1、.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论人工智能三大科学问题李昂生北京航空航天大学2023 人工智能基础报告北京,2023 年 1 月 10 日.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Outline1.信息世界的科学范式Book I2.信息世界的数学原理Book II3.学习的数学理论：知彼Book III4.自我意识的数学理论：知己:Book III5.博弈的数学理论：谋算理论:Book III6.计算 vs 谋算Details are referred to my book:Angsheng Li,Mathemat

2、ical Principles ofInformation World,To appear.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论物理世界物理世界由很多对象构成物理世界研究物理对象内在性质：一个物理对象的内在性质由该物理对象完全决定.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论物理世界基本性质物理世界的对象是可分的物理世界的对象是可积的例子：一块石头砸碎了还是石头，合起来还是石头.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论物理世界的科学范式分而治之为什么？物理世界的对象也很复杂，要知道它是什

3、么，就砸碎了来看。.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论物理世界的数学度量Numbers 数Shapes 形数与形可以定义和度量一个物理对象的内在性质.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论物理世界分析的数学原理Differential calculus 微分演算Integrating calculus 积分演算数学原理:Calculuses 微积分.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论信息世界信息世界由很多对象构成信息世界研究对象的语法与语义性质：语法：结构语义：功能、作用一

4、个对象的语法与语义由该对象及它和其它对象的关系来决定.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论信息世界基本性质信息世界的对象不是可分的信息世界的对象不是可积的例子：一个 DNA 包含了一个生命体的所有信息，然而如果把 DNA 剪碎，它就不再是 DNA 了，剪碎了就合不起来了一个信息世界的对象本身是一个系统，它包含有不同抽象层谱的功能模块信息科学揭示信息世界对象各个抽象层谱的功能模块（知识模块）.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论信息世界的科学范式层谱抽象层谱抽象就是揭示信息世界对象抽象层谱功能模块的数学模型.信息世界

5、的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论信息世界的数学度量Information 信息：消除的不确定性消除不确定性需要动作或者操作Structure 结构信息与结构是定义和度量一个信息世界对象的基本度量，即钥匙语法决定语义，即结构决定功能.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论信息世界分析的数学原理信息世界的微分：Encoding Tree 编码树信息世界的积分：Structural Entropy,Decoding Information 结构熵、解码信息数学原理:Calculuses of Information,信息演算理

6、论.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论信息世界分析的策略Generating Strategy 生成策略Decoding Strategy 解码策略生成原理:生成信息极大化解码原理:解码信息极大化.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论知识：信息的姐妹概念信息：消除的不确定性Knowledge 知识：信息的语义，即消除的不确定性的语义知识原理:信息是知识的数学原理要想获得知识就要获得信息，即消除不确定性知识从哪里来：从信息来！.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论学习：信息的

7、姐妹概念学习的实质:解码信息生成信息学习目标:知识发现规律揭示基于知识与规律的创造.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论学习理论：知彼学习策略:观察学习根本问题:学习的数学理论观察学习解决：知彼.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论自我意识学习理论：知己自我意识:区分自己与外界自我意识学习:层谱抽象感知与认知自我意识学习:外界的确定性和不确定性的认知根本问题:自我意识的数学理论自我意识学习解决：知己.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论博弈的数学理论：谋算理论谋全局、全时编码

8、直觉推理信息论概念算计算局部推理、逻辑推理谋算原理:信息科学与计算科学相结合的科学思想，孙子兵法的精髓.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论智能：信息的相伴概念智能的实质：学习：知彼自我意识学习：知己谋算数学原理:中华文明最伟大的科学思想.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论思想与方法思想：信息方法：抽象层谱抽象中国思想（思维方式）:谋算欧洲思想（思维方式）:计算.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Irreducible MatricesTheoremLet P 0 be

9、a probability transition matrix,that is,every rowsum of P is 1.If P is irreducible,then there is a unique vectorTsatisfying:T 0T P=Tand|1=1,meaning that Tis a probability distribution with each of itscoordinate greater than 0.We call the unique Tthestationary distributionofthe movements defined by t

10、he matrix P.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论One-Dimensional StructuralEntropy of An Irreducible MatrixDefinitionLet Ann 0 be an irreducible matrix.Suppose that Pnn 0be the normalized of A so that each row sum of P is 1.Let Tbe the unique stationary distribution of P.Define theone-dimensional s

