Mechanism Reuse in a Graphical Cognitive

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19 Οκτ 2013 (πριν από 3 χρόνια και 11 μήνες)

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From Memory to Problem Solving:
Mechanism Reuse in a Graphical Cognitive
Architecture

Paul S. Rosenbloom


8/5/2011

The

projects

or

efforts

depicted

were

or

are

sponsored

by

the

U
.
S
.

Army

Research,

Development,

and

Engineering

Command

(RDECOM)

Simulation

Training

and

Technology

Center

(STTC
)

and

the

Air

Force

Office

of

Scientific

Research,

Asian

Office

of

Aerospace

Research

and

Development

(AFOSR/AOARD)
.

The

content

or

information

presented

does

not

necessarily

reflect

the

position

or

the

policy

of

the

Government,

and

no

official

endorsement

should

be

inferred
.

2

Cognitive Architecture


Symbolic working memory


Long
-
term memory of rules


Decide what to do next
based on preferences
generated by rules


Reflect when can’t decide


Learn results of reflection


Interact with world

Soar 3
-
8


Cognitive architecture
: hypothesis about fixed
structure underlying intelligent behavior


Defines core memories, reasoning processes, learning
mechanisms, external interfaces, etc.


Yields intelligent behavior when add knowledge and skills


May serve as


a

Unified Theory of Cognition


the core of
virtual humans
and

intelligent agents
or

robots


the basis for
artificial general intelligence

ICT 2010

3

Hybrid Short
-
Term Memory

Prediction
-
Based Learning

Hybrid Mixed Long
-
Term Memory

Graphical Architecture

D
e
c
i
s
i
o
n


How to build architectures that combine:


Theoretical elegance, simplicity, maintainability, extendibility


Broad scope of capability and applicability


Embodying a superset of
existing architectural capabilities


Cognitive
, perceptuomotor, emotive, social, adaptive,


Diversity Dilemma

Soar 9

Soar

3
-
8

4

Goals of
T
his Work


Extend
graphical memory architecture

to (Soar
-
like)
problem solving


Operator generation, evaluation, selection and application


Reuse existing memory mechanisms, based on
graphical
models
, as much as possible


Evaluate ability to extend architectural functionality
while retaining simplicity and elegance


Evidence for ability of approach to resolve diversity dilemma




5

Problem Solving in Soar


Base level


Generate, evaluate, select and apply operators


Generation: Retractable rule firing


LTM(WM)


WM


Evaluation: Retractable rule firing


LTM(WM)


PM (Preferences)


Selection: Decision procedure


PM(WM)


WM


Application: Latched rule firing


LTM(WM)


WM


Meta level (not focus here)

LTM

PM

WM

Selection


Decision Cycle


Elaboration Cycle


Match Cycle

Elaboration cycles + decision

Parallel rule match + firing

Pass token within Rete rule
-
match network

D

6


Enable efficient computation over multivariate functions by
decomposing them into products of subfunctions


Bayesian/Markov networks, Markov/conditional random fields, factor graphs






Yield broad capability from a uniform base


State of the art performance across
symbols
,
probabilities
and
signals
via
uniform representation and reasoning algorithm


(Loopy) belief propagation, forward
-
backward algorithm, Kalman filters, Viterbi algorithm, FFT,
turbo decoding, arc
-
consistency and production match, …


Support mixed and hybrid processing


Several neural network models map onto
them

Graphical Models

w

y

x

z

u

p
(
u
,
w
,
x
,
y
,
z
) =
p
(
u
)
p
(
w
)
p
(
x
|
u
,
w
)
p
(
y
|
x
)
p
(
z
|
x
)

f
1

w

f
3

f
2

y

x

z

u

f
(
u
,
w
,
x
,
y
,
z
) =
f
1
(
u
,
w
,
x
)
f
2
(
x
,
y
,
z
)
f
3
(
z
)

7

The Graphical Architecture

Factor Graphs

and the
Summary Product Algorithm


Summary product

processes messages on links


Messages are distributions over domains of variables on
link


At variable nodes messages are combined via
pointwise product


At factor nodes input product is multiplied with factor function and
then all variables not in output are summarized out

f
1

w

f
3

f
2

y

x

z

u

f
(
u
,
w
,
x
,
y
,
z
) =
f
1
(
u
,
w
,
x
)
f
2
(
x
,
y
,
z
)
f
3
(
z
)

.2

.4

.1

.3

.2

.1

.06

.08

.01

A single settling of the graph
can efficiently compute:



Variable marginals


Maximum a posterior (MAP) probs
.

8

A
Hybrid
Mixed Function/Message Representation


Represent both messages and factor functions as
multidimensional continuous functions



Approximated as
piecewise linear
over

rectilinear regions






Discretize domain

for discrete distributions & symbols

[
1,2>=.2, [2,3>=.5, [3,4>=.3, …




Booleanize

range

(and add symbol table) for symbols

[0,1>
=
1



Color(
x
,
Red
)=
True
,
[
1,2>
=
0



Color(
x
,
Green
)=
False


y
\
x

[0,10>

[10,25>

[25,50>

[0,5>

0

.2
y

0

[5,15>

.5
x

1

.1+.2
x
+.4
y

0
0.2
0.4
0.6
9

Graphical Memory Architecture


Developed general knowledge representation layer
on top of factor graphs and summary product


