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String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric…
Graph rewriting is a popular tool for the optimisation and modification of graph expressions in domains such as compilers, machine learning and quantum computing. The underlying data structures are often port graphs - graphs with labels at…
Graph of Thoughts (GoT), a generalized form of recent prompting paradigms for large language models (LLMs), has been shown to be useful for elaborate problem solving. By executing a graph of operations, thoughts of the LLM are structured as…
A cyclic permutation $\pi:\{1, \dots, N\}\to \{1, \dots, N\}$ has a \emph{block structure} if there is a partition of $\{1, \dots, N\}$ into $k\notin\{1,N\}$ segments (\emph{blocks}) permuted by $\pi$; call $k$ the \emph{period} of this…
Bigraphs are a versatile modelling formalism that allows easy expression of placement and connectivity relations in a graphical format. System evolution is user defined as a set of rewrite rules. This paper presents a practical, yet…
Human-like planning skills and dexterous manipulation have long posed challenges in the fields of robotics and artificial intelligence (AI). The task of reinterpreting calligraphy presents a formidable challenge, as it involves the…
The technique of \emph{equality saturation}, which equips graphs with an equivalence relation, has proven effective for program optimisation. We give a categorical semantics to these structures, called \emph{e-graphs}, in terms of Cartesian…
We study non-terminating graph rewriting models, whose local rules are applied non-deterministically -- and yet enjoy a strong form of determinism, namely space-time determinism. Of course in the case of terminating computation it is…
A mathematical theory is presented for the representation of knowledge in the form of a directed acyclic hierarchy of objects in a category where all paths between any given pair of objects are required to be equal. The conditions under…
In this article, we revise Conway's Law from a mathematical point of view. By introducing a task graph, we first rigorously state Conway's Law based on the homomorphisms in graph theory for the software system and the organizations that…
Legal retrieval is a widely studied area in Information Retrieval (IR) and a key task in this domain is retrieving relevant cases based on a given query case, often done by applying language models as encoders to model case similarity.…
Any permutation in the finite symmetric group can be written as a product of simple transpositions $s_i = (i~i+1)$. For a fixed permutation $\sigma \in \mathfrak{S}_n$ the products of minimal length are called reduced decompositions or…
Representation learning on text-attributed graphs (TAGs) integrates structural connectivity with rich textual semantics, enabling applications in diverse domains. Current methods largely rely on contrastive learning to maximize cross-modal…
Combining ideas of Pham, Sah, Sawhney, and Simkin on spread perfect matchings in super-regular bipartite graphs with an algorithmic blow-up lemma, we prove a spread version of the blow-up lemma. Intuitively, this means that there exists a…
Recently, there has been an increasing need to develop agents capable of solving multiple tasks within the same environment, especially when these tasks are naturally associated with language. In this work, we propose a novel approach that…
We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this…
The classical algebra $\Lambda$ of symmetric functions has a remarkable deformation $\Lambda^*$, which we call the algebra of shifted symmetric functions. In the latter algebra, there is a distinguished basis formed by shifted Schur…
Representing the temporal evolution of legal norms is a critical challenge for automated processing. While foundational frameworks exist, they lack a formal pattern for granular, component-level versioning, hindering the deterministic…
Conditional term rewriting is an intuitive yet complex extension of term rewriting. In order to benefit from the simpler framework of unconditional rewriting, transformations have been defined to eliminate the conditions of conditional term…
There has been an increased interest in applying machine learning techniques on relational structured-data based on an observed graph. Often, this graph is not fully representative of the true relationship amongst nodes. In these settings,…