State of ACT-R Research Agenda:

State of ACT-R Research

Agenda:1. Review the ACT-R 5.0/6.0 architecture. 2. Illustrate its application to two experiments

on learning to solve equations -- one with children and with adults.

3. Show how fMRI data provide converging data for architectural assumptions.

4. Show off nearly parameter-free predictions.5. Discuss future goals.

Mostof theTime

ACT-R versus ACT*1. Common: Cognition has declarative & procedural

systems.2. Common: Each system has subsymbolic & symbolic

aspects.3. ACT-R 2.0: Rational analysis guiding the subsymbolic level.4. ACT-R 4.0: Central cognition integrated with perceptual-

motor.5. ACT-R 4.0/5.0: Different types of learning that really work.

Declarative Procedural

Symbolic Passive recording of thecontents of various buffersas chunks which cacheresults for the future

Production compilationCollapses production rulesinto single rules that leads tospecialization of methods

Subsymbolic Chunk activations areestimated by a Bayesianalgorithm reflect likelihoodthat a chunk will be needed.

Production utilities areestimated by a reinforcementlearning to estimate expectedpayoff of various rules

6. ACT-R 5.0: has biologically-inspired module and buffer structure. 7. ACT-R 6.0: Use of this structure to foster cumulative science.

Knowledge Level Learning: Module products recorded as chunks -- focus on instruction and examples

ACT-R 5.0/6.0 Modules and Buffers

ManualControl

ProblemState

DeclarativeMemory

VisualPerception

ControlState

ProductionSystem

ACT-R Parse3x-5=7

Retrieve7+5=12

“Unwinding”“Retrieving”

Hold3x=12

Typex=4

1. 11-14 year-olds just about to start Algebra 12. Day 0: Instruction, paper & pencil practice,

coaching3. Days 1 - 5: Computer-based practice

The First Experiment Qin, Anderson, Silk, Stenger, & Carter (2004)

Example of equations:step equation0 step 1x + 0 = 031 step 3x + 0 = 12

1x + 9 = 122 step 6x + 5 = 23

4.Student types answer by pressing finger in data glove.5. Imaged in fMRI scanner on Day 1 and 5.

1. To solve an equation, encode it and a. If the right side is a number then image that number as the result

and then focus on the left side and unwind it.b. If the left side is a number then ..

2. To unwinda. If the expression is the variable then the result is the answer.b. If a number is on the right unwind-rightc. If a number is on the left unwind-left

3. To unwind-right, encode the expression anda. If the expression is _ + 0 then focus on the left part and unwindb. Otherwise invert the operator, image it as the operator in the result,

image the right part of the expression as the second argument in the result, evaluate the result, and then focus on the left part and unwind

4. To unwind-left encode the expression anda. If the expression is 1 * _ then focus on the right part and unwindb. Otherwise check that the operator is symmetric, invert the operator,

image it as the operator in the result, …

Unwind Instructions that ACT-R Parses into an Internal Declarative

Representation

Instruction 1a: Create image “=38”Instruction 2b: Unwind-right 7*x+3Instruction 3b: Change image to “=38-3”, this to

“=35”, and focus on 7*xInstruction 2c: Unwind-left 7*xInstruction 4b: Change image to “=35/7”, this to

“=5”, and focus on xInstruction 2a: The answer is 5, key it.

1. Initially instructions are retrieved and interpreted.

2. Eventually production compilation produces task-specific production rules.

ACT-R’s General Procedures for Interpreting and Following Declarative Representations of Procedures applied

to 7x + 3 =38

Examples of Production Rules

General InterpretiveIf one has retrieved an instruction for achieving a goalTHEN retrieve the first step of that instruction

Prior KnowledgeIF one is evaluating the expression “a operator b”THEN try to retrieve a fact of the form “a operator b = ?”

