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We introduce regular languages of morphisms in free monoidal categories, with their associated grammars and automata. These subsume the classical theory of regular languages of words and trees, but also open up a much wider class of…
A connected component labeling algorithm is developed for implicitly-defined domains specified by multivariate polynomials. The algorithm operates by recursively subdividing the constraint domain into hyperrectangular subcells until the…
We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidth, graph decomposition width, tree independence number,…
With the increased interest in machine learning, and deep learning in particular, the use of automatic differentiation has become more wide-spread in computation. There have been two recent developments to provide the theoretical support…
It is well-known that combinatorial circuits are modeled mathematically by string diagrams in a monoidal category. Given a gate set $\Sigma$, the circuits over $\Sigma$ can be thought of as string diagrams in the free monoidal category…
We show how to define forward- and reverse-mode automatic differentiation source-code transformations or on a standard higher-order functional language. The transformations generate purely functional code, and they are principled in the…
We address the novel structures arising in quantum and string integrable theories, as well as construct methods to obtain them and provide further analysis. Specifically, we implement the automorphic symmetries on periodic lattice systems…
This paper introduces the concept of distorted monoidal categories, a generalization of monoidal and braided monoidal categories that supports non-reversible and direction-sensitive tensor structures. Unlike the classical setting, where the…
Anomalous sound detection (ASD) encounters difficulties with domain shift, where the sounds of machines in target domains differ significantly from those in source domains due to varying operating conditions. Existing methods typically…
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…
We provide a new approach to categorical graph and hypergraph theory by using categorical syntax and semantics. For each monoid $M$ and action on a set $X$, there is an associated presheaf topos of $(X,M)$-graphs where each object can be…
Self-supervised learning methods have achieved promising performance for anomalous sound detection (ASD) under domain shift, where the type of domain shift is considered in feature learning by incorporating section IDs. However, the…
A string diagram is a two-dimensional graphical representation that can be described as a one-dimensional term generated from a set of primitives using sequential and parallel compositions. Since different syntactic terms may represent the…
Hierarchical text classification, which aims to classify text documents into a given hierarchy, is an important task in many real-world applications. Recently, deep neural models are gaining increasing popularity for text classification due…
Music auto-tagging is often handled in a similar manner to image classification by regarding the 2D audio spectrogram as image data. However, music auto-tagging is distinguished from image classification in that the tags are highly diverse…
The ability of deep neural networks to learn hierarchical features is widely regarded as a key mechanism underlying their success in high-dimensional learning. Existing theory partially supports this view by establishing approximation rates…
Equality saturation, a technique for program optimisation and reasoning, has gained attention due to the resurgence of equality graphs (e-graphs). E-graphs represent equivalence classes of terms under rewrite rules, enabling simultaneous…
We present a technique for applying (forward and) reverse-mode automatic differentiation (AD) on a non-recursive second-order functional array language that supports nested parallelism and is primarily aimed at efficient GPU execution. The…
Acoustic identification of individual animals (AIID) is closely related to audio-based species classification but requires a finer level of detail to distinguish between individual animals within the same species. In this work, we frame…
Eight categorical soundness and completeness theorems are established within the framework of algebraic theories. Exactly six of the eight deduction systems exhibit complete semantics within the cartesian monoidal category of sets. The…