Functional encoding in memory for goals
ACT-R workshop August 1999
Erik M. Altmann (altmann@gmu.edu)
J. Gregory Trafton (trafton@itd.nrl.navy.mil)
Means-ends tasks
• Means-ends behavior:
– Suspend a goal
– Work on subgoals
– Resume the goal at an appropriate time
• Examples:
– Monkey and bananas
– Giving a talk
– Making photocopies
The Tower of Hanoi
• The foundational means-ends task
– In cognitive science
• Understood in terms of the goal stack
• Completely understood
– Or is it?
• Good data (Anderson, Kushmerick, & Lebiere, 1993)
The Tower of Hanoi
Subgoal 3:B
Goal 4:C
1
2
3
3
4
4
B
A
C
A stack model
Recall 3:B perfectly,
despite lag
Stack height
Push 3:B
1:B
4:C
3:B
4:C
2:C
3:B
4:C
2:C
3:B
4:C
Time
2:C
3:B
4:C
3:B
4:C
1:C
3:B
4:C
...
The stack as representation
• The typical assumption in task analysis
– Implicit in problem behavior graph
– Explicit in GPS, GOMS, ...
• The standard theory of goal management
– In cognitive architectures
• ACT-R, Soar
– In cognitive models generally
• E.g., ACT-PRO, 3CAPS Better Raven, ...
The stack as representation
• The appeal:
– Robust and general
– Applies to a wide variety of tasks
– Supported by empirical data
• At some level of abstraction
• The problem:
– At best, a high-level simplification
– At worst, wrong
Goal-selection order
• LIFO order not used when not needed
– Selection order in arithmetic (VanLehn)
• Order depends on context
– Display-based problem-solving, situated action,
distributed representation
– Capture error
Pending goals
•
•
•
•
Displaced by memory load (Just & Carpenter)
Decay when not rehearsed (Byrne & Bovair)
Intrude when rehearsed (Altmann & Trafton, 1999b)
Affected by goal content
– Intention superiority (Goschke & Kuhl)
• Suggesting that activation affects availability
Research approach
• Model Tower of Hanoi data without a stack
– For goals
• Ask how to make up the lost functionality
– Domain knowledge
– External cues
– Existing memory theory
• If it suffices, the theory is strengthened
• If it fails, then at least we know why
Memory as goal store (MAGS)
• Memory = encoding + retention + retrieval
• Assume passive retention
• Assume strategic encoding
– Using knowledge of retrieval context
• Assume strategic retrieval
– Using knowledge to select retrieval cues
Analytical framework: Activation
• What happens to a goal’s activation over time?
• Two kinds of activation (in ACT-R):
– Base-level activation from use
– Priming from context
• Total activation predicts current need
– So memory returns the most active element
Encoding to resist decay
• Strengthen base-level activation
• Strength test to say how much is enough
– Cognition asking itself, “Got it?”
• If yes, stop strengthening and move on
• If no, strengthen some more
– Test interleaved with strengthening
• Strengthen enough but not too much
Encoding to resist decay
Base-level activation
Strength test
2:C, 1:B, 2:C
Retrieval threshold
Time
The strength test
• Cognition can anticipate retrieval context
– Retrieval cue — “3” for 3:B
– Retention interval — 5 to 10 seconds
• Anticipations are just knowledge
– Represent as cue chunks
• Test-retrieve the goal
– If test fails, encode some more
Focussed retrieval
3:B
Test retrieval
cue:
sink:
3
S
disk:
3
from: A
to:
B
blocked: t
Encoding context
Goal
Retrieval
cue:
3
disk:
3
from: A
to:
B
blocked: t
Retrieval focus
Main focus
Retrieval context
Retrieval production
(p retrieve
=focus>
isa retrieval
=goal>
isa goal
disk =disk
to =peg
==>
=focus>
disk =disk
to =peg
!pop!)
