相关论文: Abstract homotopical methods for theoretical compu…

We present a light formalism for proofs that encodes their inferential structure, along with a system that transforms these representations into flow-chart diagrams. Such diagrams should improve the comprehensibility of proofs. We discuss…

This paper presents a novel connection between homotopical algebra and mathematical logic. It is shown that a form of intensional type theory is valid in any Quillen model category, generalizing the Hofmann-Streicher groupoid model of…

Powerful detectors at modern experimental facilities routinely collect data at multiple GB/s. Online analysis methods are needed to enable the collection of only interesting subsets of such massive data streams, such as by explicitly…

Mainstream flow matching methods typically focus on learning the local velocity field, which inherently requires multiple integration steps during generation. In contrast, Mean Velocity Flow models establish a relationship between the local…

We survey the theory and applications of Goodwillie's calculus of homotopy functors and related topics.

Counterfactual explanation is a form of interpretable machine learning that generates perturbations on a sample to achieve the desired outcome. The generated samples can act as instructions to guide end users on how to observe the desired…

The strict globular $\omega$-categories formalize the execution paths of a parallel automaton and the homotopies between them. One associates to such (and any) $\omega$-category $\C$ three homology theories. The first one is called the…

This article surveys recent progress of results in topology and dynamics based on techniques of closed one-forms. Our approach allows us to draw conclusions about properties of flows by studying homotopical and cohomological features of…

In this note, we discuss the mean curvature flow of graphs of maps between Riemannian manifolds. Special emphasis will be placed on estimates of the flow as a non-linear parabolic system of differential equations. Several global existence…

In this paper, we develop a drift homotopy implicit particle filter method. The methodology of our approach is to adopt the concept of drift homotopy in the resampling procedure of the particle filter method for solving the nonlinear…

We prove that any globular subdivision of multipointed $d$-spaces gives rise to a dihomotopy equivalence between the associated flows. As a straightforward application, the flows associated to two multipointed $d$-spaces related by a finite…

Let $D$ be a large category which is cocomplete. We construct a model structure (in the sense of Quillen) on the category of small functors from $D$ to simplicial sets. As an application we construct homotopy localization functors on the…

"Concurrence topology" (Ellis and Klein \emph{Homology, Homotopy, and Applications,} \textbf{16}) is a TDA method for binary data. The idea is to construct a filtration consisting of Dowker complexes then compute persistent homology.…

We use a version of the Trotter-Kato approximation theorem for strongly continuous semigroups in order to study flows on growing networks. For that reason we use the abstract notion of direct limits in the sense of category theory.

Continuous diffusion and flow matching models could represent a powerful alternative to autoregressive approaches for language modelling (LM), as they unlock a host of advantages currently reserved for continuous modalities, including…

Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent…

Flows are a topological model of concurrency which enables to encode the notion of refinement of observation and to understand the homological properties of branchings and mergings of execution paths. Roughly speaking, they are Grandis'…

Based on the well-established theory of discrete conjugate nets in discrete differential geometry, we propose and examine discrete analogues of important objects and notions in the theory of semi-Hamiltonian systems of hydrodynamic type. In…

Modern networks carry increasingly diverse and encrypted traffic types that demand classification techniques beyond traditional port-based and payload-based methods. This tutorial provides a practical, end-to-end guide to building…

These are lecture notes for a Master 2 course on rough differential equations driven by weak geometric Holder p-rough paths, for any p>2. They provide a short, self-contained and pedagogical account of the theory, with an emphasis on flows.…