Related papers: Generic Level Polymorphic N-ary Functions
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…
Hypergraphs offer a natural modeling language for studying polyadic interactions between sets of entities. Many polyadic interactions are asymmetric, with nodes playing distinctive roles. In an academic collaboration network, for example,…
This paper gives two new categorical characterisations of lenses: one as a coalgebra of the store comonad, and the other as a monoidal natural transformation on a category of a certain class of coalgebras. The store comonad of the first…
Graph neural networks (GNNs) have gained significant popularity due to the powerful capability to extract useful representations from graph data. As the need for efficient GNN computation intensifies, a variety of programming abstractions…
We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires…
Big data programming frameworks have become increasingly important for the development of applications for which performance and scalability are critical. In those complex frameworks, optimizing code by hand is hard and time-consuming,…
Collaborative work on shared documents was revolutionized by web services like Google Docs or Etherpad. Multiple users can work on the same document in a comfortable and distributed way. For the synchronization of the changes a replication…
Transformers often struggle with length generalization, meaning they fail to generalize to sequences longer than those encountered during training. While arithmetic tasks are commonly used to study length generalization, certain tasks are…
Current graph neural networks (GNNs) lack generalizability with respect to scales (graph sizes, graph diameters, edge weights, etc..) when solving many graph analysis problems. Taking the perspective of synthesizing graph theory programs,…
Many NLP tasks including machine comprehension, answer selection and text entailment require the comparison between sequences. Matching the important units between sequences is a key to solve these problems. In this paper, we present a…
The purpose of this dissertation is to set up a theory of generalized operads and multicategories, and to use it as a language in which to propose a definition of weak n-category. Included is a full explanation of why the proposed…
We propose a functional description of rewriting systems on topological vector spaces. We introduce the topological confluence property as an approximation of the confluence property. Using a representation of linear topological rewriting…
Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful…
Graph machine learning models have been successfully deployed in a variety of application areas. One of the most prominent types of models - Graph Neural Networks (GNNs) - provides an elegant way of extracting expressive node-level…
We are concerned with the arithmetic of solutions to ordinary or partial nonlinear differential equations which are algebraic in the indeterminates and their derivatives. We call these solutions D-algebraic functions, and their equations…
In this study, a subclass of an univalent function with negative coefficients which is defined by a new general Linear operator have been introduced. The sharp results for coefficients estimators, distortion and closure bounds, Hadamard…
We introduce "synchronous algebras", an algebraic structure tailored to recognize automatic relations (aka. synchronous relations, or regular relations). They are the equivalent of monoids for regular languages, however they conceptually…
Neural fields offer continuous, learnable representations that extend beyond traditional discrete formats in visual computing. We study the problem of learning neural representations of repeated antiderivatives directly from a function, a…
Agda is a dependently-typed functional programming language, based on an extension of intuitionistic Martin-L\"of type theory. We implement first order natural deduction in Agda. We use Agda's type checker to verify the correctness of…
We introduce Conflict-Aware Replicated Data Types (CARDs). CARDs are significantly more expressive than Conflict-free Replicated Data Types (CRDTs) as they support operations that can conflict with each other. Introducing conflicting…