No indexing or chaining
Noisy retrieval without
partial matching
Empirical test
• Anderson, Kushmerick, & Lebiere (1993)
– Subjects instructed in goal-recursion strategy
– Response-time data are from perfect trials
• Cognition on those trials most stack-like
• Strongest test of the MAGS model
Prediction
• Encoding a goal is expensive
– Not a cost-free push operation
– A second or so per goal
• Prediction from serial attention model
Data
Time (sec)
Large peaks = Goal encoding
12
10
8
6
4
2
0
Observed (AK&L 93)
Simulated (MAGS), R 2 = .99
1
3
5
7
9
11
Move in solution path
13
15
Prediction
• People avoid unnecessary retrievals
– Retrieval is effortful and error-prone
• Use move heuristics when they apply:
Don’t-undo
IF
the just-moved disk was 1, and
X is the smaller of the two other top disks, and
Y is the larger of the two other top disks,
THEN move X on top of Y.
Data
Valleys = Don’t-undo
12
10
8
6
4
2
0
1
3
5
7
9
11
Move in solution path
13
15
Prediction
• Prefer goal retrieval to re-planning
• Depends on selecting the right retrieval cue
– No perfect pop operation
• Cue selection heuristic:
Retrieve-uncovered
IF
the uncovered disk is X,
THEN try to retrieve X:?
Data
Small peaks = goal retrieval
12
10
8
6
4
2
0
1
3
5
7
9
11
Move in solution path
13
15
Five-disk data
16
14
Simulated (MAGS), R2 = .95
12
10
8
6
4
2
0
1
3
5
7
9 11 13 15 17 19 21 23 25 27 29 31
Move in solution path
Parameters
• ACT-R defaults:
– W = 1.0, F = 1.0, d = 0.5
• Adopted from other models:
– Perceptual encoding time = 185 msec
(Anderson, Matessa, & Lebiere, 1997)
– t = 4.0, s = 0.3
(Altmann & Gray)
• No unconstrained parameters
Prediction
• Retrieval is error prone
– E.g., might retrieve 3:C instead of 3:B
• From a previous plan or previous trial
– Incorrect retrieval starts a garden path
Data
Length of solution path
60
Predicted (MAGS)
Observed (AK&L 93)
50
40
Optimal
30
20
10
Optimal
0
Four disks
Five disks
MAGS vs. stack model (A&L 98)
• Based on declarative memory
– Not on a privileged stack
• Broader empirical coverage
– Detailed account of RT and error
– Only ToH model to address both (before today)
• Functional encoding and retrieval processes
– Specified at ACT-R’s atomic level
– Generic — adapted from serial attention
(Altmann & Gray, 1999b)
Implications
• Need a two-high architectural stack
– A main focus for problem state
– A retrieval focus for concentrating
• Main and retrieval focuses are mutually
exclusive (Altmann & Trafton, 1999b)
– One is reliable
– One is predictive
Conclusions
• Don’t need a goal stack
– Anything it can do, MAGS can do better
– And without that much more analysis
• Don’t want a goal stack
– Too easy and too wrong
– Masks real goal-management mechanisms
Conclusions
• 40 years of research on the Tower of Hanoi
• Yet retrieve-uncovered is unpublished
– Missing from Simon’s perceptual strategies
– Missing from Anzai and Simon protocol
Conclusions
• Why now?
– Detailed data
– A precise memory theory
– Throwing away the goal stack
References
Model code: hfac.gmu.edu/people/altmann/toh
Altmann & Trafton (1999a). Memory for goals: An
architectural perspective. Proc. Cog. Sci. 21.
Altmann & Trafton (1999b). Memory for goals in
means-ends behavior. Manuscript submitted for
publication.
The encoding process
Focussed retrieval
with a “sink”
4:C
Test-retrieval
Test-strength
cue:
sink:
4
S
disk:
4
from: A
to:
C
blocked: t
disk:
4
from: A
to:
C
blocked: t
Strengthen-goal
Test-passes/fails
disk:
4
from: A
to:
C
blocked: t
Test-fails