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.
Normalizes pseudo-Einstein contact forms for easier analysis.
Robustly computes intrinsic coordinates on point clouds using resampling and averaging.
Solving tasks with sparse rewards is one of the most important challenges in reinforcement learning. In the single-agent setting, this challenge is addressed by introducing intrinsic rewards that motivate agents to explore unseen regions of their state spaces; however, applying these techniques naively to the multi-age…
Extracts intrinsic spatial coordinates for complex agent systems to learn PDEs.
We develop a deep autoencoder architecture that can be used to find a coordinate transformation which turns a nonlinear PDE into a linear PDE. Our architecture is motivated by the linearizing transformations provided by the Cole-Hopf transform for Burgers equation and the inverse scattering transform for completely int…
We give an intrinsic (coordinate-free) construction of the tangent groupoid of a filtered manifold.
Intrinsically motivated reinforcement learning aims to address the exploration challenge for sparse-reward tasks. However, the study of exploration methods in transition-dependent multi-agent settings is largely absent from the literature. We aim to take a step towards solving this problem. We present two exploration m…
We provide an intrinsic description of the notion of modular class for an even symplectic manifold and study its properties in this coordinate free setting.
The aim of the present paper is to provide an intrinsic investigation of projective changes in Finlser geometry, following the pullback formalism. Various known local results are generalized and other new intrinsic results are obtained. Nontrivial characterizations of projective changes are given. The fundamental proje…
Conformal Autoencoders infer intrinsic dimensionality and impose invariance.
The paper provides an intrinsic proof of a theorem about Landsberg spaces.
Manifold embedding algorithms map high-dimensional data down to coordinates in a much lower-dimensional space. One of the aims of dimension reduction is to find intrinsic coordinates that describe the data manifold. The coordinates returned by the embedding algorithm are abstract, and finding their physical or domain-r…
Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear is a central challenge in modern dynamical systems. These transformations have the potential to enable prediction, estimation, and control of nonlinear systems using standard linear theory. The Koopman operator has emerged…
Adopting the pullback approach to global Finsler geometry, the aim of the present paper is to provide new intrinsic (coordinate-free) proofs of intrinsic versions of the existence and uniqueness theorems for the Cartan and Berwald connections on a Finsler manifold. To accomplish this, the notions of semispray and nonli…
A new method calculates intrinsic effective sample size for manifold-valued data.
A classical theorem of Riemannian geometry, due in its original form to Cartan, states that the Taylor expansion of the metric in geodesic normal coordinates is a universal formal power series involving only the symmetrizations of the iterated covariant derivatives of the curvature tensor; this is known as the jet isom…
Geometric mechanics approach to constrained and floating multibody systems using Hamel's equations.
Study investigates Hashiguchi connection's uniqueness and existence in Finsler geometry.
Catenaries defined on any Riemannian surface using intrinsic distance.
In this contribution we present an intrinsic description of time-variant Port Hamiltonian systems as they appear in modeling and control theory. This formulation is based on the splitting of the state bundle and the use of appropriate covariant derivatives, which guarantees that the structure of the equations is invari…
Given two observers, we define the "relative velocity" of one observer with respect to the other in four different ways. All four definitions are given intrinsically, i.e. independently of any coordinate system. Two of them are given in the framework of spacelike simultaneity and, analogously, the other two are given i…
For particles constrained on a curved surface, how to perform quantization within Dirac's canonical quantization scheme is a long-standing problem. On one hand, Dirac stressed that the Cartesian coordinate system has fundamental importance in passing from the classical Hamiltonian to its quantum mechanical form while p…
TOFU-POV tackles partially observed linear bandits, achieving sublinear regret with low-dimensional action vectors.
Rust library solves complex equations on abstract simplicial complexes.
Proves harmonic coordinates for weak immersions in even dimensions.
Unified framework for singular statistical models using observable charts.
Develops intrinsic Gaussian process regression for manifold-valued data.
The paper explores the geometric structure of cost functions in multiple dimensions.
High-dimensional models trained on smooth manifolds achieve optimal rates in Wasserstein metrics.
We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships. The model allows straightforward variatio…
A comparative analysis of two different versions of the Legendre transformation is presented. We provide an almost complete although somewhat superficial review of the geometric background for analytical mechanics. Complete coordinate characterizations of all structures are provided. Intrinsic constructions of most of …
By attaching a Lie algebra of germs of analytic vector fields to every point of a (real or complex) analytic variety V we construct the Nagano foliation of the variety. We prove that the Nagano foliation of V is a stratification. The treatment of the subject is totally coordinate free but relies on the Oka-Cartan-Serre…
New method for long-term sampling of complex dynamics on curved spaces.
New surfaces in Lorentz-Minkowski space with constant mean curvature identified.
The paper analyzes finite element methods on manifolds with approximate metrics.
We provide the proof that the space of time series data is a Kolmogorov space with -separation axiom using the loop space of time series data. In our approach we define a cyclic coordinate of intrinsic time scale of time series data after empirical mode decomposition. A spinor field of time series data comes fro…
We explore the geometry that underlies the osculating nilpotent group structures of the Heisenberg calculus. For a smooth manifold with a distribution analysts use explicit (and rather complicated) coordinate formulas to define the nilpotent groups that are central to the calculus. Our aim in this p…
The paper studies steady motions of fibre-reinforced fluids on curved surfaces.
Reconstructs Riemannian geometry from diffusion properties.
Two cross caps in Euclidean -space are said to be formally isometric if their Taylor expansions of the first fundamental forms coincide by taking a suitable local coordinate system. For a given cross cap , we give a method to find all cross caps which are formally isometric to . As an application, w…
We are concerned with the global weak rigidity of the Gauss-Codazzi-Ricci (GCR) equations on Riemannian manifolds and the corresponding isometric immersions of Riemannian manifolds into the Euclidean spaces. We develop a unified intrinsic approach to establish the global weak rigidity of both the GCR equations and isom…
A new method integrates autoencoders with geometry regularization for manifold learning.
A new coordinate system for SPD matrices simplifies computations and generative modeling.
We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new Lagrangian in an extended configuration space ---which we call D'Alambert's--- com…
Introduces intrinsic Riemannian cross-covariance for manifold-valued random objects.
Characterizes metrics on triangulated surfaces using glued Euclidean triangles.
Generalising a seminal result of Epstein and Penner for cusped hyperbolic manifolds, Cooper and Long showed that each decorated strictly convex projective cusped manifold has a canonical cell decomposition. Penner used the former result to describe a natural cell decomposition of decorated Teichmüller space of puncture…
This paper contains the technical foundations from stochastic differential geometry for the construction of geometrically intrinsic nonlinear recursive filters. A diffusion X on a manifold N is run for a time interval T, with a random initial condition. There is a single observation consisting of a nonlinear function o…