Acquired Task-SpecificIF the goal is to unwind an expression and the expression is of the form “subexpression + 0”THEN focus on the subexpression

(a) Day 1 (b) Day 5

Time Visual Production Retrieval Goal Imaginal Manual Visual Production Retrieval Goal Imaginal Manual

Instruction EncodeEncode Image-Right Solving

EncodeImage-Right Solving

Focus LeftUnwind Unwinding


EncodeTest for Skip

InstructionUnwind Evaluate

Instruction RetrievingUnwind

EncodeTest for Skip

Don't SkipUnwind

Convert PlusImage Op Inserting

Image OpImage Arg

Image ArgEvaluate

EvaluateRetrieving

Retrieve FactFocus Left Continuing


8 - 3 = 5

2.25

1.25

1.50

1.75

2.00

= 38

Ex + 3 = 38

= 38 - 3

Encode Equation

"Exp = 38"

Encode Left Side

"Exp + 3"

Exp + 3 = 38 -

Encode Left Side

"5 * X"

= 35

= 38

Ex + 3 = 38

8 - 3 = 5

= 38 - 3

0.75

1.00

0.00

Encode Equation

"Exp = 38"

Encode Left Side

"Exp + 3"

0.25

0.50

ProductionCompilation

ProductionCompilation

ACT-R Modules: The first 2+ Seconds: 7x+3=38

RetrievalSpeed up

Parallel module activity, limited by long encoding

ACT-R Modules: The middle 2+ Seconds: 7x+3=38

Day 1 Day 5


EncodeTest for Skip

EvaluateRetrieving

Retrieve FactFocus Left Continuing


InstructionUnwind Retrieve Fact

Instruction Focus Right ContinuingUnwind

Encode Focus RightTest for Skip Unwind Unwinding

Don't SkipUnwind

SymmetricInvert Op

Convert Times Press KeyImage Op Inserting Done

Image OpImage Arg

Image ArgEvaluate

EvaluateRetrieving

2.25

35 / 7 = 5

Encode Left Side

"5 * X"

4.25

4.50

Press Key4.00 7*x = 35 /

= 35 / 7

= 5

3.50 7 * x = 35

Encode Right Side "X"

3.75

8 - 3 = 5

7 * x = 352.50

35 / 7 = 5

2.75

= 35

3.00

3.25

= 35 / 7

ACT-R Modules: The last 2+ Seconds: 7x+3=38

Day 1 Day 5


Retrieve FactFocus Right Continuing

Focus RightUnwind Unwinding

InstructionTest Var

Press KeyDone

35 / 7 = 5

Press Key6.00

6.25

5.00

5.25

= 35

5.50Encode Right

Side "X"

5.75

4.75

4.50

0

1000

2000

3000

4000

5000

6000

7000

8000

0 1 2 3 4 5

Days

Time to Solve (msec.)

0 Step: Data 1 Step: Data 2 Step: DataO Step: Theory 1 Step: Theory 2 Step: Theory

Learning over 6 Days of Experiment

Comments on the ACT-R Model

1. Virtue: It actually does the task -- interacts with same software as subjects.

2. Virtue: The model is not hand crafted but learns from instruction (albeit the instructions are a little hand-crafted to facilitate parsing).

3. Fact: Two parameters were estimated to fit the latency data -- the latency scale for retrieval and the visual encoding time.

4. Doubt: There is an great deal of theoretical complexity for a rather simple set of numbers.

5. Resolution: We will use brain imaging to test for distinct patterns predicted by different modules in the model.

ACT-R Modules and Buffers

ManualControl

ProblemState

DeclarativeMemory

VisualPerception

ControlState

ProductionSystem

ACT-R Parse3x-5=7

Retrieve7+5=12

“Unwinding”“Retrieving”

Hold3x=12

Typex=4

FusiformGyrus

PrefrontalCortex

AnteriorCingulate

ParietalCortex

MotorCortex

BasalGanglia

Our Modules (all left lateralized) as 100 (5x5x4) Voxel Regions

Motor/Manual: BA 3/4 (x = -37, y = -25, z =

47)

