1、.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論人工智能三大科學問題李昂生北京航空航天大學2023 人工智能基礎報告北京,2023 年 1 月 10 日.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論Outline1.信息世界的科學范式Book I2.信息世界的數學原理Book II3.學習的數學理論：知彼Book III4.自我意識的數學理論：知己:Book III5.博弈的數學理論：謀算理論:Book III6.計算 vs 謀算Details are referred to my book:Angsheng Li,Mathemat

2、ical Principles ofInformation World,To appear.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論物理世界物理世界由很多對象構成物理世界研究物理對象內在性質：一個物理對象的內在性質由該物理對象完全決定.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論物理世界基本性質物理世界的對象是可分的物理世界的對象是可積的例子：一塊石頭砸碎了還是石頭，合起來還是石頭.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論物理世界的科學范式分而治之為什么？物理世界的對象也很復雜，要知道它是什

3、么，就砸碎了來看。.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論物理世界的數學度量Numbers 數Shapes 形數與形可以定義和度量一個物理對象的內在性質.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論物理世界分析的數學原理Differential calculus 微分演算Integrating calculus 積分演算數學原理:Calculuses 微積分.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論信息世界信息世界由很多對象構成信息世界研究對象的語法與語義性質：語法：結構語義：功能、作用一

4、個對象的語法與語義由該對象及它和其它對象的關系來決定.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論信息世界基本性質信息世界的對象不是可分的信息世界的對象不是可積的例子：一個 DNA 包含了一個生命體的所有信息，然而如果把 DNA 剪碎，它就不再是 DNA 了，剪碎了就合不起來了一個信息世界的對象本身是一個系統，它包含有不同抽象層譜的功能模塊信息科學揭示信息世界對象各個抽象層譜的功能模塊（知識模塊）.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論信息世界的科學范式層譜抽象層譜抽象就是揭示信息世界對象抽象層譜功能模塊的數學模型.信息世界

5、的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論信息世界的數學度量Information 信息：消除的不確定性消除不確定性需要動作或者操作Structure 結構信息與結構是定義和度量一個信息世界對象的基本度量，即鑰匙語法決定語義，即結構決定功能.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論信息世界分析的數學原理信息世界的微分：Encoding Tree 編碼樹信息世界的積分：Structural Entropy,Decoding Information 結構熵、解碼信息數學原理:Calculuses of Information,信息演算理

6、論.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論信息世界分析的策略Generating Strategy 生成策略Decoding Strategy 解碼策略生成原理:生成信息極大化解碼原理:解碼信息極大化.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論知識：信息的姐妹概念信息：消除的不確定性Knowledge 知識：信息的語義，即消除的不確定性的語義知識原理:信息是知識的數學原理要想獲得知識就要獲得信息，即消除不確定性知識從哪里來：從信息來！.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論學習：信息的

7、姐妹概念學習的實質:解碼信息生成信息學習目標:知識發現規律揭示基于知識與規律的創造.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論學習理論：知彼學習策略:觀察學習根本問題:學習的數學理論觀察學習解決：知彼.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論自我意識學習理論：知己自我意識:區分自己與外界自我意識學習:層譜抽象感知與認知自我意識學習:外界的確定性和不確定性的認知根本問題:自我意識的數學理論自我意識學習解決：知己.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論博弈的數學理論：謀算理論謀全局、全時編碼

8、直覺推理信息論概念算計算局部推理、邏輯推理謀算原理:信息科學與計算科學相結合的科學思想，孫子兵法的精髓.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論智能：信息的相伴概念智能的實質：學習：知彼自我意識學習：知己謀算數學原理:中華文明最偉大的科學思想.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論思想與方法思想：信息方法：抽象層譜抽象中國思想（思維方式）:謀算歐洲思想（思維方式）:計算.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論Encoding TreeFigure:Encoding Tree.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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).信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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).信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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).信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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、息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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).信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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).信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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).信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知

30、己博弈：謀算理論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).信息世界的科學范式信息演算理論學習理論：知彼自我

31、意識理論：知己博弈：謀算理論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).信息世界的科學范式信息演算理論學習理論：知彼自我意識理論

32、：知己博弈：謀算理論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).信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論

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).信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論信息科學總結1.信息科學:確定性和不確定性及其相互轉化的規律與作用2.度量:熵：不確定性，如果熵是負：有規律3.轉化的動作:策略4.生成策略:由確定性到不確定性轉化5.解

35、碼策略:由不確定性到確定性轉化.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論基本問題1.主體:自我意識體2.客體:現實世界/信息世界3.目標:知識、規律、創造4.實質，學習策略:生成信息：提出問題、解碼信息：解決問題5.方法:生成策略、解碼策略.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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).信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論Generating StrategiesMajor generating strategies include:1.a

49、ssociating2.imagining3.creatingGenerating strategy produces an informationsystem based on a raw system of observing.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論Generating PrincipleEntropy Maximization Principle:The generated system has embedded themaximal amount of information.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論

