Related papers: Iterating Non-Aggregative Structure Compositions
We develop a framework for applying treewidth-based dynamic programming on graphs with "hybrid structure", i.e., with parts that may not have small treewidth but instead possess other structural properties. Informally, this is achieved by…
A non-commutative, planar, Hopf algebra of rooted trees was proposed in L. Foissy, Bull. Sci. Math. 126 (2002) 193-239. In this paper we propose such a non-commutative Hopf algebra for graphs. In order to define a non-commutative product we…
The mechanisms of comprehension during language processing remains an open question. Classically, building the meaning of a linguistic utterance is said to be incremental, step-by-step, based on a compositional process. However, many…
We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
Aggregate computation in relational databases has long been done using the standard unary aggregation and binary join operators. These implement the classical model of computing joins between relations two at a time, materializing the…
In tasks like semantic parsing, instruction following, and question answering, standard deep networks fail to generalize compositionally from small datasets. Many existing approaches overcome this limitation with model architectures that…
We study non-autonomous conformal iterated function systems, with finite or countably infinite alphabet alike. These differ from the usual (autonomous) iterated function systems in that the contractions applied at each step in time are…
Additive composition (Foltz et al, 1998; Landauer and Dumais, 1997; Mitchell and Lapata, 2010) is a widely used method for computing meanings of phrases, which takes the average of vector representations of the constituent words. In this…
A commutative but not cocommutative graded Hopf algebra $\Hn$, based on ordered rooted trees, is studied. This Hopf algebra generalizes the Hopf algebraic structure of unordered rooted trees $\Hc$, developed by Butcher in his study of…
Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution…
We investigate the problem of multiplex graph embedding, that is, graphs in which nodes interact through multiple types of relations (dimensions). In recent years, several methods have been developed to address this problem. However, the…
A braided Frobenius algebra is a Frobenius algebra with braiding that commutes with the operations, that are related to diagrams of compact surfaces with boundary expressed as ribbon graphs. A heap is a ternary operation exemplified by a…
Taking a Feynman categorical perspective, several key aspects of the geometry of surfaces are deduced from combinatorial constructions with graphs. This provides a direct route from combinatorics of graphs to string topology operations via…
Humans understand new combinations of words encountered if they are combinations of words recognized from different contexts, an ability called Compositional Generalization. The COGS benchmark (Kim and Linzen, 2020) arXiv:2010.05465 reports…
Algorithms for convex feasibility find or approximate a point in the intersection of given closed convex sets. Typically there are only finitely many convex sets, but the case of infinitely many convex sets also has some applications. In…
Combinatorial Hopf algebras of trees exemplify the connections between operads and bialgebras. Painted trees were introduced recently as examples of how graded Hopf operads can bequeath Hopf structures upon compositions of coalgebras. We…
A foundational theory of compositional categorical rewriting theory is presented, based on a collection of fibration-like properties that collectively induce and intrinsically structure the large collection of lemmata used in the proofs of…
Recent years have witnessed the rise of compositional semantics as a foundation for formal verification of complex systems. In particular, interaction trees have emerged as a popular denotational semantics. Interaction trees achieve…
Regular word grammars are restricted context-free grammars that define all the recognizable languages of words. This paper generalizes regular grammars from words to certain classes of graphs, by defining regular grammars for unordered…