11、tructural entropy of AasH1(A)=ni=1ilogi,(1)where T=(1,2,n).Intuition:H1(A)is the amount of uncertainty that is embeddedin the movement defined by the linear transformation A.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Encoding TreeFigure:Encoding Tree.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Encoding TreeEnc

12、oding tree is alossless encodingEncoding tree is themodel of hierarchicalabstractingEncoding tree is thedata structureof hierarchicalabstractingHierarchical abstractingcan be mathematicallyrealized.As we will see,encoding treedoes decodeinformation from an information systemEncoding tree is adiffere

13、ntial operatorof discretesystem.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Structural Entropy of IrreducibleNonnegative MatricesLet Ann 0 be irreducible.Let B be the matrices obtainedfrom A by normalizing each of the rows of A so that the rowsum is 1.Let =(1,2,n)be the unique stationary distribution ofB.

14、Defineprobability of going from x to yasp(x,y)=x bxy,(2)where bxyis the xy-entry of B.Note thatbxy=axyz1,2,naxz(3).信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Structural Entropy of Matrix ADefinitionLet T be the encoding tree of the set 1,2,n of rows of A.Define thestructural entropy of encoding tree Tin

15、AasHT(A)=T,=plogVV=TplogVV(4)VX=yxXp(y,x),V=VT(5)pX=yXxXp(y,x),p=pT(6).信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Structural EntropyDefinition(Structural entropy)Let G=(V,E)be an irreducible graph.We define thestructural entropy of Gas follows:H(G)=minTHT(G),(7)where T ranges over all of the encoding tre

16、es of G.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Decoding Information of anEncoding Tree from an InformationSystemDefinition(Decoding information of an information system by an encodingtree)For an irreducible information system A,suppose that T isan encoding tree of A.We define thedecoding information

17、of theencoding tree T from Aas follows:DT(A)=H1(A)HT(A).(8).信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Decoding InformationDefinition(Decoding information)Let A be an irreducible informationsystem.We define the decoding information of A as follows:D(A)=maxTDT(A),(9)where T ranges over all of the encoding

18、 trees of A.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Compressing Information byEncoding TreeDefinitionWe define the compressing information of the encodingtree T from A as follows:CT(A)=T,=qlog2VV=TqlogVV.(10)where qis the probability that a randm walk stays in T,Visthe volume of set T,namely,the sum o

19、f the probabilities of allthe nodes in T.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论qq=xTyTp(x,y).(11)p(x,y)=x ax,y,(12)where ax,yis the(x,y)-entry of A,T=(1,n)is theunique stationary distribution of A.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Compressing InformationDefinition(Compressing information)Let A b

20、e an irreducible informationsystem.We define thecompressing information of Aas follows:C(A)=maxTCT(A),(13)where T ranges over all of the encoding trees of A.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Compressing and DecodingPrinciple of Irreducible InformationSystemTheoremLet A be an irreducible informat

21、ion system.Then:C(A)=H1(A)H(A)=D(A).(14)Therefore,for any irreducible information system anyinformation lost in the compression of data can belosslessly decoded by an encoding tree,the decoder.This means thatFor either unstructured or structured data,datacompression will never loss any information.信

22、息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Decoding Information Principle-IAn encoding tree T of an irreducible information system Ais a mathematical model and a data structure of ahierarchical abstracting of A.The definition of structural entropy provides the principle ofinformation processing of an irre

23、ducible informationsystem:Structural EntropyMinimization Principle.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论General Principle of InformationDecodingGeneral Principle of InformationDecoding:Entropy minimizationGiven an irreducible information system A,find theoptimal strategy Ssuch that Seliminates the

24、maximum amount of uncertainty embeddedin A.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Structural Entropy of a DeductingDefinition(Structural entropy of deducting in an encoding tree)Let A be anonnegative irreducible system,and T be an encoding tree ofA.For every T with =,we define the structural entropy

25、ofthe deducting from to asHT(A;(,)=plogVV.(15).信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Hierarchical Abstracting in anEncoding TreeDefinition(Hierarchical abstracting in an encoding tree)Let A be anonnegative irreducible system,and T be an encoding tree ofA.For every T with =,we say that the path from

