arXiv research

The paper extends portfolio theory to include contingent claim functions for option pricing.

Generative method avoids function estimation for data generation.

Proposes a generalized XGBoost method for nonconvex loss functions.

Derives PF-ODE for infinite-dimensional functions, improving function generation tasks.

Almost twenty years ago, E.R. Fernholz introduced portfolio generating functions which can be used to construct a variety of portfolios, solely in the terms of the individual companies' market weights. I. Karatzas and J. Ruf recently developed another methodology for the functional construction of portfolios, which lea…

We show that for smooth manifolds X and Y, any isomorphism between the special algebra of Colombeau generalized functions on X, resp. Y is given by composition with a unique Colombeau generalized function from Y to X. We also identify the multiplicative linear functionals from the special algebra of Colombeau generaliz…

Based on Colombeau's theory of algebras of generalized functions we introduce the concepts of generalized functions taking values in differentiable manifolds as well as of generalized vector bundle homomorphisms. We study their basic properties, in particular with respect to some new point value concepts for generalize…

FFM generates functions between Gaussian and data distributions.

Generative models for function-valued data in infinite dimensions.

The paper generalizes inequalities on almost Kähler manifolds.

Neural FGP learns portfolio generating functions from data.

The paper classifies singularities of plane congruences and affine distance functions.

Study one-dimensional topological theories with linear generating functions.

Distance function to a finite set is a topological Morse function.

FDPs generalize diffusion models to function spaces, enabling efficient image generation.

New $L$-functions for 3-manifolds connect to Witten invariants and relate to generalized Bernoulli polynomials.

Study shows infoGAN's generalization error bound for two-layer networks.

FunDiff models physical functions using diffusion and autoencoders.

Generative neural network simulates characteristic functions.

New insights into risk aversion for complex decision models.

Causal effect estimation relies on separating the variation in the outcome into parts due to the treatment and due to the confounders. To achieve this separation, practitioners often use external sources of randomness that only influence the treatment called instrumental variables (IVs). We study variables constructed …

We propose fast approximations for the generalized sliced-Wasserstein distance.

New GAN loss functions improve image generation quality and stability.

Sharp bounds for approximating Sobolev functions by ridge functions and networks.

Paper develops efficient RL algorithm for general value function approximation.

Generative model learns functional vector fields for pharmacokinetics.

Generative models learn distributions of continuous functions.

We extend rectified flow to infinite-dimensional Hilbert space.

Proposes a new sparse recovery method using generalized error function.

New neural network models learn symmetric functions of varying input sizes.

We present a novel and comprehensive approach to the study of the parametric Plateau problem for locally strictly convex (LSC) hypersurfaces of prescribed curvature for general convex curvature functions inside general Riemannian manifolds. We prove existence of solutions to the Plateau problem with outer barrier for L…

Estimates generalization gap for overparameterized models using Langevin approximation.

This work extends diffusion models to function space for better generative modeling.

We describe the Williams zeta functions and the twist zeta functions of sub-Lorenz templates generated by renormalizable Lorenz maps, in terms of the corresponding zeta-functions of the sub-Lorenz templates generated by the renormalized map and by the map that determines the renormalization type.

A Morse 2-function is a generic smooth map from a smooth manifold to a surface. In the absence of definite folds (in which case we say that the Morse 2-function is indefinite), these are natural generalizations of broken (Lefschetz) fibrations. We prove existence and uniqueness results for indefinite Morse 2-functions …

SFM generates smooth functional data without exposing real data.

The goal of this paper is to classify pairs of Morse functions in general position modulo the action of different groups.In particular, we obtain the classification of generic pairs of Morse functions, with or without target diffeomorphisms, and that of quotients of Morse functions.We will also present a lemma which gi…

We study the smooth structure of convex functions by generalizing a powerful concept so-called self-concordance introduced by Nesterov and Nemirovskii in the early 1990s to a broader class of convex functions, which we call generalized self-concordant functions. This notion allows us to develop a unified framework for …

We extend the problem of finding Hamiltonian-invariant volume forms on a Poisson manifold to the problem of construction of Hamiltonian-invariant generalized functions. For this we introduce the notion of generalized center of a Poisson algebra, which is the space of generalized Casimir functions. We study as the case …

The vicinal risk minimization (VRM) principle, first proposed by \citet{vapnik1999nature}, is an empirical risk minimization (ERM) variant that replaces Dirac masses with vicinal functions. Although there is strong numerical evidence showing that VRM outperforms ERM if appropriate vicinal functions are chosen, a compre…

A new method uses deep learning to efficiently sample rare transitions for estimating committor functions.

Improved GSPGS estimators reduce bias in noisy function measurements.

Extends Tanimoto kernel to real-valued functions.

Establishes Poincaré's lemma for formal manifolds.

We discuss the nature of structure-preserving maps of varies function algebras. In particular, we identify isomorphisms between special Colombeau algebras on manifolds with invertible manifold-valued generalized functions in the case of smooth parametrization. As a consequence, and to underline the consistency and vali…

Consider the one-parameter generalizations of the logarithmic and exponential functions which are obtained from the integration of non-symmetrical hyperboles. These generalizations coincide to the one obtained in the context of non-extensive thermostatistics. We show that these functions are suitable to describe and un…

The study optimizes bounds for comparing training and population loss.

In this paper, we study monotonicity formulas of eigenvalues and entropies along the rescaled List's extended Ricci flow. We derive some monotonicity formulas of eigenvalues of Laplacian which generalize those of Li in [8] and Cao-Hou-Ling in [3]. Moreover, we also consider monotonicity formulas of $\mathcal{F}_k$-func…