1. CS621: Artificial Intelligence Lecture 27: Backpropagation applied to recognition problems; start of logic Pushpak Bhattacharyya Computer Science and Engineering Department IIT Bombay

2. Backpropagation algorithm Fully connected feed forward network Pure FF network (no jumping of connections over layers) Hidden layers Input layer (n i/p neurons) Output layer (m o/p neurons) j i w ji ….

3. General Backpropagation Rule General weight updating rule: Where for outermost layer for hidden layers

4. Local Minima Due to the Greedy nature of BP, it can get stuck in local minimum m and will never be able to reach the global minimum g as the error can only decrease by weight change.

5. Momentum factor 1.Introduce momentum factor.  Accelerates the movement out of the trough.  Dampens oscillation inside the trough.  Choosing β : If β is large, we may jump over the minimum.

6. Symmetry breaking If mapping demands different weights, but we start with the same weights everywhere, then BP will never converge. w 2 =1w 1 =1 θ = 0.5 x1x2x1x2 x1x2x1x2 x1x1 x2x2 1.5 11 XOR n/w: if we s started with identical weight everywhere, BP will not converge

7. Backpropagation Applications

8. Problem defined Decided by trial error Problem defined O/P layer Hidden layer I/P layer Feed Forward Network Architecture

9. Digit Recognition Problem Digit recognition: – 7 segment display – Segment being on/off defines a digit 1 2 3 6 7 4 5

10. 9 O 8 O 7 O... 2 O 1 O Hidden layer Full connection 7 O 6 O 5 O... 2 O 1 O Seg-7 Seg-6 Seg-5 Seg-2 Seg-1

11. Example - Character Recognition Output layer – 26 neurons (all capital) First output neuron has the responsibility of detecting all forms of ‘A’ Centralized representation of outputs In distributed representations, all output neurons participate in output

12. An application in Medical Domain

13. Expert System for Skin Diseases Diagnosis Bumpiness and scaliness of skin Mostly for symptom gathering and for developing diagnosis skills Not replacing doctor’s diagnosis

14. Architecture of the FF NN 96-20-10 96 input neurons, 20 hidden layer neurons, 10 output neurons Inputs: skin disease symptoms and their parameters – Location, distribution, shape, arrangement, pattern, number of lesions, presence of an active norder, amount of scale, elevation of papuls, color, altered pigmentation, itching, pustules, lymphadenopathy, palmer thickening, results of microscopic examination, presence of herald pathc, result of dermatology test called KOH

15. Output 10 neurons indicative of the diseases: – psoriasis, pityriasis rubra pilaris, lichen planus, pityriasis rosea, tinea versicolor, dermatophytosis, cutaneous T-cell lymphoma, secondery syphilis, chronic contact dermatitis, soberrheic dermatitis

16. Training data Input specs of 10 model diseases from 250 patients 0.5 is some specific symptom value is not knoiwn Trained using standard error backpropagation algorithm

17. Testing Previously unused symptom and disease data of 99 patients Result: Correct diagnosis achieved for 70% of papulosquamous group skin diseases Success rate above 80% for the remaining diseases except for psoriasis psoriasis diagnosed correctly only in 30% of the cases Psoriasis resembles other diseases within the papulosquamous group of diseases, and is somewhat difficult even for specialists to recognise.

18. Explanation capability Rule based systems reveal the explicit path of reasoning through the textual statements Connectionist expert systems reach conclusions through complex, non linear and simultaneous interaction of many units Analysing the effect of a single input or a single group of inputs would be difficult and would yield incor6rect results

19. Explanation contd. The hidden layer re-represents the data Outputs of hidden neurons are neither symtoms nor decisions

21. Discussion Symptoms and parameters contributing to the diagnosis found from the n/w Standard deviation, mean and other tests of significance used to arrive at the importance of contributing parameters The n/w acts as apprentice to the expert

22. Exercise Find the weakest condition for symmetry breaking. It is not the case that only when ALL weights are equal, the network faces the symmetry problem.

23. Logic

24. Logic and inferencing Vision NLP Expert Systems Planning Robotics  Search  Reasoning  Learning  Knowledge Obtaining implication of given facts and rules -- Hallmark of intelligence

25. Inferencing through − Deduction (General to specific) − Induction (Specific to General) − Abduction (Conclusion to hypothesis in absence of any other evidence to contrary) Deduction Given:All men are mortal (rule) Shakespeare is a man (fact) To prove:Shakespeare is mortal (inference) Induction Given:Shakespeare is mortal Newton is mortal (Observation) Dijkstra is mortal To prove:All men are mortal (Generalization)

26. If there is rain, then there will be no picnic Fact1: There was rain Conclude: There was no picnic Deduction Fact2: There was no picnic Conclude: There was no rain (?) Induction and abduction are fallible forms of reasoning. Their conclusions are susceptible to retraction Two systems of logic 1) Propositional calculus 2) Predicate calculus

27. Propositions − Stand for facts/assertions − Declarative statements − As opposed to interrogative statements (questions) or imperative statements (request, order) Operators => and ¬ form a minimal set (can express other operations) - Prove it. Tautologies are formulae whose truth value is always T, whatever the assignment is

28. Model In propositional calculus any formula with n propositions has 2 n models (assignments) - Tautologies evaluate to T in all models. Examples: 1) 2) - e Morgan with AND

29. Semantic Tree/Tableau method of proving tautology Start with the negation of the formula α-formula β-formula α-formula - α - formula - β - formula - α - formula

30. Example 2: BC BC Contradictions in all paths X α-formula (α - formulae) (β - formulae) (α - formula)

31. A puzzle (Zohar Manna, Mathematical Theory of Computation, 1974) From Propositional Calculus

32. Tourist in a country of truth-sayers and liers Facts and Rules: In a certain country, people either always speak the truth or always lie. A tourist T comes to a junction in the country and finds an inhabitant S of the country standing there. One of the roads at the junction leads to the capital of the country and the other does not. S can be asked only yes/no questions. Question: What single yes/no question can T ask of S, so that the direction of the capital is revealed?

33. Diagrammatic representation S (either always says the truth Or always lies) T (tourist) Capital

34. Deciding the Propositions: a very difficult step- needs human intelligence P: Left road leads to capital Q: S always speaks the truth

35. Meta Question: What question should the tourist ask The form of the question Very difficult: needs human intelligence The tourist should ask – Is R true? – The answer is “yes” if and only if the left road leads to the capital – The structure of R to be found as a function of P and Q

36. A more mechanical part: use of truth table PQS’s Answer R TTYesT TF F FTNoF FF T

37. Get form of R: quite mechanical From the truth table – R is of the form (P x-nor Q) or (P ≡ Q)

38. Get R in English/Hindi/Hebrew… Natural Language Generation: non-trivial The question the tourist will ask is – Is it true that the left road leads to the capital if and only if you speak the truth? Exercise: A more well known form of this question asked by the tourist uses the X-OR operator instead of the X-Nor. What changes do you have to incorporate to the solution, to get that answer?