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Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
Behavior Models
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Behavior Models
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Behavior Models

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  • 1.  Instructor: David A. Townsend  Email:  Class Web Page:
  • 2. RESCORLA-WAGNER THEORY: BACKGROUND  Research by Rescorla and Kamin requires a change in our conception of conditioning.  Animals do not evaluate CS-US pairings in isolation.  Evaluation occurs against a background that includes: unpaired presentations of CS and US, or presentations of other CSs, or general experimental context.  Conditioning is most likely to occur when evaluation of entire situation reveals that a CS is best available predictor of US.
  • 3. RESCORLA-WAGNER THEORY: BACKGROUND  This view of Pavlovian conditioning makes conditioning process appear much more complex than it had seemed.  How do animals do it?  By what means do animals keep track of CSs and USs, estimate probabilities, compute probability differences, and make CRs to CS?  If such calculations do occur, then animals are likely to make them automatically.  We need an account of the mechanism by which such automatic calculation might occur.
  • 4. RESCORLA-WAGNER THEORY: BACKGROUND  In last 30 years, many different theories have been advanced to explain rich details of Pavlovian conditioning.  Most influential account was that of Robert A. Rescorla and Allan R. Wagner in 1972.  All later theories have been responses to shortcomings of Rescorla-Wagner account.  So, we will focus on Rescorla-Wagner theory.
  • 5. RESCORLA-WAGNER THEORY: PRELUDE  Kamin’s blocking effect set stage for RescorlaWagner model.  Blocking effect suggested to Kamin that USs were only effective when they were SURPRISING or unpredicted by CSs.  However, USs were not effective when they were unsurprising or predicted by CSs.  Added CS was not associated with any change in US.
  • 6. RESCORLA-WAGNER THEORY: OVERVIEW  Rescorla-Wagner theory explains complex contingency analysis in terms of simple associations of the sort Pavlov envisioned.  It can account for most standard conditioning phenomena in Chapter 3 as well as many newer phenomena in Chapter 4.  Theory is also precise; specified in such clear detail that one can derive predictions about behavior in untested experimental situations. Mathematically
  • 7. RESCORLA-WAGNER THEORY: TUTORIALS If you need help, then please consult: http://psy.uq.oz.au/~landcp/PY269/rwmodel/index.html http://www.biols.susx.ac.uk/home/Martin_ Yeomans/Learning/Lecture6.html http://www.psych.ualberta.ca/~msnyder/Ac ademic/Psych_281/C5/Ch5page.html
  • 8. RESCORLA-WAGNER THEORY: ACQUISITION  Standard conditioning curves are negatively accelerated.  Changes in conditioning strength are very substantial early in training.  But, as training proceeds, a leveling-off point, or asymptote, is approached.  Generally speaking, changes in strength of conditioning get smaller with each trial.
  • 9. RESCORLA-WAGNER THEORY: ACQUISITION  Negatively accelerated learning curve suggests that organism does not profit equally from each training trial.  How much one profits depends on how much one already knows: When one knows nothing, profits are substantial (US surprise is high). When one knows a great deal, profits from further trials are small (US surprise is low).
  • 10. RESCORLA-WAGNER THEORY: ACQUISITION  Rather than learning a fixed amount with each trial, one learns a fixed proportion of difference between one’s present level of learning and maximum possible.  As difference gets smaller (as one learns more), amount of new learning produced by further trials gets smaller.  Rescorla-Wagner model simply builds in a mathematical expression that conforms to negatively accelerated learning function.
  • 11. RESCORLA-WAGNER THEORY: ACQUISITION  Here is the equation: ∆Vn = K( — Vn-1)  V, associative strength, is measure of learning.  It is a theoretical quantity.  It is not equivalent to magnitude or probability of any particular CR.  But, it is assumed to be closely related to such measures of conditioned responding.
  • 12. RESCORLA-WAGNER THEORY: ACQUISITION  ∆Vn = K( — Vn-1)  K reflects salience of CS.  K can vary between 0 and 1 (0 ≤ K ≤ 1).  Bigger K, bigger change in V on any given trial.  Thus, salient stimuli mean large Ks, which mean large ∆Vs, which mean large changes in association from trial to trial. Intensity Sensory modality Organism Types of US’s employed ( belongingness)
  • 13. RESCORLA-WAGNER THEORY: ACQUISITION  ∆Vn = K( — Vn-1)  indicates that different USs support different maximum levels of conditioning.  Asymptote of conditioning will vary with US; different asymptotes are reflected by different s.  More intense US, higher asymptote of conditioning, and higher .  is always equal to or greater than 0 ( ≥ 0).
