Foundations of brick diagrams

基于范畴论通用图表的货币会计宏观经济基础

Macroeconomic Foundation of Monetary Accounting by Diagrams of Categorical Universals

本文提出货币宏观经济会计理论（MoMaT）的范畴论表述，用范畴论提升微观会计一致性至宏观层面，通过五个部门主体举例并展示动态收敛性，助力跨学科协作构建货币会计系统数字孪生。

Categorical Tools for Natural Language Processing

This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide a unified model of syntactic structures in formal grammars. Second, functors compute semantics by turning diagrams into logical, tensor, neural or quantum computation. Third, the resulting functorial models can be composed to form games where equilibria are the solutions of language processing tasks. This framework is implemented as part of DisCoPy, the Python lib…

String diagrams for game theory

This paper presents a monoidal category whose morphisms are games (in the sense of game theory, not game semantics) and an associated diagrammatic language. The two basic operations of a monoidal category, namely categorical composition and tensor product, correspond roughly to sequential and simultaneous composition of games. This leads to a compositional theory in which we can reason about properties of games in terms of corresponding properties of the component parts. In particular, we give a definition of Nash equilibrium which is recursive on the causal structure of the game. The key tech…

结构化可逆流程图语言的范畴基础：可靠性与充分性

A categorical foundation for structured reversible flowchart languages: Soundness and adequacy

本文基于带联结的逆范畴为结构化可逆流程图语言建立范畴语义，推广扩展性概念以表示谓词，并证明其计算可靠、充分及在特定条件下方程完全抽象。

图解学习：一种用于组合式训练机制的图形语言

DiagrammaticLearning: A Graphical Language for Compositional Training Regimes

本文提出学习图这一图形语言，将参数化训练表示为可编译为唯一损失函数的数据，统一描述多任务学习、知识蒸馏和多模态学习等机制，并通过范畴论赋予其严格语义。

Mathematical Foundations for a Compositional Distributional Model of Meaning

We propose a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, for which we rely on the algebra of Pregroups, introduced by Lambek. This mathematical framework enables us to compute the meaning of a well-typed sentence from the meanings of its constituents. Concretely, the type reductions of Pregroups are `lifted' to morphisms in a category, a procedure that transforms meanings of constituents into a meaning of the (well-typed) whole. Importantly, meanings of whole sentences live i…