50、：知己博弈：謀算理論The Roles of Generating Strategies1.generating strategy determines theuniverse oflearning見多識廣，不斷探索新世界2.growing upis a generating strategy.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論Decoding PrincipleDecoding information maximizationprinciple:Find the strategy that decodes the maximumamount of information from an

53、informationsystemT=argmaxTI(A;T)(24).信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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).信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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).信息世界的科學范式信息演算理論學習理論：知彼

55、自我意識理論：知己博弈：謀算理論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).信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論學習總結1.主體:自我意識體2.客體:現實世界/信息世界3.目標:知識、規律、創造4.實質:生成信息、解碼信息5.方法:生成策略：提出問題、解碼策略：回答問題.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論Law of NatureEvery real world object competes to keep itsown existence and state.現實世界對象總是要保持自己的存在性和狀態的例子：物理世界

59、信息世界.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論現實世界對象的定義與表示現實世界的一個對象本身是一個系統例子：細胞、DNA、人、公司、國家現實世界對象是層譜抽象可定義的層譜抽象定義了對象在各個抽象層譜的功能模塊（每一個模塊有一個支撐結構，即該功能模塊的語法）.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論自我意識的實質：層譜抽象感知與認知對自我的存在性層譜抽象認知（語法）對自身的功能模塊的層譜抽象認知（語義）對自我需求的層譜抽象認知（需求）對自身愿望的層譜抽象認知（愿望）對自身在環境中的確定性和不確定性的認知（不確定性認知）.

60、信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論Law I of LifeA life object is the result of the joint actionsof

61、 certainty and uncertainty.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論Law III of Life生命體通過遺傳來延續存在性，傳遞信息，累計信息信息是可以繼承的信息的繼承、累計信息促

62、進智能生成.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知

64、彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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).信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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).信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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).信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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).信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：

82、知己博弈：謀算理論Law ICompeting is a natural and fundamentalphenomenon of the real world.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論Law IIITo prevent every avoidable conflict or confrontation is the firstprinciple for a rational player.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論Law V1.if an enemy has power,it must release its power敵人有力量是一定要釋放的2.the only rule of real world game is no-rul

85、e現實世界博弈的唯一規則就是沒有規則.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論重大科學問題三：博弈的數學理論是什么？謀算理論：現實世界博弈的數學理論區別于馮諾伊曼（1925）、納什等博弈（1951）基于信息科學數學原理的新理論破解人工智能科學障礙.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論孫子模型1.學習：知彼2.自我意識學習：知己3.博弈設計：策略4.決策：智能決策5.行動：智能控制6.評估：收益理論.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論Learning:知彼Identifying:

86、intruderscompetitorscooperators.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論Hierarchical Abstracting of the realworld-I天時:全局屬性全時屬性.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論Hierarchical Abstracting of the realworld-II環境:地利.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論Aware Learning:知己自我層譜抽象認知:我是誰我從哪里來我有什么，沒有什么我的目標是什

87、么，路線圖是什么，障礙是什么.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論博弈的數學理論：謀算理論謀全局、全時編碼、設計、規劃、創造直覺推理信息科學概念算計算局部推理、邏輯推理謀算原理:信息科學與計算科學相結合的科學思想，孫子兵法的精髓.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論StrategiesMaximizing the enemys uncertaintyprincipleMinimizing the enemys structural force 敵人是可分的Minimizing ones own uncertaint

88、yprincipleMaximizing ones own structural force.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論Force Generating Principleforces are generated from structuresthe system of force unitsthe encoding of the system.信息世界的科學范式信息演算理論學

90、習理論：知彼自我意識理論：知己博弈：謀算理論概念與度量威脅結構能、結構力安全性分布方向熵方向解碼信息方向能、方向力.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論Subjectivity所有的策略、行動都是基于玩家主觀認知與判斷做出的.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論Criterion勝負評判的主、客觀一致性準則：主觀判斷跟真實情況符合者獲勝獲利。.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論智能的實質智能的實質：學習：知彼自我意識：知己謀算.信息世界的科學范式信息演算理論學習理論：知彼自

91、我意識理論：知己博弈：謀算理論謀算：21 世紀科學突破核心思想孫子謀算:中華文明最偉大的科學思想中國科學祖師:孫子-可數學地證明、有用、管幾千年、現在還是最高智慧、涉及很多學科的學科群、21 世紀再顯科學、智慧之光中國科學自信的源泉！習主席講了很多自信，我們還要科學自信.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論思想與思維流程思想：信息方法：抽象層譜抽象中國思想（思維方式）:謀算歐洲思想（思維方式）:計算當代美國思想（思維方式）:算計（科學角度的觀察，供戰略家和智庫參考）.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論總結核心概念

92、:信息數學表示:信息系統：非負矩陣：整個理論體系基于非負矩陣來建立數學度量:信息；結構數學實質:生成信息；解碼信息：提出問題、消除不確定性（回答問題）基本策略:抽象、層譜抽象、計算.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論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.信息世界的科學范式信息演算理論學習理論：知彼自我意識理論：知己博弈：謀算理論Thank You!Email: