{"title":"Algebras of actions in an agent's representations of the world","authors":"Alexander Dean, Eduardo Alonso, Esther Mondragón","doi":"10.1016/j.artint.2025.104403","DOIUrl":null,"url":null,"abstract":"<div><div>Learning efficient representations allows robust processing of data, data that can then be generalised across different tasks and domains, and it is thus paramount in various areas of Artificial Intelligence, including computer vision, natural language processing and reinforcement learning, among others. Within the context of reinforcement learning, we propose in this paper a mathematical framework to learn representations by extracting the algebra of the transformations of worlds from the perspective of an agent. As a starting point, we use our framework to reproduce representations from the symmetry-based disentangled representation learning (SBDRL) formalism proposed by <span><span>[1]</span></span> and prove that, although useful, they are restricted to transformations that respond to the properties of algebraic groups. We then generalise two important results of SBDRL –the equivariance condition and the disentangling definition– from only working with group-based symmetry representations to working with representations capturing the transformation properties of worlds for any algebra, using examples common in reinforcement learning and generated by an algorithm that computes their corresponding Cayley tables. Finally, we combine our generalised equivariance condition and our generalised disentangling definition to show that disentangled sub-algebras can each have their own individual equivariance conditions, which can be treated independently, using category theory. In so doing, our framework offers a rich formal tool to represent different types of symmetry transformations in reinforcement learning, extending the scope of previous proposals and providing Artificial Intelligence developers with a sound foundation to implement efficient applications.</div></div>","PeriodicalId":8434,"journal":{"name":"Artificial Intelligence","volume":"348 ","pages":"Article 104403"},"PeriodicalIF":4.6000,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Artificial Intelligence","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0004370225001225","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
Learning efficient representations allows robust processing of data, data that can then be generalised across different tasks and domains, and it is thus paramount in various areas of Artificial Intelligence, including computer vision, natural language processing and reinforcement learning, among others. Within the context of reinforcement learning, we propose in this paper a mathematical framework to learn representations by extracting the algebra of the transformations of worlds from the perspective of an agent. As a starting point, we use our framework to reproduce representations from the symmetry-based disentangled representation learning (SBDRL) formalism proposed by [1] and prove that, although useful, they are restricted to transformations that respond to the properties of algebraic groups. We then generalise two important results of SBDRL –the equivariance condition and the disentangling definition– from only working with group-based symmetry representations to working with representations capturing the transformation properties of worlds for any algebra, using examples common in reinforcement learning and generated by an algorithm that computes their corresponding Cayley tables. Finally, we combine our generalised equivariance condition and our generalised disentangling definition to show that disentangled sub-algebras can each have their own individual equivariance conditions, which can be treated independently, using category theory. In so doing, our framework offers a rich formal tool to represent different types of symmetry transformations in reinforcement learning, extending the scope of previous proposals and providing Artificial Intelligence developers with a sound foundation to implement efficient applications.
期刊介绍:
The Journal of Artificial Intelligence (AIJ) welcomes papers covering a broad spectrum of AI topics, including cognition, automated reasoning, computer vision, machine learning, and more. Papers should demonstrate advancements in AI and propose innovative approaches to AI problems. Additionally, the journal accepts papers describing AI applications, focusing on how new methods enhance performance rather than reiterating conventional approaches. In addition to regular papers, AIJ also accepts Research Notes, Research Field Reviews, Position Papers, Book Reviews, and summary papers on AI challenges and competitions.