Related papers: Decomposition of zero-dimensional persistence modu…
A standard way of approximating or discretizing a metric space is by taking its Rips complexes. These approximations for all parameters are often bound together into a filtration, to which we apply the fundamental group or the first…
A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a…
Consider a system F of n polynomial equations in n unknowns, over an algebraically closed field of arbitrary characteristic. We present a fast method to find a point in every irreducible component of the zero set Z of F. Our techniques…
We propose a modular framework for multi-relational learning via tensor decomposition. In our learning setting, the training data contains multiple types of relationships among a set of objects, which we represent by a sparse three-mode…
The goal of Feature Selection - comprising filter, wrapper, and embedded approaches - is to find the optimal feature subset for designated downstream tasks. Nevertheless, current feature selection methods are limited by: 1) the selection…
Many computer vision systems require low-cost segmentation algorithms based on deep learning, either because of the enormous size of input images or limited computational budget. Common solutions uniformly downsample the input images to…
This paper introduces a novel $k$-cell decomposition method for pursuit-evasion problems in polygonal environments, where a searcher is equipped with a $k$-modem: a device capable of seeing through up to $k$ walls. The proposed…
In this paper (as in [Ken15]), we consider an effective version of the characterization of separable metric spaces as zero-dimensional iff every nonempty closed subset is a retract of the space (actually, it is a relative result for closed…
In this paper, the problem of the minimal description of the structure of a vector function f(x) over an $N$-dimensional interval is studied. Methods adaptively subdividing the original interval in smaller subintervals and evaluating f(x)…
We determine the decomposition numbers of the partition algebra when the characteristic of the ground field is zero or larger than the degree of the partition algebra. This will allow us to determine for which exact values of the parameter…
This paper deals with the estimation of the modes of an univariate mixture when the number of components is known and when the component density are well separated. We propose an algorithm based on the minimization of the "kp" criterion we…
Several topological and analytical notions of continuity and fading memory for causal and time-invariant filters are introduced, and the relations between them are analyzed. A significant generalization of the convolution theorem that…
Parts represent a basic unit of geometric and semantic similarity across different objects. We argue that part knowledge should be composable beyond the observed object classes. Towards this, we present 3D Compositional Zero-shot Learning…
Many neural networks deployed in the real world scenarios are trained using cross entropy based loss functions. From the optimization perspective, it is known that the behavior of first order methods such as gradient descent crucially…
The modular subset sum problem consists of deciding, given a modulus $m$, a multiset $S$ of $n$ integers in $0..m-1$, and a target integer $t$, whether there exists a subset of $S$ with elements summing to $t \mod m $, and to report such a…
Many vision-related tasks benefit from reasoning over multiple modalities to leverage complementary views of data in an attempt to learn robust embedding spaces. Most deep learning-based methods rely on a late fusion technique whereby…
Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…
We demonstrate that the integration of the recently developed dynamic mode decomposition (DMD) with a multi-resolution analysis allows for a decomposition method capable of robustly separating complex systems into a hierarchy of…
The set of all permutations, ordered by pattern containment, forms a poset. This paper presents the first explicit major results on the topology of intervals in this poset. We show that almost all (open) intervals in this poset have a…
We define a class of invariants, which we call homological invariants, for persistence modules over a finite poset. Informally, a homological invariant is one that respects some homological data and takes values in the free abelian group…