Differentiates long
-
term and working memories


Long
-
term memory defines a graph


Working memory specifies peripheral factor nodes


Working memory consists of instances of
predicates


(
Next
ob1:O1
ob2
:O2)
,

(
weight object:O1 value
:10)


Provides fixed
evidence

for a single settling of the graph


Long
-
term memory consists of
conditionals


Generalized rules defined via
predicate

patterns

and
functions


Patterns define
conditions
,
actions

and
condacts

(a neologism)


Functions are
mixed hybrid

over
pattern variables

in conditionals


Each predicate induces own working memory node

WM

10

Conditionals

CONDITIONAL

Transitive


c
onditions
: (Next

ob1:
a

ob2:
b
)


(Next

ob1:
b

ob2:
c
)


a
ctions
: (Next

ob1:
a

ob2:
c
)

WM

Pattern

Join

w
\
c

Walker

Table



[1,10>

.01
w

.001
w



[10,20>

.2
-
.01
w





[20,50>

0

.025
-
.00025
w



[50,100>







CONDITIONAL

Concept
-
Weight


c
ondacts
: (concept

object:
O1

c
lass:
c
)



(weight

o
bject:
O1

v
alue:
w
)



function:

WM

Pattern

Join

Function

Conditions

test WM

Actions

propose changes to WM

Condacts

test
and

change WM

Functions

modulate variables

All four can be freely mixed

11


A rule
-
based procedural memory


Semantic and episodic declarative memories


Semantic: Based on cued object features, statistically predict
object’s concept plus all uncued features


A constraint memory


Beginnings of an imagery memory


Memory Capabilities Implemented

CONDITIONAL Transitive


Conditions:
Next(
a
,
b
)


Next(
b
,
c
)


Actions:
Next(
a
,
c
)

WM

Pattern

Join

w
\
c

Walker

Table



[1,10>

.01
w

.001
w


=
[10,20>

.2
-
.01
w




=
[20,50>

0

.025
-
.00025
w



[50,100>






=
Function:

CONDITIONAL
ConceptWeight


Condacts: Concept(O1,
c
)



Weight
(O1,
w
)

Concept (S)

Legs (D)

Mobile (B)

Weight (C)

Color (S)

Alive (B)

12

Additional Aspects Relevant to Problem Solving

Open World versus
C
losed
W
orld Predicates


Predicates may be
open world

or
closed world


Do unspecified WM regions default to false (0) or unknown (1)?


A key distinction between declarative and procedural memory


Open world allows changes within a graph cycle


Predicts unknown values within a graph cycle


Chains within a graph cycle


Retracts when WM basis changes


Closed world only changes across cycles


Chains only across graph cycles


Latches results in WM

13


Predicate variables may be
universal

or
unique


Universal act like rule variables


Determine all matching values


Actions insert all (non
-
negated) results into WM


And delete all negated results from WM


Unique act like random variables


Determine distribution over best value


Actions insert only a single best value into WM


Negations clamp values to 0

Additional Aspects Relevant to Problem Solving

Universal versus Unique Variables

Join

Negate

WM

Changes

+



Action combination subgraph:

14


The last message sent along each link in the graph
is cached on the link


Forms a set of
link memories

that last until messages change


Subsume
alpha

&
beta

memories in Rete
-
like rule match cycle

Additional Aspects Relevant to Problem Solving

Link Memory

15

Problem Solving in the

Graphical Architecture


Base level


Generate, evaluate, select and apply operators


Generation: (Retractable) Open world actions


LTM(WM)


WM


Evaluation: (Retractable) Actions + functions


LTM(WM)


LM


Selection: Unique variables


LM(WM)


WM


Application: (Latched) Closed world actions


LTM(WM)


WM


Meta level (not focus here)

LTM

L
M

WM

Selection


Graph Cycle


Message Cycle

Message cycles + WM change

Process message within factor graph

16

Eight Puzzle Results


Preferences encoded via functions and negations









Total of 19 conditionals* to solve simple problems in
a Soar
-
like fashion (without reflection)


747 nodes (404 variable, 343 factor) and 829 links


Sample problem takes 6220 messages over 9 decisions (13 sec)


CONDITIONAL

goal
-
best

; Prefer operator that moves a tile into its desired location


:conditions

(blank
state:
s

cell:
cb
)


(acceptable
state:
s

operator:
ct
)


(location
cell:
ct

tile:
t
)


(goal
cell:
cb

tile:
t
)


:actions

(selected state
s

operator:
ct
)


:function

10



CONDITIONAL

p
revious
-
reject

; Reject previously moved operator


:conditions

(acceptable
state:
s

operator:
ct
)


(previous
state:
s

operator:
ct
)


:actions

(selected
-

state:
s

operator:
ct
)

17

Conclusion


Soar
-
like base
-
level problem solving grounds directly
in mechanisms in graphical memory architecture


Factor graphs

and
conditionals


knowledge in problem solving


Summary product algorithm



processing


Mixed functions



symbolic and numeric preferences


Link memories



preference memory


Open world

vs.
closed world



generation vs. application


Universal

vs.
unique



generation vs. selection


Almost total reuse augurs well for diversity dilemma


Only added architectural
selected

predicate for operators


Also progressing on other forms of problem solving


Soar
-
like reflective processing (e.g., search in problem spaces)


POMDP
-
based operator evaluation (decision
-
theoretic
lookahead
)