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.
A new DR formulation improves metric learning for faster and more stable performance.
Defines a metric and form for a bundle moduli space, leading to a zero-curvature formulation.
Metric SYZ conjecture proved using non-archimedean geometry.
New formulations for Ricci flows without smoothness.
Introduces new metric for Riemannian metrics, extending unbalanced optimal transport.
New formulations for comparing metric measure spaces with arbitrary positive measures.
This paper introduces a new formulation of the Conic Gromov-Wasserstein distance for comparing complex network structures.
New metric for probability measures connects physics and geometry.
Study improves confidence measures in medical imaging pipelines by addressing bias.
This paper introduces a new mathematical formulation and numerical approach for the computation of distances and geodesics between immersed planar curves. Our approach combines the general simplifying transform for first-order elastic metrics that was recently introduced by Kurtek and Needham, together with a relaxatio…
New formulation of Schrödinger connections preserves vector lengths in geometry.
New framework for efficient optimal transport distances between Markov chains.
On a convex body in a Euclidean space, we introduce a new variational formulation for its Funk metric, a Finsler metric compatible with the tautological Finsler structure of the convex body. We generalize the metric on Teichmuller spaces with the Weil-Petersson distance function. A set of similarities the resulting met…
We propose a method that enables practitioners to conveniently incorporate custom non-decomposable performance metrics into differentiable learning pipelines, notably those based upon neural network architectures. Our approach is based on the recently developed adversarial prediction framework, a distributionally robus…
We revisit the task of learning a Euclidean metric from data. We approach this problem from first principles and formulate it as a surprisingly simple optimization problem. Indeed, our formulation even admits a closed form solution. This solution possesses several very attractive properties: (i) an innate geometric app…
We formulate an approach to the geometry of Riemann-Cartan spaces provided with nonholonomic distributions defined by generic off-diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be modelled by moving nonholonomic frames on (pseudo) Riemannian manifolds and desc…
Investigates O(n)-invariant metrics on SPD matrices, extending kernel metrics.
Fairness-aware classification is receiving increasing attention in the machine learning fields. Recently research proposes to formulate the fairness-aware classification as constrained optimization problems. However, several limitations exist in previous works due to the lack of a theoretical framework for guiding the …
This paper provides details of the construction, properties and some applications of the ambient metric associated to a conformal class of metrics on a smooth manifold. Existence and uniqueness of formal expansions defining such metrics are considered. Equivalence with the expansions of associated Poincare metrics is e…
In this paper we show that the Hamiltonian Monte Carlo method for compact Lie groups constructed in \cite{kennedy88b} using a symplectic structure can be recovered from canonical geometric mechanics with a bi-invariant metric. Hence we obtain the correspondence between the various formulations of Hamiltonian mechanics …
We introduce the tractor formalism from conformal geometry to the study of smooth metric measure spaces. In particular, this gives rise to a correspondence between quasi-Einstein metrics and parallel sections of certain tractor bundles. We use this formulation to give a sharp upper bound on the dimension of the vector …
Improved robustness in multivariate regression and classification with DRO under Wasserstein metric.
We prove that the results regarding the Isoperimetric inequality and Cheeger constant formulated in terms of the Minkowski content, obtained by the authors in previous papers in the framework of essentially non-branching metric measure spaces verifying the local curvature dimension condition, also hold in the stronger …
Intrinsic formulation of noncommutative geometry for quantum gravity.
Proves existence of smooth metrics with specific curvature properties.
This paper improves QoS metric prediction in DTNs using diffusion models.
We investigate connections between pairs of (pseudo-)Riemannian metrics whose sum is a (tensor) product of a covector field with itself. A bijective mapping between the classes of Euclidean and Lorentzian metrics is constructed as a special result. The existence of such maps on a differentiable manifold is discussed. S…
This dissertation uses ILP to learn Bayesian network structures efficiently.
A local deformation property for uniform embeddings in metric manifolds (LD) is formulated and its behaviour is studied in a formal view point. It is shown that any metric manifold with a geometric group action, typical metric spaces (Euclidean space, hyperbolic space and cylinders) and for κ\leq 0 the κ-cone ends over…
New examples found of complex manifolds with special metrics.
New stability theorem for hyperbolic metrics without volume bounds.
In this paper, we formulate a procedure to obtain a generalization of Milnor frames for left-invariant pseudo-Riemannian metrics on a given Lie group. This procedure is an analogue of the recent studies on left-invariant Riemannian metrics, and is based on the moduli space of left-invariant pseudo-Riemannian metrics. A…
New derivation of Type IIA flow metrics.
We reformulate the compatibility condition between a generalized metric and a small (non-maximal rank) Dirac structure in an exact Courant algebroid found in the context of the gauging of strings and formulated by means of two connections in purely Dirac-geometric terms. The resulting notion, a transverse generalized m…
Building on author's previous results in singular semi-Riemannian geometry and singular general relativity, the behavior of gauge theory at singularities is analyzed. The usual formulations of the field equations at singularities are accompanied by infinities which block the evolution equations, mainly because the metr…
Proposes sigmoidF1 loss for multilabel classification, improving performance metrics.
Curve shortening flow is not unique on certain metrics.
Differential calculus on metric spaces is contained in the algebraic study of normed groupoids with -structures. Algebraic study of normed groups endowed with dilatation structures is contained in the differential calculus on metric spaces. Thus all algebraic properties of the small world of normed groups with dilat…
A new supervised tree-Wasserstein distance improves document classification.
We formulate and discuss two conjectures concerning recursive formulae for Branson's -curvatures. The proposed formulae describe all -curvatures on manifolds of all even dimensions in terms of respective lower order -curvatures and lower order GJMS-operators. They are universal in the dimension of the underlyi…
The study connects manifold topology to metrics with positive intermediate curvature.
Paper uses Sinkhorn distances to improve imitation learning effectiveness.
Generative Adversarial Networks have been shown to be powerful in generating content. To this end, they have been studied intensively in the last few years. Nonetheless, training these networks requires solving a saddle point problem that is difficult to solve and slowly converging. Motivated from techniques in the reg…
Study characterizes -rectifiable sets in homogeneous groups.
We consider the volume expansion of the Blaschke metric, which is a projectively invariant metric on a strictly convex domain in a locally flat projective manifold. When the boundary is even dimensional, we express the logarithmic coefficient L as the integral of affine invariants over the boundary. We also formulate a…
Study on -structures manifold geometry.
Researchers find counterexamples to inverse problems for wave equations.
In this paper, we shall use the Kähler geometry formulation to study the global behavior of the Ricci flow on . The geometric feature of our Ricci flow is that it has finite width. Our aim is to determine the limiting metric (which corresponds an eternal Ricci flow) obtained by L.F.Wu. We can use the classificatio…