Related papers: A Non-Archimedean Approach to Stratifications

Manifold learning flows are a class of generative modelling techniques that assume a low-dimensional manifold description of the data. The embedding of such a manifold into the high-dimensional space of the data is achieved via learnable…

This paper describes the construction of a canonical compactification of the space of trajectories and of the unstable/stable sets of a generic gradient like vector field on a closed manifold as well as a canonical structure of a smooth…

We introduce a quantization of the graded algebra of functions on the canonical cone of an algebraic curve C, based on the theory of formal pseudodifferential operators. When C is a complex curve with Poincar\'e uniformization, we propose…

Learning to quantify (a.k.a.\ quantification) is a task concerned with training unbiased estimators of class prevalence via supervised learning. This task originated with the observation that "Classify and Count" (CC), the trivial method of…

Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately, current approaches are only available for the most basic geometries and fall short when the underlying…

We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…

Anomaly detection is a challenging task that frequently arises in practically all areas of industry and science, from fraud detection and data quality monitoring to finding rare cases of diseases and searching for new physics. Most of the…

The consideration of nonstandard models of the real numbers and the definition of a qualitative ordering on those models provides a generalization of the principle of maximization of expected utility. It enables the decider to assign…

We derive a canonical form for smooth vector fields on $\Re^{n+1}$. We use this to demonstrate the local multi-Hamiltonian nature of the corresponding flows. Associated with the canonical form is an inhomogenious linear PDE whose solutions…

We give an introduction to discrete functional analysis techniques for stationary and transient diffusion equations. We show how these techniques are used to establish the convergence of various numerical schemes without assuming…

We consider the estimation of regression models on strata defined using a categorical covariate, in order to identify interactions between this categorical covariate and the other predictors. A basic approach requires the choice of a…

We propose a new approach to the theory of normal forms for Hamiltonian systems near a non-resonant elliptic singular point. We consider the space of all Hamiltonian functions with such an equilibrium position at the origin and construct a…

We introduce a theory for encoding and manipulating algebraic data on categories via $\textit{concentration structures}$, which are equivalence relations on morphisms that satisfy certain axioms. For any category with a concentration…

We present a hierarchical convolutional document model with an architecture designed to support introspection of the document structure. Using this model, we show how to use visualisation techniques from the computer vision literature to…

A hierarchy of type universes is a rudimentary ingredient in the type theories of many proof assistants to prevent the logical inconsistency resulting from combining dependent functions and the type-in-type rule. In this work, we argue that…

The main purpose of this paper is to lay the foundations of a general theory which encompasses the features of the classical Hough transform and extend them to general algebraic objects such as affine schemes. The main motivation comes from…

Given a planar curve defined by means of a real rational parametrization, we prove that the affine values of the parameter generating the real singularities of the offset are real roots of a univariate polynomial that can be derived from…

The theory uses methods and language of linear algebra to study nonlinear spaces. These techniques can be used particularly to describe analytic geometry of non-linear elliptic, hyperbolic, De Sitter and Anti de Sitter spaces. The main…

This notebook tutorial demonstrates a method for sampling Boltzmann distributions of lattice field theories using a class of machine learning models known as normalizing flows. The ideas and approaches proposed in arXiv:1904.12072,…

Although it is relatively easy to apply, the gradient method often displays a disappointingly slow rate of convergence. Its convergence is specially based on the structure of the matrix of the algebraic linear system, and on the choice of…