Parietal/Imaginal: BA 39/40 (x = -23, y = -64, z

= 34)

Prefrontal/Retrieval: BA 45/46 (x = -40, y = 21, z =

21)

Our Modules (all left lateralized) as 100 (5x5x4) Voxel Regions

Ant Cing/Goal:BA 24/32 (x = -5, y = 10,

z = 38)

Caudate/Procedural: (x = -5, y = 9, z = 2) Actually 4 x

4 x 4

21.6 Second Structure of fMRI Trial

+ 3x+2=17 *

Prompt Equation ITI

1.2 s 12 s 8.4 s1 scan 10 scans 7 scans

fMRI Response to Events

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 1 2 3 4 5 6 7 8 9 101112131415161718192021Time (sec.)

Activation

First

Second

Third

Total

A

ctiv

atio

n

ModuleActivity

Mapping Module Activity onto the BOLD Response

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Time during Trial (Sec.)

ProceduralRetrievalGoalImaginalManual

Day 1: f(t) 2 steps

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Time during Trial (sec.)


Day 5: f(t) 2 steps

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0



Day 5: f(t) 2 steps€

CB( t) = f (x)B(t− x)dx0

t

∫

Predicted BOLD Response

Module Demand Function

0.0

0.2

0.4

0.6

0.8

1.0

0 5 10 15 20 25 30Time

s =1.5, a =3s=3, a = 3s=0.75,a=6s=1.5, a =6

BOLDFunction

Motor: r = .975

-0.1

0.0

0.1

0.2

0.3

0.4

0 3 6 9 12 15 18 21

Time During Trial (Sec.)

0 Operation1 Operation2 Operation0 Operation1 Operation2 Operation


47)

ResponseDelay

Motor: r = .972

-0.1

0.0

0.1

0.2

0.3

0.4

0 3 6 9 12 15 18 21


Percent Change in Bold

Response

Day 1Day 5Day 1Day 5

0

0.2

0.4

0.6

0.8

1

0 3 6 9 12 15 18 21Time (sec)

Density

Distribution ofResponses

01 2

Prefrontal: r = .963

-0.1

0.0

0.1

0.2

0.3

0.4

0 3 6 9 12 15 18 21



Response



21) Almost no Effect


-0.1

0.0

0.1

0.2

0.3

0.4

0 3 6 9 12 15 18 21



Response


Anterior Cingulate: r = .981

-0.1

0.0

0.1

0.2

0.3

0.4

0 3 6 9 12 15 18 21



Anterior Cingulate: r = .982

-0.1

0.0

0.1

0.2

0.3

0.4

0 3 6 9 12 15 18 21



Response



z = 38)

Almost noLearning


= 34)

Parietal: r = .969

-0.1

0.0

0.1

0.2

0.3

0.4

0 3 6 9 12 15 18 21



Parietal: r = .955

-0.1

0.0

0.1

0.2

0.3

0.4

0 3 6 9 12 15 18 21



Response


Rather directly reflects time because of skipping steps in equation representation

Caudate/Procedural: (x = -5, y = 9, z = 2)

Caudate: r = .975

-0.1

0.0

0.1

0.2

0.3

0.4

0 3 6 9 12 15 18 21



Caudate: r = .973

-0.1

0.0

0.1

0.2

0.3

0.4

0 3 6 9 12 15 18 21



Response


Rather directly reflects time because of production rule collapsing

Identical Respons

eDifferen

t Peaks

Operation

LargeLearning

Weak

Operation

MediumLearning Medium

Operation

MediumLearning Medium

Little Respons

e in 0 Operatio

n

2 measures of Match between Regions and Modules--small is good (<130 nonsignificant)

Motor Prefrontal Cingulate Parietal CaudateManual 88.93 452.05 724.66 426.40 333.89

Retrieval 493.22 82.60 350.32 101.88 133.13Goal 255.91 194.94 123.27 171.74 111.01

Imaginal 384.66 125.66 210.47 95.21 101.82Procedural 347.05 163.76 286.28 114.93 81.03

1. While the analysis has been about ACT-R fitting the learning of algebra the same methods can be used to relate many different information-processing theories to many tasks.

