Related papers: An Instruction Sequence Semigroup with Involutive …
In this paper we explore the task of modeling semi-structured object sequences; in particular, we focus our attention on the problem of developing a structure-aware input representation for such sequences. Examples of such data include user…
Entity alignment is to find identical entities in different knowledge graphs. Although embedding-based entity alignment has recently achieved remarkable progress, training data insufficiency remains a critical challenge. Conventional…
Learning good representations without supervision is still an open issue in machine learning, and is particularly challenging for speech signals, which are often characterized by long sequences with a complex hierarchical structure. Some…
Machine learning on sets towards sequential output is an important and ubiquitous task, with applications ranging from language modeling and meta-learning to multi-agent strategy games and power grid optimization. Combining elements of…
Semi-supervised learning algorithms typically construct a weighted graph of data points to represent a manifold. However, an explicit graph representation is problematic for neural networks operating in the online setting. Here, we propose…
Let L^1(G) and M(G) be group algebra and measure algebra of a locally compact group G, respectively and D:L^1(G)-->M(G) be a continuous linear map. We consider D behaving like derivation or anti-derivation at orthogonal elements for several…
We define several "standard" subgroups of the automorphism group Aut(G) of a partially commutative (right-angled Artin) group and use these standard subgroups to describe decompositions of Aut(G). If C is the commutation graph of G, we show…
$C^*$-algebra-valued kernels could pave the way for the next generation of kernel machines. To further our fundamental understanding of learning with $C^*$-algebraic kernels, we propose a new class of positive definite kernels based on the…
We study isometric representations of product systems of correspondences over the semigroup $\mathbb{N}^k$ which are minimal dilations of finite dimensional, fully coisometric representations. We show the existence of a unique minimal…
Pretraining has been widely explored to augment the adaptability of graph learning models to transfer knowledge from large datasets to a downstream task, such as link prediction or classification. However, the gap between training…
Standard architectures used in instruction following often struggle on novel compositions of subgoals (e.g. navigating to landmarks or picking up objects) observed during training. We propose a modular architecture for following natural…
This paper contributes to the mathematical foundations of logic programming by introducing and studying the sequential composition of answer set programs. On the semantic side, we show that the immediate consequence operator of a program…
We demonstrate that the notions of derivative representation of a Lie algebra on a vector bundle, of semi-linear representations of a Lie group on a vector bundle, and related concepts, may be understood in terms of representations of Lie…
The paper is an overview of recent results on algebraic structures (semigroups, groupoids, algebras, inverse semigroups, and groups) associated with objects with a rich set of partial symmetries. We discuss etale groupoids and inverse…
An assembly is a large population of neurons whose synchronous firing is hypothesized to represent a memory, concept, word, and other cognitive categories. Assemblies are believed to provide a bridge between high-level cognitive phenomena…
This course introduces the use of semigroup methods in the solution of linear and nonlinear (quasi-linear) hyperbolic partial differential equations, with particular application to wave equations and Hermitian hyperbolic systems. Throughout…
In this paper we describe the mathematical foundations of a new approach to semi-supervised Machine Learning. Using techniques of Symbolic Computation and Computer Algebra, we apply the concept of persistent homology to obtain a new…
In this paper, we investigate *-homomorphisms between C*-algebras associated to \'etale groupoids. First, we prove that such a *-homomorphism can be described by closed invariant subsets, groupoid homomorphisms and cocycles under some…
A Hom-group G is a nonassociative version of a group where associativity, invertibility, and unitality are twisted by a map \alpha: G\longrightarrow G. Introducing the Hom-group algebra KG, we observe that Hom-groups are providing examples…
The notion of associativity (which differs from the straightforward generalization of the usual associativity given by the move of parentheses in the relevant expression) for operations of high arity is introduced. It is proved that the…