26、goingup to is a hierarchical abstracting from X=Tto V=T.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Structural Entropy of AHierarchical AbstractingDefinition(Structural entropy of abstracting in an encoding tree)Let A bea nonnegative irreducible system,and T be an encoding tree ofA.For every T with =,we d

27、efine the structural entropy ofthe hierarchical abstracting from to asHT(A;(,)=HT(A;).(16).信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Structural Entropy of a SubsetDefinition(Structural entropy of a subset of T)Let A be a nonnegativeirreducible system,and T be an encoding tree of A.For anysubset M T,defi

28、ne the structural entropy of T at M asHT(A;M)=M=plogVV.(17).信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Hierarchically AbstractingDefinabilityDefinition(Hierarchical definability of objects in an encoding tree)Let Abe a nonnegative irreducible system and T be an encoding treeof A.For every T with =,we say

29、 that the path from to in T is a hierarchically abstracting definition of X=T.In particular,for every leaf node T,if T=x,then we saythat the path from to in T is a hierarchically abstractingdefinition of individual x.Individuals are hierarchically(abstracting)definable.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知

30、己博弈：谋算理论Structural Entropy of A Subtree ofthe Encoding TreeDefinition(Structural entropy of a subtree)Let A be a nonnegativeirreducible system,and T be an encoding tree of A.For T,let Tbe the subtree of T with root.The structural entropy ofTis defined asHT(A;T)=T=plogVV.(18).信息世界的科学范式信息演算理论学习理论：知彼自我

31、意识理论：知己博弈：谋算理论Conditional Structural EntropyDefinition(Conditional structural entropy of T)Let A be a nonnegativeirreducible system,and T be an encoding tree of A.For anysubset M,N T,define the condition structural entropy of Munder condition N asHT(A;M|N)=MN=plogVV.(19).信息世界的科学范式信息演算理论学习理论：知彼自我意识理论

32、：知己博弈：谋算理论Structural Mutual InformationDefinition(Structural mutual information)Let A be a nonnegativeirreducible system,and T be an encoding tree of A.For anysubset M,N T,define the conditional structural mutualinformation of M and N asIT(A;M N)=MN=plogVV.(20).信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论

33、Partial Structural EntropyLet Annbe a nonnegative irreducible information system.LetV=1,2,n.The metric of structural entropy of A can beextended to the metrics of structural entropies of an arbitrarilygiven subset X V.Definition(Partial structural entropy of a partial encoding tree from asystem)Give

34、n a nonnegative irreducible system Ann,letV=1,2,n.For an X V,let T be an encoding tree ofX,then thepartial structural entropy of X with Tfrom Ais defined asXHT(A)=T=plogVV.(21).信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论信息科学总结1.信息科学:确定性和不确定性及其相互转化的规律与作用2.度量:熵：不确定性，如果熵是负：有规律3.转化的动作:策略4.生成策略:由确定性到不确定性转化5.解

35、码策略:由不确定性到确定性转化.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论基本问题1.主体:自我意识体2.客体:现实世界/信息世界3.目标:知识、规律、创造4.实质，学习策略:生成信息：提出问题、解码信息：解决问题5.方法:生成策略、解码策略.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Model of Learning1.(Subject)Aware Object2.(Knowledge and Law)Real world knowledge K and law L3.(Observing strategy O)Observ

36、ing real world to generate araw system G04.(Generating strategy G)Generate an information system Abased on G05.(Decoding strategy D)Let D be an encoding strategy6.(Decoding information)ID(A):the information that strategyD obtained from A7.(Decoder)If ID(A)is appropriately large,then there is adecode

37、r D,satisfyingD(A;D)=K,L.(22).信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Privacy of LearningLearning is a procedure belonging to anobject,which is an aware object,i.e.,thelearner.1.the aware object gains from its learning2.different learners may gain very different knowledge on thesame material3.3.1 info

38、rmation exists in systems3.2 knowledge exists in systems3.3 laws exist in systems3.4 forces exist in systems3.5 energy exists in systems3.6 the information embedded in a system is the foundation forthe knowledge,laws,forces,energy of the system3.7 information is power,and hence,knowledge,laws,energy

