Chapter4_Part3 DifferentialHeb learning Differential Competitive learning Tutor:Prof.Gao Reporter:WangYing
Chapter4_Part3 Differential Heb learning & Differential Competitive learning Tutor : Prof. Gao Reporter : WangYing
Review 一P >Signal Heb Learning Law my =-my +S,S, Competitive Learning Law riny =S,[S,-mg ring =-S my +S,S, 2006.10.30
2006.10.30 Review ➢ Signal Heb Learning Law ➢ Competitive Learning Law m m S S ij ij i j = − + m S m S S ij j ij i j = − + m S S m ij j i ij = −
Part I:Differential Heb Learning Learning law m,=-m,+S,S,+S,S Its simpler version m,=-m,+S,S Hebbian correlations promote spurious causal associations among concurrently active units. Differential correlations estimate the concurrent and presumably causal variation among active units. 2006.10.30
2006.10.30 Part I: Differential Heb Learning Learning law Its simpler version Hebbian correlations promote spurious causal associations among concurrently active units. Differential correlations estimate the concurrent and presumably causal variation among active units. m m S S S S ij ij i j i j = − + + m m S S ij ij i j = − +
Differential Heb Learning >Fuzzy Cognitive Maps (FCMs >Adaptive Causal Inference >Klopfs Drive Reinforcement Model >Concomitant Variation as Statistical Covariance >Pulse-Coded DifferentialHebbian Learning 2006.10.30
2006.10.30 Differential Heb Learning ➢ Fuzzy Cognitive Maps (FCMs) ➢ Adaptive Causal Inference ➢ Klopf’s Drive Reinforcement Model ➢ Concomitant Variation as Statistical Covariance ➢ Pulse-Coded Differential Hebbian Learning
Fuz2 y Cognitive Maps(模糊认知映射 Fuzzy signed directed graphs with feedback.It model the world as a collection of classes and causal relations between classes. C:Se瓜of computers C:Profits The directededge efrom causal concept C,to concept C measures fow much C causes C 2006.10.30
2006.10.30 Fuzzy Cognitive Maps (模糊认知映射) Fuzzy signed directed graphs with feedback. It model the world as a collection of classes and causal relations between classes. The directed edge from causal concept to concept measures how much causes . ij e Ci Cj Ci Cj Ci Cj ij e : Sells of computers : Profits Ci Cj
Fuzzy Cognitive Map of South African Politics 外国投资 矿业 雇用黑人 + C 4 白人种族 工作保 黑人种 激进主义 留法律 族联合 8 C 政府管 民族政党 C 种族隔离 理力度 支持者 2006.10.30
2006.10.30 Fuzzy Cognitive Map of South African Politics 外国投资 矿业 雇用黑人 白人种族 激进主义 工作保 留法律 黑人种 族联合 种族隔离 政府管 理力度 民族政党 支持者 1 c + C2 C3 C4 C5 C6 C7 C8 C9 + + + + + + + + + + + + − − − − − − − − − +
Causal Connection Matrix C C2 C3 Ca Cs Co C Cs Co 0 00 011 0 1 0-1011 00110-1 E C; 0 -1 00110 00-1-10 100-10 0- 0-10 01 2006.10.30
2006.10.30 Causal Connection Matrix E = 1 2 3 4 5 6 7 8 9 C C C C C C C C C 0 1 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 − − − − − − − − − C C C C C C C C C 1 2 3 4 5 6 7 8 9
TAM recall process We start with the foreign investment policy C=(100000000) Then CE=(011000011) →(111000011)=C2 The arrow indicates the thresholdoperation with,say,th as the thresholdvalue. So zero causal input produces zero causal output.C,contains C equals 1 because we are testing the foreign-investment policy option.Next C2E=(0121-1-1-141) Next →(11110001)=C3 C3E=(0121-10041) →(111100011)=C3 So is afixed point of the FCM dynamical system. 2006.10.30
2006.10.30 TAM recall process C2 C1 We start with the foreign investment policy Then The arrow indicates the threshold operation with, say, ½ as the threshold value. So zero causal input produces zero causal output. contains equals 1 because we are testing the foreign-investment policy option. Next Next So is a fixed point of the FCM dynamical system. C1 = (1 0 0 0 0 0 0 0 0) C E1 = (0 1 1 0 0 0 0 1 1) →(1 1 1 0 0 0 0 1 1) = C2 C E2 = − − − (0 1 2 1 1 1 1 4 1) →(1 1 1 1 0 0 0 1 1) = C3 C E3 = − (0 1 2 1 1 0 0 4 1) → = (1 1 1 1 0 0 0 1 1) C3 C3
Strengths and weafnesses of FCM Advantages Experts:1.represent factual and evaluative concepts in an interactive framework;2.quicky draw FCMpictures or respond to questionnaires; 3.consent or dissent to the local causal structure and perhaps the global equilibrations. © FCM Fnowledge representation and inferencing structure:reduces to simple vector-matrixoperations,favors integrated-circuit implementation,and allows extension to neural statistical or dynamical systems techniques. ①isadvantages It equally encodes the expert's knowledge or ignorance,wisdom or prejudice. Since different experts differin how they assign causal strengths to edges, and in which concepts they deem causally relevant,the FCM seems merely to encode its designer's biases,and may not even encode them accurately. 2006.10.30
2006.10.30 Strengths and weaknesses of FCM ➢ Advantages ☺Experts: 1.represent factual and evaluative concepts in an interactive framework; 2.quickly draw FCM pictures or respond to questionnaires; 3.consent or dissent to the local causal structure and perhaps the global equilibrations. ☺FCM knowledge representation and inferencing structure: reduces to simple vector-matrix operations, favors integrated-circuit implementation, and allows extension to neural, statistical, or dynamical systems techniques. ➢ Disadvantages It equally encodes the expert’s knowledge or ignorance, wisdom or prejudice. Since different experts differ in how they assign causal strengths to edges, and in which concepts they deem causally relevant, the FCM seems merely to encode its designer’s biases, and may not even encode them accurately
Combination of FCMs We combined arbitrary FCM connection matrices E.Eby adding augmented)FCMmatricesF...We add the F pointwise to yield the combined FCM matrix F: F=∑E Some experts may be more credible than others.We can weight each expert with a nonnegative credibility weight @by multiplicatively weighting the expert's augmented FCM matrix F=∑@，E Adding FCM matrices represents a simple form of causal learning. 2006.10.30
2006.10.30 Combination of FCMs We combined arbitrary FCM connection matrices by adding augmented(增广)FCM matrices . We add the pointwise to yield the combined FCM matrix : Some experts may be more credible than others. We can weight each expert with a nonnegative credibility weight by multiplicatively weighting the expert’s augmented FCM matrix: Adding FCM matrices represents a simple form of causal learning. 1 ,..., E Ek 1 ,..., F Fk Fi F i i F F = i i i i F F =