Contingency & The Rescorla-Wagner Model

Question 1

What is contiguity?

Answer 1

• Contiguity was the first principle identified by the Associationists
• Contiguity refers to the connectedness in time and space of items
―The more closely together (contiguous) in space and time two items occur, the more likely they will be associated
• As the delay increases between the CS-US, the rate of learning decreases (….and the CS also becomes less useful as a predictor of the US)

Question 2

Is contiguity sufficient?

Answer 2

Its important but not sufficient
• Kamin’s seminal study on blocking also showed that contiguity alone wasn’t sufficient
• Delay and Trace conditioning demonstrate that contiguity is
necessary for classical conditioning
• but simultanteous and backward conditioning and the
phenomena of blocking demonstrate it is not sufficient
• There must also be a consistent relationship between the CS and the US
• The CS must provide reliable information about the US

Question 3

What is contingency?

Answer 3

• Contingency refers to the predictability of the occurrence of one stimulus from the presence of another
• Increasing the delay between the CS and US results in the CS becoming less useful as a predictor of the US
• Contingency is the probabilistic relationship with the US given that a CS has occurred
• This probabilistic relationship between the occurrence of the US and the CS is the basis of a prominent mathematical model of classical conditioning- The Rescorla-Wagner Model

Question 4

What is the contingency theory?

Answer 4

• Contingency theory - a conditioned response (CR) develops when the conditioned stimulus (CS) is able to predict the occurrence of the unconditioned stimulus (US).
• After repeated CS-US pairings, the individual can begin to predict when the US is coming based on the CS being present.
• When the CS is presented, the individual forms an expectancy of the US. This expectancy is what drives the CR.

Question 5

What is the role of expectations and surprise?

Answer 5

Surprise = new mappings between CS and US => learning

Without surprise, there is no learning

Question 6

What are the 2 things that contingency relies on?

Answer 6

• Reliability of CS-US pairing:
― How often is the CS followed by US?
― What is the probability that the US will occur given that the CS has just occurred?

• Uniqueness of CS-US pairing:
― How often does US happen without CS?
― What is the probability of the US occurring given that no CS has occurred?

Question 7

How can we quantify contingency relationships?

Answer 7

Contingency refers to the predictive relationship between stimuli (CSs and USs)
The CS has to convey information about US occurrence.
Rescorla used the following expression to describe these relationships:
p(US/CS) > p(US/no CS)
The probability of a US occurring given that a CS is present
is greater than
The probability of a US given that NO CS is present
If this condition is met, learning (excitatory conditioning) will occur

Question 8

What does p(US/CS) mean?

Answer 8

Percentage/proportion of CSs that are temporally contiguous (paired) with a US
• If p = 1.0 then 100% of CSs are paired with USs
• If p = 0.5 then 50% CSs are paired with USs and 50% of CSs are presented alone
• If p = 0.0 then all the CSs are presented alone, there are no CS-US pairings

Question 9

What does p(US/no CS) mean?

Answer 9

Percentage/proportion of time intervals without a CS in which
a US occurs
• If p = 1.0 then USs are presented on 100% of the time intervals with No CS present
• If p = 0.5 then USs are presented on 50% of the time intervals with No CS present
• If p = 0.0 then USs are never presented when No CS is present

Question 10

How do we get Positive contingency between CS and US?

Answer 10

• If the CS is a reliable predictor of the presence of the US, then the CS and US are positively correlated
p(US/CS) > p(US/no CS)

Question 11

How do we get No contingency between CS and US?

Answer 11

• If the CS is an unreliable predictor of the US, then the CS and US are not correlated
p(US/CS) = p(US/no CS)

Question 12

How do we get Negative contingency between CS and US?

Answer 12

• If the CS reliably predicts the absence of the US, then the CS
and US are negatively correlated
p(US/CS) < p(US/no CS)

Question 13

What is the effect of contingency on classical conditioning?

Answer 13

For both groups there’s only a 40% chance that bells will be followed by shock. However, for Group B, shock is less likely when no bell is sounded, and, for this group, the bell becomes a fearful stimulus.

Question 14

What was Rescorla’s classic contingency experiment?

Answer 14

Basic Method:
Conditioned emotional response (CER) procedure with rats:
Phase1: Operant conditioning to establish steady bar pressing
Phase 2: Classical conditioning to establish CER
CER training (daily for 5 days):
• All rats exposed to 12 tones (the CS)
• The tones were 2-min long and mean inter-tone interval was 8 min
• The probability of shock (the US) during tone was .40 for all rats
• Groups differed in probability of shock during the inter-tone interval
During the inter-tone interval:
• Group 0 : no shocks
• Group .1: shocked with a probability of .1
• Group .2: shocked with a probability of .2
• Group .4: shocked with a probability of .4
Phase 3: After CER training, the rats were returned to bar pressing for food.
While the rats were bar pressing, the tones were presented as before, but no shocks were given
- If tone triggers the conditioned fear response (freezing etc.) it interferes with (suppresses) the expression of the operant conditioned response (bar pressing)
- Conditioning was assessed by a suppression ratio (the lower the ratio, the greater the suppression, the stronger the conditioning)
Rescorla demonstrated differences in conditioning despite
fixed contiguity between groups
As the probability of the US occurring without a CS grows from 0 to .4, the uniqueness of the CS to predict the US conditioning declines
• These results suggest that contiguity is not the only associative principle necessary to produce learning
• All rats experienced the same degree of contiguity between tone and shock, they differed in the extent to which the shock was contingent on the tone.

Question 15

What are the results of CS-US correlation?

Answer 15

• Whenever p(US|CS) > p(US|NO CS):
― CS is an EXCITATORY CS
― that is, CS predicts US
― Amount of learning depends on size difference between p(US/CS) and p(US/no CS)

• Whenever p(US|CS) < p(US|NO CS):
― CS is an INHIBITORY CS
― that is, CS predicts ABSENCE of US
― Amount of learning depends on size difference between p(US/CS) and p(US/no CS)

• Whenever p(US|CS) = p(US|NO CS):
― CS is a NEUTRAL CS
― CS doesn’t predict or not predict CS
― No learning will occur because there is no predictability

Question 16

Why is contiguity necessary but not sufficient?

Answer 16

Although contiguity is necessary for classical conditioning to occur, it is not enough (it is not sufficient). The CS and the US must be correlated either positively or negatively

Question 17

What is the Rescorla-Wagner Model?

Answer 17

• A mathematical model designed to predict the outcome of classical conditioning procedures on a trial-by-trial basis
• Learning will occur only when the subject is surprised, that is, when what actually happens is different from what the subject expected to happen
• Always 3 possibilities in conditioning trials:
1.excitatory conditioning
2.inhibitory conditioning
3.no conditioning and all
• Which of these three possibilities actually occurs depends upon:
1.The strength of the subjects’ expectation of what will occur
2.The strength of the US that is actually presented

Question 18

What are the 6 rules of the Rescorla-Wagner model?

Answer 18

1. If the strength of the actual US is greater than the strength of the subjects’ expectation, all CSs that were paired with the US will receive excitatory conditioning.
2. If the strength of the actual US is less than the strength of the subjects’ expectation, all of the CS is that were paired with the US will receive some inhibitory conditioning.
3. If the strength of the actual US is equal to the strength of the subjects expectation, there will be no conditioning.
4. The larger the discrepancy between the strength of the expectation and the strength of the US, the greater the conditioning that occurs (either excitatory or inhibitory)
5. More salient CSs will condition faster
6. If two or more CSs are presented together, the subjects’ expectation will be equal to their total strength (with excitatory and inhibitory stimuli tending to cancel each other out)

Question 19

How does acquisition work for R-W?

Answer 19

• With each successive conditioning trial, the expectation of the US following the CS should get stronger, and so the difference between the strength of the expectation and the strength of the US gets smaller
• Therefore, the fastest growth in excitatory conditioning occurs in the first trial, and there’s less and less additional conditioning as the trials proceed
• When the CS elicits an expectation that is as strong as the US, the asymptote of learning is reached, and no further excitatory conditioning will occur with any additional CS-US pairings

The R-W model explains Hull’s Theoretical Learning Curve:
The increases in height in the curve à smaller across trials.
The most learning occurs when surprise is greatest and expectation least
As the CS comes to be expected little further learning occurs

Question 20

Does learning really asymptote?

Answer 20

The R-W model says no learning is occurring after asymptote reached…
But it’s important to remember that this asymptote reflects the maxing out of the behavioural performance/response that can be measured. Learning might still be occurring

Question 21

How does R-W explain blocking?

Answer 21

• When two CSs are presented, the subject’s expectation is based on the total expectations of both.
• No conditioning occurs to the added CS because there is no surprise – the strength of the subject’s expectation matches the strength of the US
• Increasing the size/strength of the US when presenting the compound CS may prevent blocking effects

Question 22

How does R-W explain extinction and conditioned inhibition?

Answer 22

• The strength of the expected US is greater than that of the actual US, leading to a decrease in the association between the CS and the US.
― Following acquisition: CS –> No-US (surprise)
• This leads any CS or compound CS to acquire some inhibitory conditioning
― CS –> No-US learning occurs until the absence of the US is no longer surprising
― CS –> conditioned inhibitor

Question 23

How does R-W explain combined CSs?

Answer 23

• When two CSs that elicit CRs on their own are combined, the expected US of the compound CS is roughly equal to their total strength.

Question 24

How does R-W predict the over-expectation effect?

Answer 24

• There is a decline in responding to a pair of well established conditioned stimuli (CSs) when they are presented as a compound.
• Over-Expectation Effect: If two CSs are conditioned separately and then together, the animal has an over-expectation about the size of the US, and both CSs will experience some inhibitory conditioning
― The animal expects twice the US, so if only the same US follows the compound CS as did each CS alone, this does not meet the animals expectations
• The Frequency principle of CS-US pairings would predict a stronger CR to the compound stimulus
― i.e., the more trials linking the CS and US, the stronger the CR
• It would not be expected that more CS-US pairings would result in a weakening of CS-US associations, yet this occurs in conditions like these where compound CSs experience
inhibitory conditioning due to the over-expectation effect

Question 25

Why can The Rescorla-Wagner model be thought of as a model of US effectiveness?

Answer 25

• Unpredicted (surprising) US is effective in promoting learning
• Well-predicted US is ineffective in promoting learning

Question 26

What are alternative theories of classical conditioning?

Answer 26

• Alternative theories focus on attention to the CS instead
• A common feature of these theories is the assumption that the learner will pay attention to informative CSs but not to uninformative CSs
• These theories might also be called theories of CS effectiveness, because they assume that the conditionability of a CS, not the effectiveness of the US, changes from one situation to another

Question 27

Why doesn’t the R-W model explain latent inhibition?

Answer 27

• When the (to-be-CS) stimulus is presented by itself before the training, the expected US is zero, and the actual US is zero
• According to the Rescorla-Wagner model, since the actual US = expected US, there should be no learning of any kind during the pre-exposure
• However, subjects evidently do learn something during the pre-exposure trials, which reduces their ability to later develop a CS –> US association
• Attention-based theories are able to explain the pre-exposure effect
―Because the CS predicts nothing during the pre-exposure, attention to the CS decreases, and so conditioning is slower when the CS is first paired with the US at the beginning of the conditioning phase

Question 28

What are comparator theories of conditioning?

Answer 28

Comparator theories assume that the animal compares two likelihoods:
• The likelihood that the US will occur in the presence of the CS
• The likelihood that the US will occur in the absence of the CS
They do not make predictions on a trial-by-trial basis
1. They assume what is important is not the events of individual trials but rather the overall long-term correlation between a CS and the US
2. They propose that the correlation between CS and US does not affect the learning of a CR but rather its performance
― e.g. Subjects may learn an association between a CS and a US that cannot initially be seen in their performance, but this learning can be unmasked if the strength of a competing CS is weakened
1) Unlike R-W, comparator theories assume that both the CS and contextual stimuli can acquired equal excitatory strengths, because both have been paired with the US.
2) Comparator theories also assume that a CS will not elicit a CR unless it has greater excitatory strength than the contextual stimuli.
The animal has learned something about the CS: that the US sometimes occurs in its presence, but the animal will not respond to the CS unless it is a better predictor of the US than the context
Context plays a critical role in determining the response

Question 29

How might we unmask learning in blocking?

Answer 29

Phase 1: Train Light CS
Phase 2: Train Light CS in compound with neutral (but
equally salient) Metronome CS
Phase 3: Revaluation of US Extinguish CR to Light and
unblock metronome
Phase 4: Test metronome: conditioning to Metronome
is revealed
Blocking is a performance issue rather than a learning one
They are learning about the second CS but you just cant measure it in a normal blocking test

Question 30

What are the Common Themes in the Rescorla-Wagner, Attentional and Comparator Theories?

Answer 30

• The predictiveness or informativeness of the stimulus is a critical determinant of whether a CR will occur
• The predictiveness or informativeness of a stimulus cannot be judged in isolation
• It must be compared to the predictiveness of other stimuli also present in the learner’s environment.
― In reality, contextual cues are present when the US is absent as well as present –> reduces the uniqueness of the relationship with the US and therefore limits learning