Related papers: Early Announcement: Parametricity for GADTs

Let $\tilde{f}(X)\in\mathbb{Z}[X]$ be a degree-$n$ polynomial such that $f(X):=\tilde{f}(X)\bmod p$ factorizes into $n$ distinct linear factors over $\mathbb{F}_p$. We study the problem of deterministically factoring $f(X)$ over…

Graph machine learning has led to a significant increase in the capabilities of models that learn on arbitrary graph-structured data and has been applied to molecules, social networks, recommendation systems, and transportation, among other…

Relational Deep Learning (RDL) is a promising approach for building state-of-the-art predictive models on multi-table relational data by representing it as a heterogeneous temporal graph. However, commonly used Graph Neural Network models…

Dynamic languages such as Python and JavaScript widely use function decorators to extend behavior. In TypeScript, a common way to type such patterns uses Parameters<T> and ReturnType<T>. In practice, this idiom relies on a function-type…

Distributional and neural approaches to natural language semantics have been built almost exclusively on conventional linear algebra: vectors, matrices, tensors, and the operations that accompany them. These methods have achieved remarkable…

This study presents a systematic approach to specifying data objects with the help of initial algebras. The primary aim is to describe the set-up to be found in modern functional programming languages such as Haskell and ML, although it can…

Generalized trigonometric functions (GTFs) are simple generalization of the classical trigonometric functions. GTFs are deeply related to the $p$-Laplacian, which is known as a typical nonlinear differential operator, and there are a lot of…

In this paper, we present a series of techniques to describe General Relativity using Geometric Algebra (GA). We emphasize the physical interpretation of quantities and provide a step-by-step guide for performing calculations. In doing so,…

Geometric relational embeddings map relational data as geometric objects that combine vector information suitable for machine learning and structured/relational information for structured/relational reasoning, typically in low dimensions.…

Context: Reynolds showed us how to use continuation-passing style and defunctionalization to transform a recursive interpreter for a language into an abstract machine for programs in that language. The same techniques explain other…

It is natural for probabilistic programs to use conditionals to express alternative substructures in models, and loops (recursion) to express repeated substructures in models. Thus, probabilistic programs with conditionals and recursion…

We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…

We remind how relationality arises as the core insight of general-relativistic gauge field theories from the articulation of the generalised hole and point-coincidence arguments. Hence, a compelling case for a manifestly relational…

The formal system $\lambda\delta$ is a typed lambda calculus derived from $\Lambda_\infty$, aiming to support the foundations of Mathematics that require an underlying theory of expressions (for example the Minimal Type Theory). The system…

One way of studying a relational structure is to investigate functions which are related to that structure and which leave certain aspects of the structure invariant. Examples are the automorphism group, the self-embedding monoid, the…

This article aims to provide a novel formalization of the concept of computational irreducibility in terms of the exactness of functorial correspondence between a category of data structures and elementary computations and a corresponding…

Large language models (LLMs) have recently been introduced to graph learning, aiming to extend their zero-shot generalization success to tasks where labeled graph data is scarce. Among these applications, inference over text-attributed…

Data-driven algorithm design automates hyperparameter tuning, but its statistical foundations remain limited because model performance can depend on hyperparameters in implicit and highly non-smooth ways. Existing guarantees focus on the…

Relational databases (RDBs) are widely regarded as the gold standard for storing structured information. Consequently, predictive tasks leveraging this data format hold significant application promise. Recently, Relational Deep Learning…

We propose the use of hyperedge replacement graph grammars for factor graphs, or factor graph grammars (FGGs) for short. FGGs generate sets of factor graphs and can describe a more general class of models than plate notation, dynamic…