Related papers: Custom Hypergraph Categories via Generalized Relat…
We present a novel work-in-progress approach to the parsing of hypergraphs generated by context-free hyperedge replacement grammars. This method is based on a new LR parsing technique for positional grammars, which is also under active…
The variety of data is one of the important issues in the era of Big Data. The data are naturally organized in different formats and models, including structured data, semi-structured data, and unstructured data. Prior research has…
Given a causal graph representing the data-generating process shared across different domains/distributions, enforcing sufficient graph-implied conditional independencies can identify domain-general (non-spurious) feature representations.…
We examine the use of classes to formulate several categorical notions. This leads to two proposals: an explicit structure for working with subobjects, and a hierarchy of $k$-classes. We apply the latter to both ordinary and higher…
Traditional treatments of formal logic provide: 1. A syntax for formulas. 2. An inference relation between sets of formulas. 3. A rule for assigning meaning to formulas (semantics) that is sound with respect to the inference relation. First…
Hypergraphs naturally represent group interactions, which are omnipresent in many domains: collaborations of researchers, co-purchases of items, and joint interactions of proteins, to name a few. In this work, we propose tools for answering…
The concept of process is ubiquitous in science, engineering and everyday life. Category theory, and monoidal categories in particular, provide an abstract framework for modelling processes of many kinds. In this paper, we concentrate on…
We study question answering over a dynamic textual environment. Although neural network models achieve impressive accuracy via learning from input-output examples, they rarely leverage various types of knowledge and are generally not…
Causal reasoning is a cornerstone of how humans interpret the world. To model and reason about causality, causal graphs offer a concise yet effective solution. Given the impressive advancements in language models, a crucial question arises:…
Causal models capture cause-effect relations both qualitatively - via the graphical causal structure - and quantitatively - via the model parameters. They offer a powerful framework for analyzing and constructing processes. Here, we…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
Many real world systems need to operate on heterogeneous information networks that consist of numerous interacting components of different types. Examples include systems that perform data analysis on biological information networks; social…
Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…
Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
Quantum supermaps provide a framework in which higher order quantum processes can act on lower order quantum processes. In doing so, they enable the definition and analysis of new quantum protocols and causal structures. Recently, key…
Probabilistic topic modeling is a popular and powerful family of tools for uncovering thematic structure in large sets of unstructured text documents. While much attention has been directed towards the modeling algorithms and their various…
Graphs have a superior ability to represent relational data, like chemical compounds, proteins, and social networks. Hence, graph-level learning, which takes a set of graphs as input, has been applied to many tasks including comparison,…
Over the last few years, machine learning over graph structures has manifested a significant enhancement in text mining applications such as event detection, opinion mining, and news recommendation. One of the primary challenges in this…
Graph theory provides a primary tool for analyzing and designing computer communication networks. In the past few decades, Graph theory has been used to study various types of networks, including the Internet, wide Area Networks, Local Area…