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.
In this paper we prove two extensions of Hamilton's maximal principle for systems pf parabolic equations which sould be useful for the study of the Ricci flow and some other geometric evolution equations. One extension is a time-dependent maximum principle and the other is a time-dependent maximum principle subject to …
Proves local existence and extension principle for Einstein Yang--Mills system with spherical symmetry.
Study proves finiteness for distance functions on curved surfaces with controlled curvature.
Classifies maximal symmetry models of CR dimension 1.
3-manifolds study Hasse norm principle, akin to number fields.
Floer field theory is a construction principle for e.g. 3-manifold invariants via decomposition in a bordism category and a functor to the symplectic category, and is conjectured to have natural 4-dimensional extensions. This survey provides an introduction to the categorical language for the construction and extension…
Based on ideas of L. Alías, D. Impera and M. Rigoli developed in "Hypersurfaces of constant higher order mean curvature in warped products", we develope a fairly general weak/Omori-Yau maximum principle for trace operators. We apply this version of maximum principle to generalize several higher order mean curvature est…
We give soft, quantitatively optimal extensions of the classical Sphere Theorem, Wilking's connectivity principle and Frankel's Theorem to the context of -th Ricci curvature. The hypotheses are soft in the sense that they are satisfied on sets of metrics that are open in the -topology.
The minimum description length (MDL) principle in supervised learning is studied. One of the most important theories for the MDL principle is Barron and Cover's theory (BC theory), which gives a mathematical justification of the MDL principle. The original BC theory, however, can be applied to supervised learning only …
We show that a conjectural extension of a fixed point formula in Arakelov geometry implies results about a tautological subring in the arithmetic Chow ring of bases of abelian schemes. Among the results are an Arakelov version of the Hirzebruch proportionality principle and a formula for a critical power of …
This paper presents a natural extension to foliated spaces of the following result due to Gromov : the h-principle for open, invariant differential relations is valid on open manifolds. The definition of openness for foliated spaces adopted here involves a certain type of Morse functions. Consequences concerning the pr…
Variational autoencoders provide a principled framework for learning deep latent-variable models and corresponding inference models. In this work, we provide an introduction to variational autoencoders and some important extensions.
In this paper, we develop a new mathematical technique which allows us to express the joint distribution of a Markov process and its running maximum (or minimum) through the marginal distribution of the process itself. This technique is an extension of the classical reflection principle for Brownian motion, and it is o…
New method extends fitted Q-evaluation for distributional off-policy reinforcement learning.
A variational principle is proposed for obtaining the Jacobi equations in systems admitting a Lagrangian description. The variational principle gives simultaneously the Lagrange equations of motion and the Jacobi variational equations for the system. The approach can be of help in finding constants of motion in the Jac…
We consider the problem of extending a conformal metric of negative curvature, given outside a neighbourhood of 0 in the unit disk $\DD$, to a conformal metric of negative curvature in $\DD$. We give conditions under which such an extension is possible, and also give obstructions to such an extension. The methods we us…
New model explains how concepts grow based on experience.
Survey of Fermat principle in general relativity and beyond.
We propose a principle for exploring context in machine learning models. Starting with a simple assumption that each observation may or may not depend on its context, a conditional probability distribution is decomposed into two parts: context-free and context-sensitive. Then by employing the log-linear word production…
This paper proposes a novel architecture, termed multiscale principle of relevant information (MPRI), to learn discriminative spectral-spatial features for hyperspectral image (HSI) classification. MPRI inherits the merits of the principle of relevant information (PRI) to effectively extract multiscale information embe…
Let be a codimension one submanifold of an -dimensional Riemannian manifold , . We give a necessary condition for an isometric immersion of into equipped with the standard Euclidean metric, , to be locally isometrically -extendable to . Even if this cond…
ProbFM provides principled uncertainty quantification for financial forecasting.
New non-existence results for harmonic maps into perturbed cones.
In this paper, we define and study sub-Riemannian structures on Banach manifolds. We obtain extensions of the Chow-Rashevski theorem for exact controllability, and give conditions for the existence of a Hamiltonian geodesic flow despite the lack of a Pontryagin Maximum Principle in the infinite dimensional setting.
Innovative extensions to option pricing models using asymmetric Brownian motion and random walk approaches.
SDAMI enhances interpretable high-dimensional regression with sparse deep learning and footprint principle.
Importance sampling has become an important tool for the computation of tail-based risk measures. Since such quantities are often determined mainly by rare events standard Monte Carlo can be inefficient and importance sampling provides a way to speed up computations. This paper considers moderate deviations for the wei…
In this work, we propose a composition/decomposition framework for adversarially training generative models on composed data - data where each sample can be thought of as being constructed from a fixed number of components. In our framework, samples are generated by sampling components from component generators and fee…
Paper reconciles two methods of describing Riemannian spaces.
The paper extends physics-based information maximization to complex bandit problems.
We establish a parametric extension -principle for overtwisted contact structures on manifolds of all dimensions, which is the direct generalization of the -dimensional result from \cite{Eli89}. It implies, in particular, that any closed manifold admits a contact structure in any given homotopy class of almost co…
Dirac structures on tangent bundles provide a unified framework for Lagrange--Dirac dynamical systems.
The key issue of few-shot learning is learning to generalize. This paper proposes a large margin principle to improve the generalization capacity of metric based methods for few-shot learning. To realize it, we develop a unified framework to learn a more discriminative metric space by augmenting the classification loss…
We give a necessary and sufficient condition for the smooth extension of a diffeomorphism between smooth strictly pseudoconvex domains in four real dimensional almost complex manifolds. The proof is mainly based on a reflection principle for pseudoholomorphic discs, on precise estimates of the Kobayashi-Royden infinite…
This paper reviews nonlinear ICA for disentangled representations in unsupervised learning.
Unified framework for MCMC algorithms simplifies their design and application.
This is an extensive (published) survey on CR geometry, whose major themes are: formal analytic reflection principle; generic properties of Systems of (CR) vector fields; pairs of foliations and conjugate reflection identities; Sussmann's orbit theorem; local and global aspects of holomorphic extension of CR functions;…
Derives stochastic and dissipative dynamics preserving Gibbs measure.
A graph bandit algorithm learns optimal paths on unknown graphs.
Study proves steady state space hypersurfaces are hyperplanes under certain curvature constraints.
When applying the support vector machine (SVM) to high-dimensional classification problems, we often impose a sparse structure in the SVM to eliminate the influences of the irrelevant predictors. The lasso and other variable selection techniques have been successfully used in the SVM to perform automatic variable selec…
Rate GENERIC extends thermodynamics principles to non-equilibrium systems.
The paper solves complex control problems using neural networks.
We introduce a natural extension of the concept of gradient Ricci soliton: the Ricci almost soliton. We provide existence and rigidity results, we deduce a-priori curvature estimates and isolation phenomena, and we investigate some topological properties. A number of differential identities involving the relevant geome…
Algorithm combines ESG ratings with pairs trading for sustainable investing.
The main aim of this paper is the construction of a smooth (sometimes called differential) extension \hat{MU} of the cohomology theory complex cobordism MU, using cycles for \hat{MU}(M) which are essentially proper maps W\to M with a fixed U(n)-structure and U(n)-connection on the (stable) normal bundle of W\to M. Cruc…
In this paper we develop a Morse Theory for timelike geodesics parameterized by a constant multiple of proper time. The results are obtained using an extension to the timelike case of the relativistic Fermat Principle, and techniques from Global Analysis on infinite dimensional manifolds. In the second part of the pape…
Empowerment is an information-theoretic method that can be used to intrinsically motivate learning agents. It attempts to maximize an agent's control over the environment by encouraging visiting states with a large number of reachable next states. Empowered learning has been shown to lead to complex behaviors, without …