A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This paper explores the impact of metric choice on Fréchet regression.
Abstract: Almost Kähler Hodge numbers vary with metric choices.
Generic smooth boundaries for isoperimetric regions in 8D manifolds.
Bayesian DL model improves DCMs for better predictive and inferential performance.
Boundary distances determine conformal metrics
Bayesian methods detect significant IIA violations in similarity choice data.
We solve the multi-criteria benchmarking problem by formalizing it as a social choice problem and identifying conditions for meaningful rankings.
This work shows how evaluation metrics can be seen as fair gambles.
In this paper we study the phenomenon of phase transitions for the geodesic flow on some geometrically finite negatively curved manifolds. We define a class of potentials going slowly to zero through the cusps of for which the pressure map exhibits a phase transition. By a careful choice of the metric at the cusp w…
Develops symmetric Cartan calculus linking to Patterson-Walker metric.
Graph neural nets improve discrete choice modeling with network effects.
We study the deformation of spherical conical metrics with at least some of the cone angles larger than . We show in this note via synthetic geometry that for one family of such metrics, there is local rigidity in the choice of cone positions if angles are fixed. This gives an evidence of the analytic obstruction c…
Note: Causality can be encoded without strict time function choice.
An extension of the ambient metric construction of Fefferman-Graham to infinite order in even dimensions is described. The main ingredients are the introduction of "inhomogeneous ambient metrics" with asymptotic expansions involving the logarithm of a defining function homogeneous of degree 2, and an invariant procedur…
Connected space of Dirac-minimal metrics in 2 and 4 dimensions.
Overconfidence and underconfidence in machine learning classifiers is measured by calibration: the degree to which the probabilities predicted for each class match the accuracy of the classifier on that prediction. How one measures calibration remains a challenge: expected calibration error, the most popular metric, ha…
A method to combine saliency metrics for better CNN pruning decisions.
We introduce a new geometric flow of Hermitian metrics which evolves an initial metric along the second derivative of the Chern scalar curvature. The flow depends on the choice of a background metric, it always reduces to a scalar equation and preserves some special classes of Hermitian structures, as balanced and Gaud…
Let be a compact 3-manifold with boundary which admits a complete, convex co-compact hyperbolic metric. For each hyperbolic metric on such that $\dr M$ is smooth and strictly convex, the induced metric on $\dr M$ has curvature , and each such metric on $\dr M$ is obtained for a unique ch…
Unique optimal symplectic connections found for submersions.
We define metrics on Culler-Vogtmann space, which are an analogue of the Teichmuller metric and are constructed using stretching factors. In fact the metrics we study are related, one being a symmetrised version of the other. We investigate the basic properties of these metrics, showing the advantages and pathologies o…
An analogue of the Riemannian Geometry for an ultrametric Cantor set (C, d) is described using the tools of Noncommutative Geometry. Associated with (C, d) is a weighted rooted tree, its Michon tree. This tree allows to define a family of spectral triples giving the Cantor set the structure of a noncommutative Riemanni…
The study connects manifold topology to metrics with positive intermediate curvature.
Constructs Lorentzian manifolds from Riemannian conformal structures.
We consider some metrics and weak metrics defined on the Teichmueller space of a surface of finite type with nonempty boundary, that are defined using the hyperbolic length spectrum of simple closed curves and of properly embedded arcs, and we compare these metrics and weak metrics with the Teichmüller metric. The comp…
Symmetric Positive Definite (SPD) matrices have been used in many fields of medical data analysis. Many Riemannian metrics have been defined on this manifold but the choice of the Riemannian structure lacks a set of principles that could lead one to choose properly the metric. This drives us to introduce the principle …
Proposes a method to select fair performance metrics through metric elicitation.
Gaussian kernel fails on circle and related spaces.
The paper studies contact pseudo-metric manifolds with a specific curvature condition.
The Gauss-Bonnet Theorem is studied for edge metrics as a renormalized index theorem. These metrics include the Poincaré-Einstein metrics of the AdS/CFT correspondence. Renormalization is used to make sense of the curvature integral and the dimensions of the -cohomology spaces as well as to carry out the heat equa…
Unified treatment of elastic metrics for curves in any dimension.
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…
The study examines surfaces in isotropic space with specific Gauss map properties.
We give new examples of compact, negatively curved Einstein manifolds of dimension . These are seemingly the first such examples which are not locally homogeneous. Our metrics are carried by a sequence of 4-manifolds previously considered by Gromov and Thurston. The construction begins with a certain sequenc…
We use a G2-structure on a 7-dimensional Riemannian manifold with a fixed metric to define an octonion bundle with a fiberwise non-associative product. We then define a metric-compatible octonion covariant derivative on this bundle that is compatible with the octonion product. The torsion of the G2-structure is then sh…
Given a holomorphic Hilbertian bundle on a compact complex manifold, we introduce the notion of holomorphic torsion, which lies in the determinant line of the twisted Dolbeault cohomology and represents a volume element there. Here we utilise the theory of determinant lines of Hilbertian modules over finite…
This article proves that if M is a smooth manifold of dimension at least four, then for generic choice of metric on M, all prime parametrized minimal surfaces in M are free of branch points and lie on nondegenerate critical submanifolds for the two-variable energy function which have the same dimension as the group of …
Ordinal regression is aimed at predicting an ordinal class label. In this paper, we consider its semi-supervised formulation, in which we have unlabeled data along with ordinal-labeled data to train an ordinal regressor. There are several metrics to evaluate the performance of ordinal regression, such as the mean absol…
New Einstein metrics found on SU(N) without being naturally reductive.
Let (T^2, g) be a two-dimensional Riemannian torus. In this paper we prove that the topological entropy of the geodesic flow restricted to the set of initial conditions of minimal geodesics vanishes, independent of the choice of the Riemannian metric.
Symmetric Positive Definite (SPD) matrices have been widely used in medical data analysis and a number of different Riemannian met-rics were proposed to compute with them. However, there are very few methodological principles guiding the choice of one particular metric for a given application. Invariance under the acti…
Defines a new metric on Fano Kaehler-Ricci solitons.
We investigate the relationship between measurable differentiable structures on doubling metric measure spaces and derivations. We prove: [1] a decomposition theorem for the module of derivations into free modules; [2] the existence of a measurable differentiable structure assuming that one can control the pointwise up…
We consider a notion of balanced metrics for triples (X,L,E) which depend on a parameter α, where X is smooth complex manifold with an ample line bundle L and E is a holomorphic vector bundle over X. For generic choice of α, we prove that the limit of a convergent sequence of balanced metrics leads to a Hermitian-Einst…
This paper investigates the question of which smooth compact 4-manifolds admit Riemannian metrics that minimize the L2-norm of the curvature tensor. Metrics with this property are called OPTIMAL; Einstein metrics and scalar-flat anti-self-dual metrics provide us with two interesting classes of examples. Using twistor m…
The paper proposes a notion of volume element for Finsler spaces with metrics of Lorentzian signature, equipped with a time orientation. This notion is based on a slight modification of the idea of Holmes-Thompson volume element working for positive definite Finsler metrics and can be used in field-theoretical applicat…
Many tasks such as retrieval and recommendations can significantly benefit from structuring the data, commonly in a hierarchical way. To achieve this through annotations of high dimensional data such as images or natural text can be significantly labor intensive. We propose an approach for uncovering the hierarchical s…
It has been observed by Maldacena that one can extract asymptotically anti-de Sitter Einstein -metrics from Bach-flat spacetimes by imposing simple principles and data choices. We cast this problem in a conformally compact Riemannian setting. Following an approach pioneered by Fefferman and Graham for the Einstein e…