  • 14. RESCORLA-WAGNER THEORY: ACQUISITION  ∆Vn = K( — Vn-1)  Change in strength on Trial n (∆Vn) is proportional to difference between and prior associative strength Vn-1.  Because V grows from trial to trial, quantity ( Vn-1) gets smaller and smaller, so ∆Vn also gets smaller and smaller, generating a negatively accelerated learning curve.  Eventually, V will equal , so that ( - Vn-1) will be 0, and conditioning will be complete (asymptote will be reached).
  • 15. ∆Vn = K( — Vn-1) ∆ (change in) Delta  V, associative strength, is measure of learning  K reflects salience of CS.  ( Lambda) indicates that different USs support different maximum levels of conditioning. Change in strength on Trial n (∆Vn) is proportional to difference between and Vn-1 prior associative strength.
  • 16. Acquisition Trials First conditioning trial: Light (CS) is paired with shock (US) ∆Vn= light (CS)=0 k = .20 = associated strength of shock = 100 ∆Vn = K( — Vn-1) ∆ (change in) Delta V, associative strength, is measure of learning K reflects salience of CS and US. ( Lambda) indicates that different USs support different maximum levels of conditioning. Change in strength on Trial n (∆Vn) is proportional to difference between and Vn-1 prior associative strength. First Trial ∆Vn=k( -Vn-1) ∆Vn= .20(100-0) ∆Vn = .20 units
  • 17. ∆Vn = K( — Vn-1) Acquisition Trials First conditioning trial: Light (CS) is paired with shock (US) ∆Vtotal= light (CS)=0 k = .20 = associated strength of shock = 100 ∆ (change in) Delta V, associative strength, is measure of learning K reflects salience of CS and US. ( Lambda) indicates that different USs support different maximum levels of conditioning. Change in strength on Trial n (∆Vn) is proportional to difference between and Vn-1 prior associative strength. Second Trial ∆Vn=k( -Vn-1) ∆Vn= .20(100-20) ∆Vn = .16 units
  • 18. ∆Vn = K( — Vn-1) Acquisition Trials First conditioning trial: Light (CS) is paired with shock (US) ∆Vtotal= light (CS)=0 k = .20 = associated strength of shock = 100 ∆ (change in) Delta V, associative strength, is measure of learning K reflects salience of CS and US. ( Lambda) indicates that different USs support different maximum levels of conditioning. Change in strength on Trial n (∆Vn) is proportional to difference between and Vn-1 prior associative strength. Third Trial ∆Vn=k( -Vn-1) ∆Vn= .20(100-36) ∆Vn = .12.8 units
  • 19. ∆Vn = K( — Vn-1) Acquisition Trials First conditioning trial: Light (CS) is paired with shock (US) ∆Vtotal= light (CS)=0 k = .20 = associated strength of shock = 100 ∆ (change in) Delta V, associative strength, is measure of learning K reflects salience of CS and US. ( Lambda) indicates that different USs support different maximum levels of conditioning. Change in strength on Trial n (∆Vn) is proportional to difference between and Vn-1 prior associative strength. Forth Trial ∆Vn=k( -Vn-1) ∆Vn= .20(100-48.8) ∆Vn = .10.2 units N= trial4, N-1= trial 3
  • 20. Rescorla-Wagner Model  Calculations from the RescorlaWagner model show a mathematical relationship to the process of conditioning 60 50 40 30 Vtotal 20 10 0 trial 0 trial 2 trail 4
  • 21. Rescorla-Wagner Theory (1972)  Organisms only learn when events violate their expectations (like Kamin’s surprise hypothesis)  Expectations are built up when ‘significant’ events follow a stimulus complex  These expectations are only modified when consequent events disagree with the composite expectation  Surprise
  • 22. First Conditioning Trial Trial 1 K ( - Vn-1 ) .5 * 100 - = 0 ∆Vn = 50 Associative Strength (V) 100 80 ∆Vn = K( — Vn-1) 60 50 40 20 0 0 0 1 2 3 4 Trials 5 6 7 8 ∆ (change in) Delta V, associative strength, is measure of learning K reflects salience of CS and US. ( Lambda) indicates that different USs support different maximum levels of conditioning. Change in strength on Trial n (∆Vn) is proportional to difference between and Vn-1 prior associative strength.
  • 23. Second Conditioning Trial K ( - Vn-1 ) .5 * 100 -50 ∆Vn 25 = = 100 Associative Strength (V) Trial 2 80 75 60 50 40 20 0 0 0 1 2 3 4 Trials 5 6 7 8
  • 24. Third Conditioning Trial K ( - Vn-1 ) .5 * 100 -75 ∆Vn 12.5 = = 100 Associative Strength (V) Trial 3 87.5 80 75 60 50 40 20 0 0 0 1 2 3 4 Trials 5 6 7 8
  • 25. 4th Conditioning Trial K ( - Vn-1 ) c (Vmax .5 * 100 - 87.5 80 ∆Vn ∆Vcs 6.25 = = = Vall) 87.5 100 Associative Strength (V) Trial Trial 4 93.75 75 60 ∆Vcs = c (Vmax – Vall) 50 40 Vall 20 0 0 0 1 2 3 4 Trials 5 6 7 8
  • 26. 5th Conditioning Trial K ( - Vn-1 ) .5 * 10 - 93.75 100 Associative Strength (V) Trial 5 87.5 80 = = 96.88 93.75 75 60 50 40 20 0 0 0 1 2 3 4 Trials 5 6 7 8 ∆Vn 3.125
  • 27. 6th Conditioning Trial K ( - Vn-1 ) .5 * 100 - 96.88 100 Associative Strength (V) Trial 6 87.5 80 = = 96.8898.44 93.75 75 60 50 40 20 0 0 0 1 2 3 4 Trials 5 6 7 8 ∆Vn 1.56
  • 28. 7th Conditioning Trial Trial 7 K ( - Vn-1 ) .5 * 100 - 98.44 Associative Strength (V) 100 87.5 80 = = 96.8898.4499.22 93.75 ∆Vn = K( — Vn-1) 75 60 50 40 20 0 0 0 1 2 ∆Vn .78 3 4 Trials 5 6 7 8 ∆ (change in) Delta V, associative strength, is measure of learning K reflects salience of CS and US. ( Lambda) indicates that different USs support different maximum levels of conditioning. Change in strength on Trial n (∆Vn) is proportional to difference between and Vn-1 prior associative strength.
  • 29. 8th Conditioning Trial K ( - Vn-1 ) .5 * 1 - 99.22 100 Associative Strength (V) Trial 8 87.5 80 ∆Vn .39 = = 93.75 96.8898.44 99.22 99.61 75 60 50 40 20 0 0 0 1 2 3 4 Trials 5 6 7 8
  • 30. 1st Extinction Trial Trial 1 K ( - Vn-1 ) .5 * 0 -99.61 ∆Vn -49.8 = = Extinction 100 80 60 40 Vall 20 0 0 1 2 3 4 Trials 5 6 7 8 Associative Strength (V) Associative Strength (V) Acquisition 100 99.61 80 60 49.8 40 20 0 0 1 2 3 Trials 4 5 6
  • 31. 2nd Extinction Trial K ( - Vn-1 ) .5 * 0 -49.8 Acquisition 60 40 93.75 87.5 80 100 Associative Strength (V) Associative Strength (V) 100 75 80 60 50 40 Vall 20 20 0 0 0 0 0 1 1 2 2 3 3 4 4 Trials Trials 5 5 6 6 7 7 8 8 ∆Vn -24.9 = = Extinction 96.88 98.44 99.22 99.61 Associative Strength (V) Trial 2 100 99.61 80 60 49.8 40 24.9 20 0 0 1 2 3 Trials 4 5 6
  • 32. Extinction Trials Trial 3 K ( Vn-1 ) .5 * 0 12.45 Less and Less surprising = = ∆Vn -12.46 4 .5 * 0 - 6.23 = -6.23 5 .5 * 0 - 3.11 = -3.11 6 .5 * 0 - 1.56 = -1.56
  • 33. Hypothetical Acquisition & Extinction Curves with K=.5 and = 100 100 Extinction Associative Strength (V) Associative Strength (V) Acquisition 80 60 40 20 100 99.61 80 60 49.8 40 24.9 20 12.45 0 0 0 1 2 3 4 Trials 5 6 7 8 6.23 0 1 2 3 Trials 4 3.11 5 1.56 6
  • 34. Acquisition & Extinction Curves with c=.5 vs. c=.2 ( = 100) Extinction 120 Associative Strength (V) Associative Strength (V) Acquisition 100 80 60 40 20 0 0 1 2 3 4 Trials 5 6 7 8 120 100 80 c=.5 60 c=.2 40 c=.5 c=.2 20 0 0 1 2 3 Trials 4 5 6
  • 35. RESCORLA-WAGNER THEORY: COMPETITION  Key feature of Rescorla-Wagner model is how it explains conditioning with compound stimuli comprising two or more elements.  Associative strength of a compound stimulus is assumed to equal the sum of associative strengths of elements.  VAX = VA + VX  Here, A and X may have different saliences, K and M, respectively.
  • 36. ∆Vn = K( — Vn-1)  ∆ (change in) Delta  V, associative strength, is measure of learning  K reflects salience of CS.  ( Lambda) indicates that different USs support different maximum levels of conditioning.  Change in strength on Trial n (∆Vn) is proportional to difference between and  Vn-1 prior associative strength. A,X symbols used for multiple CS’s Salience with multiple CS’s: A=K, X=M
  • 37. RESCORLA-WAGNER THEORY: OVERSHADOWING  VAX = VA + VX  How can theory account for overshadowing?  With equally salient stimuli, VX would attain only .50 rather than 1.00 if X alone were trained-mutual overshadowing.  Increases in salience of A would further reduce VX from .50 toward .00.  If salience of A (K) is very high and salience of X (M) is very low, then overshadowing should be complete.
  • 38. Eyeblink Conditioning: OVERSHADOWING Training: Tone/light + Shock Tone = Eyeblink  CR Light = ? No CR to light Corneal Air Puff Elicits Eyeblink Response Corneal Air Puff Given with Tone Tone Given Alone Elicits Eyeblink Response
  • 39. Overshadowing:  Overshadowing  Whenever there are multiple stimuli or a compound stimulus, then ∆Vn = Vcs1 (K) + Vcs2 (M) ∆Vn = K( — Vn-1)  Trial 1: ∆Vnoise = .2 (100 – 0) = (.2)(100) = 20 ∆Vlight = .3 (100 – 0) = (.3)(100) = 30 Total ∆Vn = ∆ (K)Vnoise + ∆Vlight = 0 +20 +30 =50  Trial 2: Noise= 30 ∆Vnoise = .2 (100 – 50) = (.2)(50) = 10 ∆Vlight = .3 (100 – 50) = (.3)(50) = 15 Light= 45 Total ∆Vn = Vn-1 + ∆Vnoise + ∆Vlight = 50+10+15=75
  • 40. Overshadowing Trial 1: VA = .40(100 – 0) = 40 Vx = .10(100 – 0) = 10 Trial 2: VA = .40(100 – 50) = 20 Vx = .10(100 – 50) = 5 T2: A=60 X=15
  • 41. RESCORLA-WAGNER THEORY: BLOCKING  VAX = VA + VX  How would theory account for blocking?  With equally salient stimuli, VX would be only .50 rather than 1.00 if AX only were trained.  Prior training with A would further reduce VX, because VA would already be substantial before AX trials were introduced.  Extensive training with A should lead to complete blocking of X.
  • 42. Blocking Group Phase 1 Experimental A Group (blocking) Control Group US Nothing Phase 2 Phase 3 AB US Test B AB US Test B Same # trials Contiguity Contingency
  • 43. RESCORLA-WAGNER THEORY: BLOCKING A Associative Strength (V) Acquisition 100 80 60 40 X 20 0 0 1 2 3 4 Trials 5 6 7 8 ?
  • 44. The Rescorla-Wagner associative model of conditioning is based upon four assumptions that refer to the process by which the CS and UC gain associative strength  (1) a particular US can only support a specific level of conditioning,  (2) associative strength increases with each reinforced trial, but depends upon prior conditioning,  (3) particular CSs and US can support different rates of conditioning and  (4) when two or more stimuli are paired with the UC, the stimuli compete for the associative strength available for conditioning.
  • 45. RESCORLA-WAGNER THEORY: CONTINGENCY  Theory can also explain animals’ ability to detect different degrees of contingency between CS and US.  Recall that fear of a CS for shock is a direct function of contingency between CS and US.  When contingency between events is zero, no learning of fear to CS occurs.  But, does a rat really compute probabilities to form a judgment of contingency?  Not according to Rescorla-Wagner model.
  • 46. RESCORLA-WAGNER THEORY: CONTINGENCY  To explain contingency sensitivity, Rescorla-Wagner theory makes use of background or contextual stimuli as Pavlovian predictors. (Context = A discrete CS)  Such contextual stimuli themselves can compete with CSs for association with USs.  Case of random presentations of CS and US provides a useful illustration.
  • 47. RESCORLA-WAGNER THEORY: CONTINGENCY  Random training can be seen to represent blocking with two kinds of trials:  A (context)-US [relatively frequent]  AX (context plus CS)-US [relatively infrequent]  As animal receives frequent A-US pairings, VA (and hence VAX) approaches asymptote.  As VAX approaches asymptote from frequent A-US pairings, VX can receive no further increments and little responding to X will be observed despite occasional AX-US pairings. CS unpaired US 0.5 s time
  • 48. RESCORLA-WAGNER THEORY: CONTINGENCY  So, blocking is basic to effect of random CS and US presentations.  Contextual cues are present whenever US occurs in absence of CS; contextual cues thus acquire excitatory strength.  On trials when CS is paired with US by chance, contextual cues are present as well.  So, context replaces Stimulus A in blocking example and randomly presented CS replaces Stimulus X.
  • 49. RESCORLA-WAGNER THEORY: INHIBITION  In Chapter 4, we saw that conditioning can be either excitatory or inhibitory.  At first glance, it is not obvious that RescorlaWagner theory can explain inhibition.  Inhibition requires a V that is less than zero; but, none of the variables in the equation can ever be less than zero. How can V become negative when none of the terms contributing to V can be negative?
  • 50. Time to Leave:
  • 51. Y Axis 1 Zero 0 X Axis

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