Related papers: Gradient Vector Fields of Discrete Morse Functions…

We present a framework enabling variational data assimilation for gradient flows in general metric spaces, based on the minimizing movement (or Jordan-Kinderlehrer-Otto) approximation scheme. After discussing stability properties in the…

Estimates of image gradients play a ubiquitous role in image segmentation and classification problems since gradients directly relate to the boundaries or the edges of a scene. This paper proposes an unified approach to gradient estimation…

The inference of minimum spanning arborescences within a set of objects is a general problem which translates into numerous application-specific unsupervised learning tasks. We introduce a unified and generic structure called edit…

Diffusion models are commonly interpreted as learning the score function, i.e., the gradient of the log-density of noisy data. However, this assumption implies that the target of learning is a conservative vector field, which is not…

Examples of Morse functions with integrable gradient flows on some classical Riemannian manifolds are considered. In particular, we show that a generic height function on the symmetric embeddings of classical Lie groups and certain…

Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function.…

Using the ordered analogue of Farley-Sabalka's discrete gradient field on the configuration space of a graph, we unravel a levelwise behavior of the generators of the pure braid group on a tree. This allows us to generalize Farber's…

We present a simple direct discretization for functionals used in the variational mesh generation and adaptation. Meshing functionals are discretized on simplicial meshes and the Jacobian matrix of the continuous coordinate transformation…

We propose a novel study of the stochastic proximal gradient method for minimizing the sum of two convex functions, one of which is smooth. Under suitable assumptions and without requiring any boundedness or control of the variance of the…

For a Poisson manifold endowed with a pseudo-Riemannian metric, we investigate degeneracies arising when the metric is restricted to symplectic leaves. Central to this work is the generalized double bracket (GDB) vector field-a geometric…

Parking functions are well researched and interesting results are found in the listed references and more. Some introductory results stemming from application to degree sequences of simple connected graphs are provided in this paper.…

Variational inference in Bayesian deep learning often involves computing the gradient of an expectation that lacks a closed-form solution. In these cases, pathwise and score-function gradient estimators are the most common approaches. The…

We study perfect discrete Morse functions on closed oriented n-dimensional manifolds. We show how to compose such functions on connected sums of closed oriented manifolds and how to decompose on connected sums of closed oriented surfaces.

Degree ssortativity is the tendency for nodes of high degree (resp.low degree) in a graph to be connected to high degree nodes (resp. to low degree ones). It is sually quantified by the Pearson correlation coefficient of the degree-degree…

Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…

Computing explicitly the {\epsilon}-subdifferential of a proper function amounts to computing the level set of a convex function namely the conjugate minus a linear function. The resulting theoretical algorithm is applied to the the class…

We investigate the homology of cosheaves over finite simplicial complexes. After constructing the Mayer-Vietoris short exact sequence for this homology theory, we apply discrete Morse theory to this setting, defining the associated Morse…

The objective of this note is to provide an interpretation of the discrete version of Morse inequalities, following Witten's approach via supersymmetric quantum mechanics, adapted to finite graphs, as a particular instance of Morse-Witten…

A stratified space is a kind of topological space together with a partition into smooth manifolds. These kinds of spaces naturally arise in the study of singular algebraic varieties, symplectic reduction, and differentiable stacks. In this…

A variety of minimal degree is one of the basic objects in projective algebraic geometry and has been classified and characterized in many aspects. On the other hand, there are also minimal objects in the category of higher secant…