39、are all powers3.8 the more information gains,the more powerful is anindividual.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论KnowledgeKnowledgeof a real world object:1.(syntax)existence,including origin,space,time,shape,and state etc2.(semantic)roles and function3.(motion)the motions of the object4.(reasons

40、)the reasons of the existence of the objectKnowledge exists in a structureof the object andthe relationships of the object with other objects.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论LawsWhat is law?Definition(Laws)Lawsare abstractions,or hierarchical abstractions ofreal world objects.DefinitionTheabst

41、ractingof an object:An abstracting of an object isto extract the mathematical features of the object such that theextracted features are shared by many other objects.Abstracting itself includes a strategy ofcreating.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Hierarchical Abstracting1.hierarchical abstrac

42、ting is anencoding2.hierarchical abstracting is the centerstrategyoflearning3.themathematical modelof hierarchical abstractingis encoding tree4.thedata structureof hierarchical abstracting isencoding tree5.encoding tree is adifferential operatorof discretesystem6.hierarchical abstracting is the foun

43、dation forintuitivereasoning,the reasoning crossing over differenthierarchies of abstracting.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Local ObservingIn real world,an individual itself is a system,consisting of manyparticles together with the relationships between the particles.However,local observation

44、 regards an individual as an entitywhich is no longer to be split1.anindividualis a unit of objects at the level ofobservation2.individuals are observable3.thedirect relationshipsbetween individuals areobservable4.the result of a local observing is asystem,referred to asraw system of individuals and

45、 their direct relationships5.the mathematical representation of a system is anonnegative matrix6.Theory of nonnegative matrixis the foundationthe theories.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Global Observing1.the result of a global observing is animage2.humans and animals naturally doglobal observ

46、ing3.in the global observing of humans and animals,there havealready been a process ofinformationprocessing4.humans global observing is a procedure ofhierarchical abstracting5.Hierarchical abstracting of an image proceeds as follows:Given an image5.1(generating strategy)generate an informationsystem

47、 of the image5.2(decoding strategy)find an encoding tree of thesystem by the principle of minimizing structural entropy.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论The Strategies of Observing1.Observingitself is the first fundamental learningstrategy.Because,humans and animals learn fromobserving2.Observi

48、ng itself is a scientificchallenge3.Theability of observingdetermines the ability oflearning4.Observing consists oflocal observing andglobal observing5.The results of observing areraw informationsystem.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Generating StrategiesMajor generating strategies include:1.a

49、ssociating2.imagining3.creatingGenerating strategy produces an informationsystem based on a raw system of observing.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Generating PrincipleEntropy Maximization Principle:The generated system has embedded themaximal amount of information.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论

50、：知己博弈：谋算理论The Roles of Generating Strategies1.generating strategy determines theuniverse oflearning见多识广，不断探索新世界2.growing upis a generating strategy.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Decoding StrategiesMajor decoding strategies include:1.hierarchical municatingetcThere exists a theory for the inf

51、ormationdecoded by a type of decoding strategies.For example:Shannon:channel transmitting,Structuralinformation:Hierarchical abstractingCalls for:Information theory of computing etc.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Decoding InformationGiven an information system A,let T be a decoding strategy,t

52、hen thedecoding information of T from Aisdefined asI(A;T)(23)be the information that is decoded by the decoding strategy Tfrom A.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Decoding PrincipleDecoding information maximizationprinciple:Find the strategy that decodes the maximumamount of information from an

53、informationsystemT=argmaxTI(A;T)(24).信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论DecoderTheprinciple of learningis the following:For an information system A,suppose that K and L are theknowledge and laws of A,for any decoding strategy T of A,ifthe decoding information I(A;T)is appropriately large,thenther

54、e exists a decoder D such thatD(A;T)=K,L(25).信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Quantification of KnowledgeDefinitionFor a nonnegative irreducible system A and an encoding tree Tof A,the knowledge of A that is decoded by encoding tree T isdefined asKT(A)=T=qlogV=TqlogV.(26).信息世界的科学范式信息演算理论学习理论：知彼

55、自我意识理论：知己博弈：谋算理论Calculus of KnowledgeDefinition(Knowledge of modules of an encoding tree)Given anonnegative irreducible information system A,and an encodingtree T of A.For every set M T,we define the knowledge ofM from T and A asK(A,T;M)=M=qlogVV.(27).信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Criteria o

