Aprendizagem Simbólica e Sub-Simbólica!

Transcription

1 Aprendizagem Simbólica e Sub-Simbólica! Andreas Wichert!! DEIC! (Página da cadeira: Fenix)!! Objectivo Geral! n Ao contrário de muitas abordagens estatísticas de aprendizagem através de máquinas, que lidam com dados não estruturados, a aprendizagem através de agentes lida com dados estruturados! n Durante a aprendizagem, a estrutura dos dados influencia o processo de aprendizagem! 1

2 Objectivo Geral! n A formulação lógica do processo de aprendizagem será examinada e abordagens diferentes da aprendizagem simbólica através de máquinas, como a aprendizagem com base na explicação ou a aprendizagem com base em casos, serão demonstradas! Objectivo Geral! n Na segunda parte das aulas iremos lidar com redes neurais artificiais hierárquicas! n Em redes neurais hierárquicas, os níveis de representação nas camadas exibem uma estrutura hierárquica! n O objectivo de tal estrutura de representação hierárquica baseia-se no facto de que a posição do símbolo no padrão de introdução torna-se menos importante, por atravessar as camadas sucessivas mais profundamente! 2

3 n Organization! n Program! n Introduction! Corpo docente! n Andreas Wichert - Teóricas! n andreas.wichert@tecnico.ulisboa.pt!!! n andreas.wichert@inesc-id.pt! 3

4 Organização das aulas! n Teóricas:! n Matéria (slides baseados no livro e artigos e...)! n Práticas! n Presentation! n Report! Avaliação! n Presentation / Homeworks (40%)! n +! n Report (60%) 4

5 Bibliografia, AI Books! n Artificial Intelligence: A Modern Approach by Stuart Russel and Peter Norvig, Prentice Hall; 2 edition (December 30, 2002)! n Luger, George F. and Stubblefield, William A. Artificial Intelligence, Structures and Strategies for Complex Problem Solving. Addison-Wesley, 2004! n Partick Henry Winston. Artificial Intelligence. Addison-Wesley, 1992! n Simon Haykin, Neural Networks, Secend edition Prentice Hall,

6 n Hofstadter, Douglas. Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought. Basic Books. 1995! n Robert Hecht-Nielsen. Neurocomputing. Addison-Wesley. 1989! n Fukushima, K. Neocognitron: A hierarchical neural network capable of visual pattern recognition. Neural Networks. 1, ! 6

7 Programa! n 1. Supervised statistical Learning! n 2. A Logical Formulation of Learning! n! Learning by Analyzing Differences! n! Learning by Explaining Experience! n 4. n! Knowledge and Learning!!Reinforcement Learning! n 5. Models of Cognition and Learning! n 6. Case Based Learning! n Copycat! n 7. Brain! n Visual System! What is Learning?! n Difficult to define! n to gain knowledge, or understanding of same skill, by study, instruction or experience! n modification of behavioral tendency by experience! n What is machine Learning?! 7

8 What is machine Learning?! n Parallels between animals and machine learning! n Many techniques derived from efforts of psychologist / biologists to make more sense animal learning through computational models! Machine Learning! n Changes in the system that perform tasks associated with AI! n Recognition! n Prediction! n Planning! n Diagnosis! 8

9 Ai agent! Learning Input output functions! 9

10 Feature / Vector space! n Sample!!! x = " $ $ # $ % $ x 1 x x d { x (n ) } x (1), x!(2),.., x!(k),..,! R d! x y! d = (x i y i ) 2 i=1 Norm! n x 0 equality only if x=0! n α x = α x! n x 1 +x 2 x 1 + x 2! n l p norm!! # x p = % $ d i=1 x i p & ( ' 1 p 10

11 Metric! n d(x,y) 0 equality holds only if x=y! n d(x,y) = d(y,x)! n d(x,y) d(x,z)+d(z,y)! d 2 (! x,! z ) = $ & % d i=1 ( ) 2 x i z i ' ) ( 1 2 Learning Input output functions! n Supervised! n With a teacher! n Unsupervised! n Without a teacher! 11

12 k-means Clustering / unsupervised learning!! d 2 (! x,! z ) = $ & % d i=1 ( ) 2 x i z i Cluster centers c 1,c 2,.,c k with clusters C 1,C 2,.,C k! ' ) ( 1 2 Error! k E = d 2 (x,c j ) 2 j=1 x C j n The error function has a local minima if,! 12

