arXiv research

Study on functional inequalities on simple edge spaces.

Simple constructions of semi-discrete and discrete surfaces using Jacobi elliptic functions.

Bayesian model uses simple functions to forecast macroeconomic data.

qEUBO optimizes decision-making with noisy feedback.

Study the space of simple polygons and their moduli.

Study Morse functions on projective plane using Reeb graphs.

Accurate approximations to density functionals have recently been obtained via machine learning (ML). By applying ML to a simple function of one variable without any random sampling, we extract the qualitative dependence of errors on hyperparameters. We find universal features of the behavior in extreme limits, includi…

Learning automatically the best activation function for the task is an active topic in neural network research. At the moment, despite promising results, it is still difficult to determine a method for learning an activation function that is at the same time theoretically simple and easy to implement. Moreover, most of…

Algorithms are increasingly used to aid, or in some cases supplant, human decision-making, particularly for decisions that hinge on predictions. As a result, two additional features in addition to prediction quality have generated interest: (i) to facilitate human interaction and understanding with these algorithms, we…

New algorithm solves complex optimization problems efficiently.

Simple neural networks approximate any continuous function with fixed neurons.

Solves asset allocation for investors with utility functions and limits.

Enhances neural models with simple functions to improve language modeling.

In this work, we develop a simple algorithm for semi-supervised regression. The key idea is to use the top eigenfunctions of integral operator derived from both labeled and unlabeled examples as the basis functions and learn the prediction function by a simple linear regression. We show that under appropriate assumptio…

Cylindrical contact homology computed for links of simple singularities.

Random SNNs are stable and simple, with low-frequency Fourier spectra.

In this note, we observe the behavior of gradient flow and discrete and noisy gradient descent in some simple settings. It is commonly noted that addition of noise to gradient descent can affect the trajectory of gradient descent. Here, we run some computer experiments for gradient descent on some simple functions, and…

A simple formula is derived for the Ricci scalar curvature of any smooth level set ${ψ(x_0,x_1,...,x_n)=C}$ embedded in the Euclidean space $\mathbb R^{n+1}$, in terms of the gradient $\nablaψ$ and the Laplacian $Δψ$. Some applications are given to the geometry of low-dimensional $p$-harmonic functions and high-dime…

We prove that the expectation value of the index function i(x) over a probability space of injective function f on any finite simple graph G=(V,E) is equal to the curvature K(x) at the vertex x. This result complements and links Gauss-Bonnet sum K(x) = chi(G) and Poincare-Hopf sum i(x) = chi(G) which both hold for arbi…

A theorem for debiasing machine learning with finite sample guarantees.

Introduces a Cost function to measure Legendrian knot obstructions.

We derive explicit reconstruction formulas for the attenuated geodesic X-ray transform over functions and, in the case of non-vanishing attenuation, vector fields, on a class of simple Riemannian surfaces with boundary. These formulas partly rely on new explicit approaches to construct continuous right-inverses for bac…

This paper deals with some simple results about spherical functions of type $δ$, namely new integral formulas, new results about behavior at infinity and some facts about the related $C_σ$ functions.

The paper reconfirms a lower bound on rational genus using Heegaard Floer homology.

We show a very simple and general total second variation formula for Perelman's $\mathcal{W}$-functional at arbitrary points in the space of Riemannian metrics. Moreover we perform a study of the properties of the variations of Kähler structures. We deduce a quite simple and general total second variation formula for P…

Characterizes geodesics on spheres with Morse index bounds and inequalities.

A very simple $\mathbb R^3$ realization of the Möbius strip, significantly simpler than the common one, is given. For any, however large width/length ratio of the strip, it is shown that this realization, in contrast with the common one, is the union of a vertical segment and the graph of a simple rational function on …

Paper proves Łojasiewicz inequalities near simple bubble trees on surfaces.

A simple method improves batch active learning without high compute.

A celebrated and deep theorem in the theory of Riemann surfaces states the existence and uniqueness of the Jenkins-Strebel differentials on a Riemann surface under some conditions, but the proof is non-constructive and examples are difficult to find. This paper deals with an example of a simple case, namely Jenkins-Str…

Ensemble techniques are powerful approaches that combine several weak learners to build a stronger one. As a meta-learning framework, ensemble techniques can easily be applied to many machine learning methods. Inspired by ensemble techniques, in this paper we propose an ensemble loss functions applied to a simple regre…

Generic metrics on manifolds yield simple Steklov eigenvalues and Morse boundary functions.

Simple rules ensure gradient descent adapts to local geometry, converging for convex and nonconvex problems.

The purpose of this note is to give a simple description of a (complete) family of functions in involution on certain hermitian symmetric spaces. This family, obtained via bi-hamiltonian approach using the Bruhat Poisson structure, is especially simple for the projective spaces, where the formulas in terms of the momen…

Global inverse function theorem proved easily using Riemannian geometry.

The main aim of this work is to construct several new families of proper biharmonic functions defined on open subsets of the classical compact simple Lie groups $\SU n$, $\SO n$ and $\Sp n$. We work in a geometric setting which connects our study with the theory of submersive harmonic morphisms. We develop a general du…

Inverse function theorem and homotopy description for L-infinity bundles.

A simple model explains inference scaling in neural models.

Study finds simple model-agreement scores perform well in various error estimation scenarios.

Paper optimizes multi-fidelity function with fast learning rates.

While conformal transformations of the plane preserve Laplace's equation, Lorentz-conformal mappings preserve the wave equation. We discover how simple geometric objects, such as quadrilaterals and pairs of crossing curves, are transformed under nonlinear Lorentz-conformal mappings. Squares are transformed into curvili…

In this note, we give a generalization of the inversion formulas of Pestov-Uhlmann for the geodesic ray transform of functions and vector fields on simple 2-dimensional manifolds of constant curvature. The inversion formulas given here hold for 2-dimensional simple manifolds whose curvatures close to a constant.

The paper characterizes graph manifolds using fold maps and embeddability of polyhedra.

Study proper sampling for X-ray transforms on simple surfaces.

We show a quite simple second variation formula for Perelman's $\mathcal{W}$-functional along the modified Kähler-Ricci flow over Fano manifolds.

We demonstrate the usage of explicit form of the Thom class found by Mathai and Quillen for the definition of generating functional of a simple supersymmetric quantum mechanical model.

Improved Frank-Wolfe algorithm for generalized self-concordant functions converges quickly.

The signature function of a knot is a locally constant integer valued function with domain the unit circle. The jumps (i.e., the discontinuities) of the signature function can occur only at the roots of the Alexander polynomial on the unit circle. The latter are important in deforming U(1) representations of knot group…