2. The unifying concept in all cases is that the BOLD response in a region reflects time a module is engaged. This allows us to map between an information-processing model and the BOLD response and so to track individual components of the model.

3. The same prespecified areas behave as predicted in many adult studies.

4. There is no claim one way or another about whether the modules are implemented in these regions.

5. The critical fact is that we have a measure of the activity of specific modules rather than just the overall behavior.

6. Challenge: Can we take this same model and fit it to another experiment.

Observations about fMRI and Modeling

Example of equations:step equation answer0 step P<->éé 4çç 5 P<->éé 4çç 5

1 step çç P <->éé 4çç 5 P<->çç 4éé 5

2 step çç Péé 4<->çç 5 P<->éé 5éé 4

The Second Experiment-- Qin, Sohn, Anderson, Stenger, Fissel, Goode, & Carter (2003)

1. Adults2. Day 0: Instruction and general practice3. Days 1 - 5: Computer-based practice4. Subject types answer by pressing thumb and

then quickly keying 4 terms.5. Scanned on Days 1 & 5.

Px4<->5

1.5 Second Scans

Prior Equation Blank Period

18 Second Structure of fMRI Trial

GiveAnswer

1-3-5-3-4

1. To solve an equation, first find the “<->”, then encode the first pair that follows, then shift attention to the next pair if there is one, then encode the second pair.

2. If this is a simple equation output it; otherwise process the left side.3. To process the left side, first find the “P”.4. If “<->” immediately follows then work on the operator that precedes the

P; otherwise first encode the pair that follows, then invert the operator, and then work on the operator that precedes the P.

5. To process the operator that preceded the P, first retrieve the transformation associated with that operator, then apply the transformation, and then output.

6. To output press 1, then output the first, then output the next, then output the next, and then output the next

Instructions for ACT-R

+ Knowledge of inverses (2-3, 4-5) and transformation rules for getting rid of 2,3,4, & 5 prefixes.

(a) Day 1 (a) Day 5

Time Visual Production Retrieval Goal Imaginal Manual Visual Production Retrieval Goal Imaginal

Instruction InstructionFind <-> First-Pair

EncodeFirst-Pair

Find NextSecond-Pair Encoding

First PairFind-Next Encoding

Find NextSecond-Pair

EncodeTest For <->

Right DoneNext?

InstructionProcess-left Fail Test

Subgoal Second-PairGo On Second Pair

Instruction RetrievingFind P

EncodeTest For <->

Fail TestGo On

InstructionSecond-Pair

Second PairInvert Encoding

Invert1Retrieving

Encode Equation

"4 <-> 2 5"

Encode Null Right

"2 5"

Encode Equation "2 P 3 4"

"2 5 3 4"

Invert 3

Invert 3

82.00

82.25

Encode Equation "2 P 3 4"

82.50

82.75

"2 5 3 4"83.00

83.25

Encode Equation

"4 <-> 2 5"

81.25

81.50 "2 5"

Encode Null Right

81.75

81.00

ACT-R Modules: 2 P 3 4 <-> 2 5

Encoding

ACT-R Modules: 2 P 3 4 <-> 2 5

Transforming

(a) Day 1 (a) Day 5

Time Visual Production Retrieval Goal Imaginal Manual Visual Production Retrieval Goal Imaginal

Invert2 Invert2Focus-Left Encoding "2 5 2 4" Focus-Left Encoding "2 5 2 4"

Subgoal Tranform1Go On Retrieving

InstructionTest-Left

Test LeftTransform

Tranform1Retrieving

TransformxOutput Encoding "3 5 3 4"

Output

Transform2Apply Encoding

Transform3Output "3 5 3 4"88.50

Invert 3

86.75

87.00

87.25

2 Transform

87.50

87.75

88.00

88.25

Invert 3

2 Transform

ACT-R Modules: 2 P 3

4 <-> 2 5Output

Learning over 6 Days of Experiment

0

2

4

6

8

10

12

0 1 2 3 4 5

Days

Time to Solve (sec.)

