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.
SGLD proves geometric ergodicity via reflection coupling for nonconvex log-concave distributions.
Paper proposes a weak approximation of reflection coupling for non-convex optimization.
A coupling by reflection of a time-inhomogeneous diffusion process on a manifold are studied. The condition we assume is a natural time-inhomogeneous extension of lower Ricci curvature bounds. In particular, it includes the case of backward Ricci flow. As in time-homogeneous cases, our coupling provides a gradient esti…
Develops non-Markovian couplings for sub-Riemannian Brownian motions.
Based on a study of the coupling by reflection of diffusion processes, a new monotonicity in time of a time-dependent transportation cost between heat distribution is shown under Bakry-Emery's curvature-dimension condition on a Riemannian manifold. The cost function comes from the total variation between heat distribut…
Probabilistic method proves gap estimates on sphere.
New method trains reflected Schrödinger bridges without complex derivatives.
In this paper, we present a family of a control-stopping games which arise naturally in equilibrium-based models of market microstructure, as well as in other models with strategic buyers and sellers. A distinctive feature of this family of games is the fact that the agents do not have any exogenously given fundamental…
We derive a diffusion approximation for the kinetic Vlasov-Fokker-Planck equation in bounded spatial domains with specular reflection type boundary conditions. The method of proof involves the construction of a particular class of test functions to be chosen in the weak formulation of the kinetic model. This involves t…
Coupled entropy corrects flaws in Tsallis entropy for complex systems.
FHRN uses continuous-time dynamics to stabilize reentrant neural computation.
Efficiently optimizes orthogonal and Stiefel matrices on parallel units.
Unified framework for Brownian motion distances on specific geometric manifolds.
New method improves sampling efficiency in complex stochastic systems.
New method estimates convergence bounds for nonlinear Markov chains.
Multi-domain translation seeks to learn a probabilistic coupling between marginal distributions that reflects the correspondence between different domains. We assume that data from different domains are generated from a shared latent representation based on a structural equation model. Under this assumption, we show th…
Modeling bank leverage dynamics to understand systemic risk in financial markets.
While it is an important problem to identify the existence of causal associations between two components of a multivariate time series, a topic addressed in Runge et al. (2012), it is even more important to assess the strength of their association in a meaningful way. In the present article we focus on the problem of d…
Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation, sentence similarities to deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground metric" is limited. In this work, we develop a nonlinear generalization of (discrete) …
We study how trading costs are reflected in equilibrium returns. To this end, we develop a tractable continuous-time risk-sharing model, where heterogeneous mean-variance investors trade subject to a quadratic transaction cost. The corresponding equilibrium is characterized as the unique solution of a system of coupled…
We develop a theory of bid and ask price dynamics where the two prices form due to interaction of buy and sell orders. In this model the two prices are represented by eigenvalues of a 2x2 price operator corresponding to "bid" and "ask" eigenstates. Matrix elements of price operator fluctuate in time which results in ph…
Generalizing previous work by two of us, we prove the non-existence of certain stationary configurations in General Relativity having a spatial reflection symmetry across a non-compact surface disjoint from the matter region. Our results cover cases such that of two symmetrically arranged rotating bodies with anti-alig…
Paper analyzes convergence of Sinkhorn algorithm for discrete probability measures on torus.
Mini-batch stochastic gradient descent and variants thereof have become standard for large-scale empirical risk minimization like the training of neural networks. These methods are usually used with a constant batch size chosen by simple empirical inspection. The batch size significantly influences the behavior of the …
We enhance autonomous materials research with problem-aware models.
Study optimal transport for stationary processes, estimating joinings and costs.
Guyon-Lekeufack model accurately predicts market volatility.
A discrete subgroup of the group of isometries of the hyperbolic space is called reflective if up to a finite index it is generated by reflections in hyperplanes. The main result of this paper is a complete classification of the reflective (and quasi-reflective) subgroups among the Bianchi groups and their extensions.
New method produces reflections with nonseparating fixed points.
Survey explores interactions between four conformal dynamics branches.
One reflection suffices for orthogonal weights, reducing GPU usage.
We study risk-sharing equilibria with general convex costs on the agents' trading rates. For an infinite-horizon model with linear state dynamics and exogenous volatilities, we prove that the equilibrium returns mean-revert around their frictionless counterparts - the deviation has Ornstein-Uhlenbeck dynamics for quadr…
Minimal surfaces in 3-sphere created by reflections from polygons, with new examples based on pentagons.
Motivated by the study of coupled Kähler-Einstein metrics by Hultgren and Witt Nyström and coupled Kähler-Ricci solitons by Hultgren, we study in this paper coupled Sasaki-Einstein metrics and coupled Sasaki-Ricci solitons. We first show an isomorphism between the Lie algebra of all transverse holomorphic vector fields…
Study thin hyperbolic reflection groups and their properties.
Exactly solvable model reveals how data geometry influences ML bias.
Defines coupled embeddability for maps on products of spaces, generating examples and nonexamples.
Minimal surfaces reflect across spheres, proving annulus uniqueness.
Solves modified conjecture for Fano manifolds using Ding stability.
UNTIE learns representations of coupled categorical data.
Hausdorff reflection keeps space shape intact.
Study extends reflective submanifold theory to compact homogeneous spaces.
Paper discusses conditions for deforming coupled Kähler-Einstein metrics.
New reflection groups derived from torus knots with finite meridians.
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of objects can be represented in the same space, or at least distances between them can…
A co-evolutionary approach for Heston model calibration reduces overfitting with diverse datasets.
A hyperbolic lattice is called \textit{-reflective} if the subgroup of its automorphism group generated by all - and -reflections is of finite index. The main result of this article is a complete classification of -reflective maximal anisotropic lattices of rank .
A hyperbolic reflection group is a discrete group generated by reflections in the faces of an -dimensional hyperbolic polyhedron. This survey article is dedicated to the study of arithmetic hyperbolic reflection groups with an emphasis on the results that were obtained in the last ten years and on the open problems.