Related papers: Generalized Composition via Nerves: Models and Alg…
One interpretation of the Kleisli construction (given by Miranda and related to work of Par\'e) is as a nerve sending a monad $P$ to the Kleisli double category of $P$. In this paper we find more general nerve constructions on the…
Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…
We provide a study of how induced model sparsity can help achieve compositional generalization and better sample efficiency in grounded language learning problems. We consider simple language-conditioned navigation problems in a grid world…
Data-to-text generation involves transforming structured data, often represented as predicate-argument tuples, into coherent textual descriptions. Despite recent advances, systems still struggle when confronted with unseen combinations of…
The ability to compose learned concepts and apply them in novel settings is key to human intelligence, but remains a persistent limitation in state-of-the-art machine learning models. To address this issue, we introduce COGITAO, a modular…
We generalize the measurement using an expanded concept of cover, in order to provide a new approach to size of set other than cardinality. The generalized measurement has application backgrounds such as a generalized problem in dimension…
We study a number of local and global classification problems in generalized complex geometry. In the first topic, we characterize the local structure of generalized complex manifolds by proving that a generalized complex structure near a…
While sequence-to-sequence models have shown remarkable generalization power across several natural language tasks, their construct of solutions are argued to be less compositional than human-like generalization. In this paper, we present…
In this note, we establish an equivalence of categories between the category of all eight-dimensional composition algebras with any given quadratic form $n$ over a field $k$ of characteristic not two, and a category arising from an action…
Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…
Machine Learning Interatomic Potentials play a fundamental role in computational chemistry and materials science, enabling applications from molecular dynamics simulations to drug design and materials discovery. While recent approaches can…
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,…
Applications such as the analysis of microbiome data have led to renewed interest in statistical methods for compositional data, i.e., multivariate data in the form of probability vectors that contain relative proportions. In particular,…
Circuits based on sum-product structure have become a ubiquitous representation to compactly encode knowledge, from Boolean functions to probability distributions. By imposing constraints on the structure of such circuits, certain inference…
The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…
While recent generative models can produce engaging music, their utility is limited. The variation in the music is often left to chance, resulting in compositions that lack structure. Pieces extending beyond a minute can become incoherent…
We present an algebraic construction of music notes and show how to associate them inseveral ways to construct music ranges. Then a family of ranges emerge with a fixed number of notes: two, three, five, seven, twelve, seventeen, etc. A…
Deep learning models struggle with systematic compositional generalization, a hallmark of human cognition. We propose \textsc{Mirage}, a neuro-inspired dual-process model that offers a processing account for this ability. It combines a…
We propose the concept of a system algebra with a parallel composition operation and an interface connection operation, and formalize composition-order invariance, which postulates that the order of composing and connecting systems is…
Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…