13 k-means Example (K=2)! x x x x Pick seeds Reassign clusters Compute centroids Reasssign clusters Compute centroids Reassign clusters Converged! Inner-product! net =<! w,! x >=! w! x cos(θ) net = n i=1 w i x i n A measure of the projection of one vector onto another! 13

14 Gradient Descent / supervised learning! n To understand, consider simpler linear unit, where! o = n i= 0 w i x i n Let's learn w i that minimize the squared error, D={(x 1,t 1 ),(x 2,t 2 ),..,(x d,t d ),..,(x m,t m )}! (t for target)! Error for different hypothesis, for w 0 and w 1 (dim 2)! 14

15 n We want to move the weight vector in the direction that decrease E! w i =w i +Δw i!!!! w=w+δw! Differentiating E! 15

16 Update rule for gradient decent! Δw i = η d D (t d o d )x id Back-propagation! n The algorithm gives a prescription for changing the weights w ij in any feedforward network to learn a training set of input output pairs {x d,t d }! n We consider a simple two-layer network! 16

17 Back-propagation! n The algorithm gives a prescription for changing the weights w ij in any feedforward network to learn a training set of input output pairs {x d,t d }! n We consider a simple two-layer network! Expressive Capabilities of ANNs! n Boolean functions:! n Every boolean function can be represented by network with single hidden layer! n but might require exponential (in number of inputs) hidden units! n Continuous functions:! n Every bounded continuous function can be approximated with arbitrarily small error, by network with one hidden layer [Cybenko 1989; Hornik et al. 1989]! n Any function can be approximated to arbitrary accuracy by a network with two hidden layers [Cybenko 1988].! 17

18 Knowledge in Learning! n Entailment constraint :!! Hypothesis Descriptions = Classifications! Cumulative Learning Representation n Symbolic tokens are necessarily represented by physical phenomena n thoughts are represented by the electrical and biochemical states of the neural network n There is an intermixing of the physical sciences with the proper subject matter of information science... n Information can be presented in a variety of forms which differ inessential from one another Natural language Symbols Acoustic speech Pictures 18

19 n Information is what remains after one abstracts from the material aspect of the physical reality... n How to do it? Chess n n Game tree in chess playing, which determines all possible consequences of alternative plays has a combinatorial complexity which surpasses the ability of any computing machine to explore it completely The complexity is however reduced by selectively omitting most of the pathways (heuristics) 19

20 n n The omitted ones are expected to be unproductive Selective omission in context of a decision problem which involves searching through a complex tree the application of heuristics procedures n AI-Example: Blocks World planing with and without similarity heuristic similarity to the target state represented as picture 20

21 What is an A?! n What makes something similar to something else (specifically what makes, for example, an uppercase letter 'A' recognisable as such)! n Metamagical Themas, Douglas Hoffstader, Basic Books, 1985! 21

22 n What is the essence of dogness or house-ness?! n What is the essence of 'A'-ness?! n What is the essence of a given person's face, that it will not be confused with other people's faces?! n How to convey these things to computers, which seem to be best at dealing with hardedged categories--categories having crystalclear, perfectly sharp boundaries?! Selective Omission of Information n n Sensory data is corrupted and modified by sensing organism in ways which greatly reduce its quantity and substantially modify its original form Retaining essential information 22

23 The Library of Babel n The universe (which others call the Library) is composed of an indefinite and perhaps infinite number of hexagonal galleries, with vast air shafts between, surrounded by very low railings n Jorge Luis Borges ( ) n The books contain every possible ordering of just a few basic characters (letters, spaces and punctuation marks)! n Though the majority of the books in this universe are pure gibberish, the library also must contain, somewhere, every coherent book ever written, or that might ever be written, and every possible permutation or slightly erroneous version of every one of those books! 23

24 n The library must contain all useful information, including predictions of the future, biographies of any person, and translations of every book in all languages! n Despite - indeed, because of -this glut of information, all books are totally useless to the reader! n Borges speculates on the existence of the "Crimson Hexagon", containing a book that contains the log of all the other books; the librarian who reads it is akin to God! 24

25 n The Library contains books! n Just one "authentic" volume, together with all those variants containing only a handful of misprints, would occupy so much space that they would fill the known universe! Constraints! n In a language! n Some letters are more frequent then others! n Some combination of letters are less probable! 25

26 A general model of the learning process! constraints An Example (Patrick Winston-1975)! 26

27 An Example (Patrick Winston-1975)! Next! n Supervised statistical machine learning! 27