56、f Knowledge:Principle ofInterpretabilityDefinition(Syntax and semantic law)The knowledge consists of both asyntax and a semantic.The quantification KT(A)supports botha syntax and a semantic of the information system A.Thesyntax and semantic of the knowledge quantification KT(A)aredefined as follows:

57、1.(The syntax and semantic law)A real world object has botha syntax and a semantic,for which the syntax representsthe existence of the object,and the semantic representsthe function or role of the object.Therefore,for every individual x V,x is therepresentation of an individual in the real world whi

58、ch hasboth a syntax and a semantic.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论学习总结1.主体:自我意识体2.客体:现实世界/信息世界3.目标:知识、规律、创造4.实质:生成信息、解码信息5.方法:生成策略：提出问题、解码策略：回答问题.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Law of NatureEvery real world object competes to keep itsown existence and state.现实世界对象总是要保持自己的存在性和状态的例子：物理世界

59、信息世界.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论现实世界对象的定义与表示现实世界的一个对象本身是一个系统例子：细胞、DNA、人、公司、国家现实世界对象是层谱抽象可定义的层谱抽象定义了对象在各个抽象层谱的功能模块（每一个模块有一个支撑结构，即该功能模块的语法）.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论自我意识的实质：层谱抽象感知与认知对自我的存在性层谱抽象认知（语法）对自身的功能模块的层谱抽象认知（语义）对自我需求的层谱抽象认知（需求）对自身愿望的层谱抽象认知（愿望）对自身在环境中的确定性和不确定性的认知（不确定性认知）.

60、信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论RequirementsGiven a real world object X,(1)X requires the information or energy to maintain theexistence of X,and(2)X requires to win a competition,if it occurs.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Law I of LifeA life object is the result of the joint actionsof

61、 certainty and uncertainty.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Law II of LifeA life object is the result of the evolution of asystem of the interactions of the objects inan environment of the real world.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Law III of Life生命体通过遗传来延续存在性，传递信息，累计信息信息是可以继承的信息的继承、累计信息促

62、进智能生成.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Laws of Motions1.Every individual needs information(an amount of certainty)to keep a state unchanged.2.Information is the amount of certainty that is generated bya structure.3.Every action needs information(the amount of certainty);every action either gene

63、rates information(i.e.,generatesuncertainty),or decodes information(that is,eliminates,orreduces uncertainty).4.Every motion of an individual needs information,that is,anamount of certainty,for the individual to move.5.A motion either generates information,or decodesinformation.信息世界的科学范式信息演算理论学习理论：知

64、彼自我意识理论：知己博弈：谋算理论Awareness HypothesesDefinition(Awareness hypotheses)(Awareness hypothesis I)Awareness is the reason for anindividual to learn the world from observing(Awareness hypothesis II)Awareness is the foundation ofhuman intelligence.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Mathematical Model of

65、 Awareness IDefinition(Mathematical model of awareness)An object X withawareness is a dynamical system At that evolves with timet,where At is the nonnegative irreducible system of the objectat the end of time step t.The system At has an encoding treeTt such that the following properties hold:(1)The

66、object is evolving with time.(2)(Structural principle)Tt is the hierarchical abstracting ofAt.(3)(Functional principle)For each node Tt,there is amodule Mt of At,satisfying:0.1 the module Mt has a syntax syn()t0.2 the module Mt has a semantic sem()t0.3 the semantic of module Mt is determined by the

67、syntaxof the module.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Mathematical Model of AwarenessII(4)(Requirement principle)For each node Tt,there is amodule Mt of At,satisfying:0.1 the module Mt has a requirement req()t0.2 the module Mt has a desire des()t(5)(Uncertainty principle)For each node Tt,there i

68、s amodule Mt of At,satisfying:the module Mt has an uncertainty unc()t.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Mathematical Model of AwarenessIII(6)(Recognition principle)The object Xt as a wholerecognizes each of its functional modules.(7)(Perception principle)A local activation generates a globalreac

69、tion of the object Xt,the object at the end of timestep t.(8)(Transmission principle)The information or energyreceived by the object Xt is distributed over all themodules of the object Xt.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Mathematical Representation ofIndividualDefinition(Mathematical representa

70、tion of an individual)Given anindividual x,suppose that y1,ynare all the individuals thatinteract with x.Let V=x,y1,yn,and A be a generatednonnegative irreducible system of V.Let Axbe a nonnegativeirreducible system of all the particles of individual x.Thehierarchical definition and representation o

71、f individual x aredefined as follows:(1)Let T1be an encoding tree of A decoded by the structuralentropy minimization principle,(2)Let Txbe an encoding tree of Axdecoded by the structuralentropy minimization principle,and(3)The hierarchical definition of individual x is defined as theencoding tree T,

72、obtained from T1by replacing thecodeword of x in T1by tree Tx.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论5-Dimensional Recognition of anObjectR(X)=syn(X),sem(X),req(X),des(X),unc(X),(28)1.the syntax of X,written syn(X),is the structural featuresthat represent the existence of X2.the semantic of X,written

73、 sem(X),is the features thatrepresent the functions or roles of X3.the requirement of X,written req(X),is the features thatrepresent the conditions guaranteeing the existence of X4.the desire of X,written des(X),is the features thatrepresent the desires of X5.the uncertainty of X,written unc(X),is t

74、he entropy of thesystem of X.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Perceptive Entropy of an IndividualDefinition(Perceptive entropy of an individual)Given an individual x,letP(x)=A,T,R be a hierarchical abstracting perception of x.Let be the codeword of x in T.Then we define the perceptiveentropy of

75、 x asPe(x)=plogVV.(29).信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Awareness of an ObjectDefinition(Awareness of an object)Let x be an object.An awareness of xis a triple of the form:A(x)=R(x),P(x),Pe(x),(30)where(i)R(x)is a 5-dimensional recognition of x,(ii)P(x)is a hierarchical abstracting perception o

76、f x,and(iii)Pe(x)is the perceptive entropy of x.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Energy of a Real World ObjectDefinition(Energy of a real world object)Let X be an intelligent object.Suppose that A is a nonnegative irreducible system generatedfrom the observations of an object X.Let T be an enco

77、dingtree of A found by a strategy of X.Suppose that T is thecodeword of X.Let Tbe the subtree of T with root.Definethe energy of X asE(X)=T=qlogVV=TqlogVV.(31).信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Hierarchical AbstractingRecognitionLet Tbe the subtree of T with root.We define thehierarchical abstra

78、cting self-recognition of X as:1.We say that Tis the hierarchical abstracting recognitionof X.2.We say that is the codeword of object X=T.Suppose that is an agent.3.recognizes every T.4.Every Tis immediately accessible to through apath in the hierarchical abstracting encoding tree T.5.identifies eve

79、ry functional modules of object X.6.distinguishes its own object from the other objects in theenvironment.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Inner Structural EntropyDefinition(Inner structural entropy of an object)Let X be an object,A bea nonnegative irreducible system generated from theobservati

80、ons of object X,and T be an encoding tree of A.Suppose that is the codeword of X in T,that is,X=T.Forevery with .We define the-inner structural entropy of X asH(X;)=T=plogVVV=TplogVV.(32).信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Outer Structural EntropyDefinition(Outer structural entropy of an object)L

81、et X be an object.Suppose that A is a nonnegative irreducible system that isgenerated form the system of the observations of the object X.Let T be an encoding tree of A.Assume that X=Tfor some T.We define the outer structural entropy of X asHO(X)=T,plogVVV=T|plogVV.(33).信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：

82、知己博弈：谋算理论Law ICompeting is a natural and fundamentalphenomenon of the real world.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Law IIThe trends of the evolution of the real world are:1.to discover new knowledge about the world,includinghumans themselves2.to explore new laws of the cosmos3.to extend the spac

83、e of human recognition4.to create based on knowledge and laws achieved.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Law IIITo prevent every avoidable conflict or confrontation is the firstprinciple for a rational player.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Law IVWhen facing an unavoidable game,the princip

84、les of a rationalplayer are:1.To win every unavoidable competition,conflict andconfrontation;and2.To maximize the benefits from the winning of the game.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Law V1.if an enemy has power,it must release its power敌人有力量是一定要释放的2.the only rule of real world game is no-rul

85、e现实世界博弈的唯一规则就是没有规则.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论重大科学问题三：博弈的数学理论是什么？谋算理论：现实世界博弈的数学理论区别于冯诺伊曼（1925）、纳什等博弈（1951）基于信息科学数学原理的新理论破解人工智能科学障碍.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论孙子模型1.学习：知彼2.自我意识学习：知己3.博弈设计：策略4.决策：智能决策5.行动：智能控制6.评估：收益理论.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Learning:知彼Identifying:

86、intruderscompetitorscooperators.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Hierarchical Abstracting of the realworld-I天时:全局属性全时属性.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Hierarchical Abstracting of the realworld-II环境:地利.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Aware Learning:知己自我层谱抽象认知:我是谁我从哪里来我有什么，没有什么我的目标是什

87、么，路线图是什么，障碍是什么.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论博弈的数学理论：谋算理论谋全局、全时编码、设计、规划、创造直觉推理信息科学概念算计算局部推理、逻辑推理谋算原理:信息科学与计算科学相结合的科学思想，孙子兵法的精髓.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论StrategiesMaximizing the enemys uncertaintyprincipleMinimizing the enemys structural force 敌人是可分的Minimizing ones own uncertaint

88、yprincipleMaximizing ones own structural force.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Winning Strategies:Non-symmetric Strategies AreWinning StrategiesInformation non-symmetric strategystructural-non-symmetric strategydefending over attacking non-symmetricstrategypermanent over movably non-symmetrics

89、trategyhigher abstracting hierarchy over lowhierarchy non-symmetric strategyhigh-dimension over low dimensionnon-symmetric strategy.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Force Generating Principleforces are generated from structuresthe system of force unitsthe encoding of the system.信息世界的科学范式信息演算理论学

90、习理论：知彼自我意识理论：知己博弈：谋算理论概念与度量威胁结构能、结构力安全性分布方向熵方向解码信息方向能、方向力.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Subjectivity所有的策略、行动都是基于玩家主观认知与判断做出的.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Criterion胜负评判的主、客观一致性准则：主观判断跟真实情况符合者获胜获利。.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论智能的实质智能的实质：学习：知彼自我意识：知己谋算.信息世界的科学范式信息演算理论学习理论：知彼自

91、我意识理论：知己博弈：谋算理论谋算：21 世纪科学突破核心思想孙子谋算:中华文明最伟大的科学思想中国科学祖师:孙子-可数学地证明、有用、管几千年、现在还是最高智慧、涉及很多学科的学科群、21 世纪再显科学、智慧之光中国科学自信的源泉！习主席讲了很多自信，我们还要科学自信.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论思想与思维流程思想：信息方法：抽象层谱抽象中国思想（思维方式）:谋算欧洲思想（思维方式）:计算当代美国思想（思维方式）:算计（科学角度的观察，供战略家和智库参考）.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论总结核心概念

92、:信息数学表示:信息系统：非负矩阵：整个理论体系基于非负矩阵来建立数学度量:信息；结构数学实质:生成信息；解码信息：提出问题、消除不确定性（回答问题）基本策略:抽象、层谱抽象、计算.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论References1.A.Li,Y.Pan,Structural Information and DynamicalComplexity of Networks,IEEE Transactions on InformationTheory,62,No.6,pp.3290-3339,2016.2.Brooks,F.P.,Jr.Three g

93、reat challenges forhalf-century-old computer science.Journal of the ACM,50(1),pp 25-26(2003).3.Angsheng Li,Xianchen Yin,Bingxiang Xu,Danyang Wang,Jimin Han,Yi Wei,Yun Deng,Ying Xiong,Zhihua Zhang,Decoding topologically associating domains with ultra-lowresolution Hi-C data by graph structural entrop

94、y,NATURECOMMUNICATIONS,(2018)9:3265.4.Angsheng Li,Structural information learning machinery:Learning from observing,associating,optimizing,decodingand abstracting,arXiv:submit/3020157 cs.AI 27 Jan.20205.Angsheng Li,Mathematical Principles of InformationWorld,To appear.信息世界的科学范式信息演算理论学习理论：知彼自我意识理论：知己博弈：谋算理论Thank You!Email: