7.2 Rescorla-Wagner Model

Question 1

General idea

Answer 1

This is a model about learning.
Main Idea: Learning is proportional to surprise

How to model surprise: Obtained - Expected = Lambda - V
How to model learning: Change in strength of association = Delta V
How to handle proportional: Salience of CS -> US = alpha

Overall:
Change in association = Salience * (Obtained - Expected)

DeltaV = a * (lambda - V)
Not full equation yet though

Question 2

Parameters

Answer 2

DeltaV: Change in strength of association/learning

V: Strength of association/CS to US

Lambda: Maximum Strength of association
Graphically: How high curve can go
Does not vary during conditioning
Often set to 100 with the US is present
Set to 0 when US not present
Low lambda = slower learning. Review graph
Affected by many factors, like type, nature, and intensity of stimuli. Ex lowlight/bright light. Also belongingess between the 2 stimuli. Ex Smell and feeling sick for food is good

a: salience
Determines rate of learning and does not vary.
Higher value equals more learning and vice versa
Always between 0 and 1. Usually low such as 0.1
Review graph of learning curves. Essentially, low a = slow learning
How much of the surprise we learn in a given trial
- Salivary took hundreds of trials
- Taste aversion took 1 trial usually. What value would we set for salience here? Almost 1

Review last strength of association learning curve

Question 3

Acquisition

Answer 3

Example:
a = 0.5
Lambda = 100
V^0 = 0

DeltaV1 = 50 | V^1 = 50
DeltaV2 = 25 | V^2 = 75
DeltaV3 = 12.5 | V^3 = 87.5
DeltaV4 = 6.25| V^4 = 93.75

Question 4

Extinction

Answer 4

Example:
a = 0.5
Lambda = 0
V^0 = 100

DeltaV1 = -50 | V^1 = 50
DeltaV2 = -25 | V^2 = 25
DeltaV3 = -12.5 | V^3 = 12.5
DeltaV4 = -6.25| V^4 = 6.25

Question 5

Blocking

Answer 5

Special Case Examples:
a = 1
Lambda = 100
V^0 = 10

DeltaV1 = 90 | V^1 = 100
DeltaV2 = 0 | V^2 = 100
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
a = 0
Lambda = 100
V^0 = 10

DeltaV1 = 0 | V^1 = 10
DeltaV2 = 0 | V^2 = 10

A blocking situation needs 2 CS and 2 conditioning phases. For example:
- Whistle and smell
- Acquisition 1 CS1 -> US (whistle with food) until well learned
- Acquisition 2 CS1 + CS2 -> US (whistle and smell with food)
CS1 blocks CS2 from, being learned

Can we model this with RW model?
No, assuming condition stimuli all learned independently

Question 6

Complete equation

Answer 6

THINK: If CS1 predicts V1, and CS2 predicts V2, what should we expect to obtain when we combine the stimuli?
V_total = Summation V_i = V_1 + V_2

In conclusion:
DeltaV_i = a_i * (lambda - SummationV_i)

Each CS -> US has a strength of association V_i
Each CS -> US has a specific salience a_i
Each V_i calculated separately
SummationV_i is the total expectation
Lambda - SummationV_i is the total surprise
Each DeltaV_i depends on the combined expectations from all CS

Examples: Whistle W + Smell S
Acquisition of W only (V_S remains at 0 throughput):
aW = 0.5
Lambda = 100
V^0W = 0

DeltaV1W = 50 | V^1W = 50
DeltaV2W = 25 | V^2W = 75
DeltaV3W = 12.5 | V^3W = 87.5
...
V^7W = 99.2

Acquisition of W + S
aW = 0.5
aS = 0.5
Lambda = 100
V^7W = 99.2
V^7S = 0

SummationV = V^7W + V^7S = 99.2
Lambda - SummationV = 0.8
Each stimuli only gets 0.4

Question 7

Overexpectation

Answer 7

2 CS with 3 conditioning phases
Acquisition 1 CS1 -> US
Acquisition 2 CS2 -> US
Overexpectation: CS1 + CS2 -> US

Overexpectation phase weakens CS1 and CS2

Question 8

Overshadowing

Answer 8

2 CS with 1 conditioning phase
Overshadowing CS1 + CS2 -> US
Also need differences in saliences between CS1 and CS2 = learning rates are different. Example: Low a_1 and high a_2

Overshadowing means one stimuli is associated more strongly than the other

Question 9

Failures and explanation

Answer 9

Fails to model other experimental findings below

Question 10

Spontaneous recovery

Answer 10

Happens when association is extinguished and time passes, but it comes back by itself:
Full acquisition
Full extinction
Pause
Association recovers

Review graph
Looks like /_\

Question 11

Facilitated reacquisition

Answer 11

Phases:
Full acquisition
Full extinction
Second acquisition

Second acquisition is facilitated, meaning it’s faster, as if salience is now stronger

Review graph
Looks like /|

Question 12

Latent inhibition

Answer 12

Happens when:
Prior exposure to CS before conditioning
Acquisition of CS -> US is then inhibited, meaning it’s slower

So we hear the bell too many times, and then associating with food is just more difficult

Question 13

Failures: Explanations

Answer 13

The model lacks a memory/history of how we got to where we are. All that matters is current strengths

But experimentally:
V_i = 0 without prior acquisition
V_i = 0 from acquisition + extinction
These are not the same