{"title":"论神经元行为的边界","authors":"Richard Borowski, Arthur Choi","doi":"10.1142/s0218213024600029","DOIUrl":null,"url":null,"abstract":"A neuron with binary inputs and a binary output represents a Boolean function. Our goal is to extract this Boolean function into a tractable representation that will facilitate the explanation and formal verification of a neuron’s behavior. Unfortunately, extracting a neuron’s Boolean function is in general an NP-hard problem. However, it was recently shown that prime implicants of this Boolean function can be enumerated efficiently, with only polynomial time delay. Building on this result, we first propose a best-first search algorithm that is able to incrementally tighten the inner and outer bounds of a neuron’s Boolean function. Second, we show that these bounds correspond to truncated prime-implicant covers of the Boolean function. Next, we show how these bounds can be propagated in an elementary class of neural networks. Finally, we provide case studies that highlight our ability to bound the behavior of neurons.","PeriodicalId":50280,"journal":{"name":"International Journal on Artificial Intelligence Tools","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Bounding the Behavior of Neurons\",\"authors\":\"Richard Borowski, Arthur Choi\",\"doi\":\"10.1142/s0218213024600029\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A neuron with binary inputs and a binary output represents a Boolean function. Our goal is to extract this Boolean function into a tractable representation that will facilitate the explanation and formal verification of a neuron’s behavior. Unfortunately, extracting a neuron’s Boolean function is in general an NP-hard problem. However, it was recently shown that prime implicants of this Boolean function can be enumerated efficiently, with only polynomial time delay. Building on this result, we first propose a best-first search algorithm that is able to incrementally tighten the inner and outer bounds of a neuron’s Boolean function. Second, we show that these bounds correspond to truncated prime-implicant covers of the Boolean function. Next, we show how these bounds can be propagated in an elementary class of neural networks. Finally, we provide case studies that highlight our ability to bound the behavior of neurons.\",\"PeriodicalId\":50280,\"journal\":{\"name\":\"International Journal on Artificial Intelligence Tools\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-04-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal on Artificial Intelligence Tools\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218213024600029\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal on Artificial Intelligence Tools","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1142/s0218213024600029","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
A neuron with binary inputs and a binary output represents a Boolean function. Our goal is to extract this Boolean function into a tractable representation that will facilitate the explanation and formal verification of a neuron’s behavior. Unfortunately, extracting a neuron’s Boolean function is in general an NP-hard problem. However, it was recently shown that prime implicants of this Boolean function can be enumerated efficiently, with only polynomial time delay. Building on this result, we first propose a best-first search algorithm that is able to incrementally tighten the inner and outer bounds of a neuron’s Boolean function. Second, we show that these bounds correspond to truncated prime-implicant covers of the Boolean function. Next, we show how these bounds can be propagated in an elementary class of neural networks. Finally, we provide case studies that highlight our ability to bound the behavior of neurons.
期刊介绍:
The International Journal on Artificial Intelligence Tools (IJAIT) provides an interdisciplinary forum in which AI scientists and professionals can share their research results and report new advances on AI tools or tools that use AI. Tools refer to architectures, languages or algorithms, which constitute the means connecting theory with applications. So, IJAIT is a medium for promoting general and/or special purpose tools, which are very important for the evolution of science and manipulation of knowledge. IJAIT can also be used as a test ground for new AI tools.
Topics covered by IJAIT include but are not limited to: AI in Bioinformatics, AI for Service Engineering, AI for Software Engineering, AI for Ubiquitous Computing, AI for Web Intelligence Applications, AI Parallel Processing Tools (hardware/software), AI Programming Languages, AI Tools for CAD and VLSI Analysis/Design/Testing, AI Tools for Computer Vision and Speech Understanding, AI Tools for Multimedia, Cognitive Informatics, Data Mining and Machine Learning Tools, Heuristic and AI Planning Strategies and Tools, Image Understanding, Integrated/Hybrid AI Approaches, Intelligent System Architectures, Knowledge-Based/Expert Systems, Knowledge Management and Processing Tools, Knowledge Representation Languages, Natural Language Understanding, Neural Networks for AI, Object-Oriented Programming for AI, Reasoning and Evolution of Knowledge Bases, Self-Healing and Autonomous Systems, and Software Engineering for AI.