Related papers: Category-Theoretic Foundations of "STCLang: State …
This is a short introduction to categories with some emphasis on coalgebras. We start from introducing basic notions (categories, functors, natural transformations), move to Kleisli tripels and monads, with a short discussion of monads in…
Symmetric monoidal categories (SMCs) are a common framework for reasoning about computation, focusing on the parallel and sequential compositionality of operations. String diagrams are a ubiquitous and powerful tool for reasoning about…
Summarizing deeply nested discussion threads requires handling interleaved replies, quotes, and overlapping topics, which standard LLM summarizers struggle to capture reliably. We introduce ThreadSumm, a multi-stage LLM framework that…
In this paper we develop a novel mathematical formalism for the modeling of neural information networks endowed with additional structure in the form of assignments of resources, either computational or metabolic or informational. The…
The framework of causal models provides a principled approach to causal reasoning, applied today across many scientific domains. Here we present this framework in the language of string diagrams, interpreted formally using category theory.…
Every Model of High-Level Computation (MHC) has an underlying composition mechanism for combining simple computing devices into more complex ones. Composition can be done by (explicitly or implicitly) defining control flow, data flow or any…
Association rule mining is a time consuming process due to involving both data intensive and computation intensive nature. In order to mine large volume of data and to enhance the scalability and performance of existing sequential…
Spectral clustering and cloud computing is emerging branch of computer science or related discipline. It overcome the shortcomings of some traditional clustering algorithm and guarantee the convergence to the optimal solution, thus have to…
Ability to use definitions occurring in the code directly in equational reasoning is one of the key strengths of functional programming. This is impossible in the case of Haskell type class methods unless a particular instance type is…
In model based development, embedded systems are modeled using a mix of dataflow formalism, that capture the flow of computation, and hierarchical state machines, that capture the modal behavior of the system. For safety analysis, existing…
Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories…
We propose a rich foundational theory of typed data streams and stream transformers, motivated by two high-level goals: (1) The type of a stream should be able to express complex sequential patterns of events over time. And (2) it should…
This paper describes a computational framework for a grammar architecture in which different linguistic domains such as morphology, syntax, and semantics are treated not as separate components but compositional domains. Word and phrase…
In this paper, we prove correctness of parallelizing a string matcher using Haskell as a theorem prover. We use refinement types to specify correctness properties, Haskell terms to express proofs and Liquid Haskell to check correctness of…
Modelling concept representation is a foundational problem in the study of cognition and linguistics. This work builds on the confluence of conceptual tools from G\"ardenfors semantic spaces, categorical compositional linguistics, and…
One goal of applied category theory is to better understand networks appearing throughout science and engineering. Here we introduce "structured cospans" as a way to study networks with inputs and outputs. Given a functor $L \colon…
Categories, n-categories, double categories, and multicategories (among others) all have similar definitions as collections of cells with composition operations. We give an explicit description of the information required to define any…
Originally, tangles were invented as an abstract tool in mathematical graph theory to prove the famous graph minor theorem. In this paper, we showcase the practical potential of tangles in machine learning applications. Given a collection…
We introduce the syntactic scaffold, an approach to incorporating syntactic information into semantic tasks. Syntactic scaffolds avoid expensive syntactic processing at runtime, only making use of a treebank during training, through a…
We introduce the notion of symplectic microfolds and symplectic micromorphisms between them. They form a monoidal category, which is a version of the "category" of symplectic manifolds and canonical relations obtained by localizing them…