Related papers: CAT-generation of ideals
In general, representations of interval orders may use an arbitrary set of interval lengths. We can define subclasses of interval orders by restricting the allowable lengths of intervals. Motivated by a recent paper of Keller, Trenk, and…
Building world models that accurately and comprehensively represent the real world is the utmost aspiration for conditional image generative models as it would enable their use as world simulators. For these models to be successful world…
Motivated by the fact that as the number of generators of an ideal grows so does the complexity of calculating relations among the generators, this paper identifies collections of monomial ideals with a growing number of generators which…
While GANs can produce photo-realistic images in ideal conditions for certain domains, the generation of full-body human images remains difficult due to the diversity of identities, hairstyles, clothing, and the variance in pose. Instead of…
Suppose that $X$ is an integral scheme (quasi-)projective over a complete local ring of mixed characteristic. Using ideas of Takamatsu-Yoshikawa and Bhatt-Ma-et. al, we define a notion of a $+$-test ideal on $X$, including for divisors and…
We investigate resolutions of letterplace ideals of posets. We develop topological results to compute their multigraded Betti numbers, and to give structural results on these Betti numbers. If the poset is a union of no more than $c$…
Current approaches to pose generation rely heavily on intermediate representations, either through two-stage pipelines with quantization or autoregressive models that accumulate errors during inference. This fundamental limitation leads to…
The interval poset of a permutation is the set of intervals of a permutation, ordered with respect to inclusion. It has been introduced and studied recently in [B. Tenner, arXiv:2007.06142]. We study this poset from the perspective of the…
This paper presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative…
Answering questions that involve multi-step reasoning requires decomposing them and using the answers of intermediate steps to reach the final answer. However, state-of-the-art models in grounded question answering often do not explicitly…
We consider the polynomial ring in finitely many variables over an algebraically closed field of positive characteristic, and initiate the systematic study of ideals preserved by the action of the general linear group by changes of…
In this paper, we study a parallel version of Galton-Watson processes for the random generation of tree-shaped structures. Random trees are useful in many situations (testing, binary search, simulation of physics phenomena,...) as attests…
Pose diversity is an inherent representative characteristic of 2D images. Due to the 3D to 2D projection mechanism, there is evident content discrepancy among distinct pose images. This is the main obstacle bothering pose transformation…
Articulated objects are central to interactive 3D applications, including embodied AI, robotics, and VR/AR, where functional part decomposition and kinematic motion are essential. Yet producing high-fidelity articulated assets remains…
We study the problem of multi-person pose estimation in natural images. A pose estimate describes the spatial position and identity (head, foot, knee, etc.) of every non-occluded body part of a person. Pose estimation is difficult due to…
Given a symmetric monoidal category $C$ with product $\sqcup$, where the neutral element for the product is an initial object, we consider the poset of $\sqcup$-complemented subobjects of a given object $X$. When this poset has finite…
In this paper we present a CAT generation algorithm for Dyck paths with a fixed length n. It is the formalization of a method for the exhaustive generation of this kind of paths which can be described by means of two equivalent strategies.…
We show that the apolar ideal to the determinant of a generic symmetric matrix is generated in degree two, and the apolar ideal to the permanent of a generic symmetric matrix is generated in degrees two and three. In each case we specify…
While category-level 9DoF object pose estimation has emerged recently, previous correspondence-based or direct regression methods are both limited in accuracy due to the huge intra-category variances in object shape and color, etc.…
The standard notion of poset probability of a finite poset P involves calculating, for incomparable $\alpha$, $\beta$ in P, the number of linear extensions of P for which $\alpha$ precedes $\beta$. The fraction of those linear extensions…