov's proof of the Royden's analogous theorem for the Teichmuller metric: we study the action of an isometry on the fron…

This paper introduces GEMINI, a new mutual information metric for unsupervised neural network training.

We study continuous groups of generalized Kerr-Schild transformations and the vector fields that generate them in any n-dimensional manifold with a Lorentzian metric. We prove that all these vector fields can be intrinsically characterized and that they constitute a Lie algebra if the null deformation direction is fixe…

The metric jets, introduced in the first chapter, generalize the jets (at order one) of Charles Ehresmann. In short, for a "good" map $f$ (said to be "tangentiable" at $a$), we define its metric jet tangent at $a$ (composed of all the maps which are locally lipschitzian at $a$ and tangent to $f$ at $a$) called the "tan…

Defines intrinsically Hölder sections in metric spaces.

We consider the problem of metric learning for multi-view data and present a novel method for learning within-view as well as between-view metrics in vector-valued kernel spaces, as a way to capture multi-modal structure of the data. We formulate two convex optimization problems to jointly learn the metric and the clas…

The tangent bundle as a $4n$-manifold is equipped with an almost hypercomplex pseudo-Hermitian structure and it is characterized with respect to the relevant classifications. A number of 8-dimensional examples of the considered type of manifold are received from the known explicit examples in that manner.

The theory of monotone Riemannian metrics on the state space of a quantum system was established by Denes Petz in 1996. In a recent paper he argued that the scalar curvature of a statistically relevant - monotone - metric can be interpreted as an average statistical uncertainty. The present paper contributes to this su…

Mild Traumatic Brain Injury (mTBI) is a significant public health problem. The most troubling symptoms after mTBI are cognitive complaints. Studies show measurable differences between patients with mTBI and healthy controls with respect to tissue microstructure using diffusion MRI. However, it remains unclear which dif…

New metrics predict human sentence comprehension across languages.

Paper extends ranking metrics theory for financial positions.

Estimates gradients of solutions on closed surfaces.

Paper extends ranking metrics theory for financial positions.

Elliptical Attention improves transformer performance by focusing on contextually relevant features.