Related papers: CAT-generation of ideals
Generative models can now produce photorealistic synthetic data which is virtually indistinguishable from the real data used to train it. This is a significant evolution over previous models which could produce reasonable facsimiles of the…
In 2012, N. Williams and the second author showed that on order ideals of ranked partially ordered sets (posets), rowmotion is conjugate to (and thus has the same orbit structure as) a different toggle group action, which in special cases…
We introduce the Iterated Global model as a deterministic graph process that simulates several properties of complex networks. In this model, for every set $S$ of nodes of a prescribed cardinality, we add a new node that is adjacent to…
Previously, Erd\H{o}s, Kierstead and Trotter investigated the dimension of random height~$2$ partially ordered sets. Their research was motivated primarily by two goals: (1)~analyzing the relative tightness of the F\"{u}redi-Kahn upper…
Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if…
A poset can be regarded as a category in which there is at most one morphism between objects, and such that at most one of Hom(c,c') and Hom(c',c) is nonempty for c not equal to c'. If we keep in place the latter axiom but allow for more…
We propose a novel generative approach for 3D human pose estimation. 3D human pose estimation poses several key challenges due to the complex geometry of the human body, self-occluding joints, and the requirement for large-scale real-world…
In machine learning and other fields, suggesting a good solution to a problem is usually a harder task than evaluating the quality of such a solution. This asymmetry is the basis for a large number of selection oriented methods that use a…
Generative adversarial networks (GANs) can now generate photo-realistic images. However, how to best control the image content remains an open challenge. We introduce LatentKeypointGAN, a two-stage GAN internally conditioned on a set of…
A probabilistic representation for initial value semilinear parabolic problems based on generalized random trees has been derived. Two different strategies have been proposed, both requiring generating suitable random trees combined with a…
Generative Adversarial Networks (GANs) have achieved remarkable results in the task of generating realistic natural images. In most successful applications, GAN models share two common aspects: solving a challenging saddle point…
'Capsule' models try to explicitly represent the poses of objects, enforcing a linear relationship between an object's pose and that of its constituent parts. This modelling assumption should lead to robustness to viewpoint changes since…
A novel approach to unstructured quadrilateral mesh generation for planar domains is presented. Away from irregular vertices, the resulting meshes have the properties of nearly conformal grids. The technique is based on a theoretical…
Let $L\subset \mathbb{Z}^n$ be a lattice and $I_L=\langle x^{\bf u}-x^{\bf v}:\ {\bf u}-{\bf v}\in L\rangle$ be the corresponding lattice ideal in $\Bbbk[x_1,\ldots, x_n]$, where $\Bbbk$ is a field. In this paper we describe minimal…
Alternating sign matrices (ASMs) are square matrices with entries 0, 1, or -1 whose rows and columns sum to 1 and whose nonzero entries alternate in sign. We present a unifying perspective on ASMs and other combinatorial objects by studying…
We consider a category-level perception problem, where one is given 2D or 3D sensor data picturing an object of a given category (e.g., a car), and has to reconstruct the 3D pose and shape of the object despite intra-class variability…
The main goal of this paper is to provide an algorithm for the random sampling of Butcher trees and the probabilistic numerical solution of ordinary differential equations (ODEs). This approach complements and simplifies a recent approach…
In this paper, we propose a novel approach to solve the pose guided person image generation task. We assume that the relation between pose and appearance information can be described by a simple matrix operation in hidden space. Based on…
We propose an approach to generate images of people given a desired appearance and pose. Disentangled representations of pose and appearance are necessary to handle the compound variability in the resulting generated images. Hence, we…
Generative models produce realistic objects in many domains, including text, image, video, and audio synthesis. Most popular models---Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs)---usually employ a standard…