Related papers: Iterating Non-Aggregative Structure Compositions
We develop a compositional framework for formal synthesis of hybrid systems using the language of category theory. More specifically, we provide mutually compatible tools for hierarchical, sequential, and independent parallel composition.…
Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…
We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…
We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…
The compositionality degree of multiword expressions indicates to what extent the meaning of a phrase can be derived from the meaning of its constituents and their grammatical relations. Prediction of (non)-compositionality is a task that…
In this extended abstract, we present a simple approach to convergence on term graphs that allows us to unify term graph rewriting and infinitary term rewriting. This approach is based on a partial order and a metric on term graphs. These…
We use axioms of abstract ternary relations to define the notion of a free amalgamation theory. These form a subclass of first-order theories, without the strict order property, encompassing many prominent examples of countable structures…
We introduce a new algebraic structure for multi-dimensional compositional embeddings, built on directional non-commutative monoidal operators. The core contribution of this work is this novel framework, which exhibits appealing theoretical…
Compositionality is a key aspect of human intelligence, essential for reasoning and generalization. While transformer-based models have become the de facto standard for many language modeling tasks, little is known about how they represent…
In the analysis of large/big data sets, aggregation (replacing values of a variable over a group by a single value) is a standard way of reducing the size (complexity) of the data. Data analysis programs provide different aggregation…
Graph pattern matching is a fundamental operation for the analysis and exploration ofdata graphs. In thispaper, we presenta novel approachfor efficiently finding homomorphic matches for hybrid graph patterns, where each pattern edge may be…
Phylogenetic networks are a generalization of phylogenetic trees that are used to represent non-tree-like evolutionary histories that arise in organisms such as plants and bacteria, or uncertainty in evolutionary histories. An…
World-set algebra is a variable-free query language for uncertain databases. It constitutes the core of the query language implemented in MayBMS, an uncertain database system. This paper shows that world-set algebra captures exactly…
A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…
A few steps are made towards representation theory of embeddability among uncountable graphs. A monotone class of graphs is defined by forbidding countable subgraphs, related to the graph's end-structure. Using a combinatorial theorem of…
We introduce a framework for constructing fractal trees via analytic generator fields, replacing discrete affine transformations and symbolic rewriting rules by the integration of smooth vector fields in an internal state space. In this…
Let $G$ be a group which admits the structure of an iterated semidirect product of finitely generated free groups. We construct a finite, free resolution of the integers over the group ring of $G$. This resolution is used to define…
We describe a basic correspondence between linear algebraic structures within vector embeddings in artificial neural networks and conditional independence constraints on the probability distributions modeled by these networks. Our framework…
We describe the E-infinity algebra structure on the complex of singular cochains of a topological space, in the context of sheaf theory. As a first application, for any algebraic variety we define a weight filtration compatible with its…
It is folklore that tree-width is monotone under taking subgraphs (i.e. injective graph homomorphisms) and contractions (certain kinds of surjective graph homomorphisms). However, although tree-width is obviously not monotone under any…