0 Step: Data 1 Step: Data 2 Step: DataO Step: Theory 1 Step: Theory 2 Step: Theory


47)

Motor: r = .977

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 3 6 9 12 15 18


Percent Change in BOLD Response


Motor: r = .979

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 3 6 9 12 15 18


Percent Change in BOLD

Response


As before, BOLD response tracks response timing


21) Almost no Effect


-0.1

0.0

0.1

0.2

0.3

0.4

0 3 6 9 12 15 18



Response



-0.1

0.0

0.1

0.2

0.3

0.4

0 3 6 9 12 15 18



Response


As before, large effects of both factors -- weak response for 0


z = 38)

Almost noLearning

Cingulate: r = .984

-0.1

0.0

0.1

0.2

0.3

0.4

0 3 6 9 12 15 18



Response


Cingulate: r = .981

-0.1

0.0

0.1

0.2

0.3

0.4

0 3 6 9 12 15 18



Response


As before, large effect for complexity, little for learning


= 34)

Parietal: r = .983

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 3 6 9 12 15 18



Response


Parietal: r = .987

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 3 6 9 12 15 18



Response


Large effect complexity, learning largely complete by Day 1

Caudate/Procedural: (x = -5, y = 9, z = 2)

Caudate: r = .834

-0.1

0.0

0.1

0.2

0.3

0 3 6 9 12 15 18


Percent Change in BOLD Response


Caudate: r = .760

-0.1

0.0

0.1

0.2

0.3

0 3 6 9 12 15 18



Response


Very Weak Response in this Experiment -- yielding poor signal to noise ratio.

Identical Respons

eDifferen

t Peaks

Operation

LargeLearning

Near Zero

Operation

MediumLearning

Weak

Poor Signal to

Noise Weak Day

5 Response

Little Respons

e in 0 Operatio

n

2 measures of Match between Regions and Modules--small is good (<90 nonsignificant)

Motor Prefrontal Cingulate Parietal CaudateManual 70.42 403.11 209.41 695.11 143.83

Retrieval 714.10 46.91 277.63 259.40 69.12Goal 197.76 214.93 48.25 131.67 103.82

Imaginal 311.67 200.83 72.13 88.86 90.53Procedural 336.22 162.80 97.57 80.23 99.56

Parameters Estimated and Fits to the Bold Response

€

B(t)=m ts ⎛ ⎝ ⎜

⎞ ⎠ ⎟a

e−(t /s)

Motor/

Manual

Prefrontal/

Retrieval

Parietal/

Imaginal

Cingulate/

Goal

Caudate/

Procedural

Magn(m)Children

Adults

0.531

0.197

0.073

0.078

0.231

0.906

0.258

0.321

0.207

0.120

Exponent(a) 3 3 3 3 3

Scale(s)Children

Adults

1.241

1.360

1.545

1.299

1.645

1.825

1.590

1.269

1.230

1.153

Motor Saturation?Larger Operations?

Magnitude Shape

Time to Peak -- a x s

1. Increased stress on parameter-free predictions.

2. Increased effort to anchor the module structure of ACT-R with brain correlations.

3. Focus on instruction -- starting our models from the beginning.

4. Goal of producing a simulated student.5. Focus on reasoning and metacognitive

processing.6. Continued effort at community support.7. Greater emphasis on re-use of

components/models8. Including making knowledge basis available to

community -- for instance, a middle-school math module.

9. Finally get concerned with representational assumptions.

10. Facilitate exchange of components between architectures.

10 Future Directions for ACT-R

Local Science

Shared Science

State of ACT-R Research Agenda:

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