Paul S Rosenbloom 7272012 The Goal of this Work A new cognitive architecture Sigma ID: 262410
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Slide1
Sigma: Towards a Graphical Architecture for Integrated Cognition
Paul S. Rosenbloom | 7/27/2012Slide2
The Goal of this Work
A new cognitive architecture – Sigma (𝚺) – based onThe broad yet theoretically elegant power of graphical modelsThe unifying potential of piecewise continuous functionsAs an approach towards integrated cognitionConsolidating the functionality and phenomena implicated in natural minds/brains and/or artificial cognitive systemsThat meets two general desiderata
Grand unifiedFunctionally elegantIn support of developing functional and robust virtual humans (and intelligent agents/robots)
And ultimately relating to a new unified theory of cognitionSlide3
Example Virtual Humans (USC/ICT)
Ada & Grace
SASO
Gunslinger
INOTSSlide4
USC/ICT – SASO
USC/ISI & UM – IFOR
Cognitive Architecture
Symbolic working memory
(x
1
^next x
2
)(x
2
^next x
3
)
Long-term memory of rules
(
a
^next
b
)(
b
^next
c
)
(
a
^next
c
)
Decide what to do next based on preferences generated by rules
Reflect when can’t decide
Learn results of reflectionInteract with world
Soar 3-8
(CMU/UM/USC)
F
ixed structure underlying intelligent behavior
Defines mechanisms for memory, reasoning, learning, interaction, etc.
Intended to yield
integrated
cognition when
add knowledge and skills
May serve as the basis for
A
Unified Theory of Cognition
V
irtual humans, intelligent agents
and
robots
Induces a language, but not just a language (or toolkit)
Embodies
theory of, and constraints on, parts and their combination
Overlaps in aims with what are variously called AGI architectures and intelligent agent/robot architectures
Examples include ACT-R,
AuRA
, Clarion, Companions, Epic, Icarus,
MicroPsi
,
OpenCog
,
Polyscheme
, RCS, Soar, and TCASlide5
Outline of Talk
DesiderataSigma’s coreProgressWrap upSlide6
DesiderataSlide7
Unified
: Cognitive mechanisms work well togetherShare knowledge, skills and uncertaintyProvide complementary functionalityGrand Unified: Extend to non-cognitive aspectsPerception, motor control, emotion, personality, …Needed for virtual humans, intelligent robots, etc.Forces important breadth up frontMixed: General symbolic reasoning with pervasive uncertaintyHybrid: Discrete and continuous
Towards synergistic robustnessGeneral combinatoric models
Statistics over large bodies of data
Desideratum I:
Grand Unified
E
xpansive
base for
mechanism development and integrationSlide8
Soar
3-8
Hybrid Mixed Short-Term Memory
Learning
Hybrid Mixed Long-Term Memory
Sigma
Decision
Soar 9
(UM)
Broad scope of functionality and applicability
Embodying a superset of
existing architectural capabilities
(cognitive, perceptuomotor, emotive, social, adaptive, …
)
Simple, maintainable, extendible & theoretically elegant
Functionality from composing a small set of general mechanisms
Desideratum II:
Functionally ElegantSlide9
Candidate Bases for Satisfying Desiderata
Programming languages (C, C++, Java, …)Little direct support for capability implementation or integrationAI languages (Lisp, Prolog, …)Neither hybrid nor mixed, nor supportive of integrationArchitecture specification languages (Sceptic, …)Neither hybrid nor mixed, nor sufficiently efficientIntegration frameworks (Storm, …)Nothing to say about capability implementationNeural networksSymbols still difficult, as is achieving necessary capability breadth
Statistical relational languages (Alchemy, BLOG, …)
Exploring a variant tuned to architecture implementation and integrationBased on graphical models with
piecewise continuous functionsSlide10
SIGMA’s CoreSlide11
Enable efficient computation over multivariate functions by decomposing them into products of subfunctions
Bayesian/Markov networks, Markov/conditional random fields, factor graphsYield broad capability from a uniform baseState 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, production match, …
Can support mixed and hybrid processingSeveral 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
)
p
(
x
|
u
,
w
)
w
y
x
z
u
p
(
y
|
x
)
p
(
z
|
x
)
p
(
u
)
p
(
w
)Slide12
Factor graphs handle arbitrary multivariate functions
Variables in function map onto
variable nodes
Factors
in
decomposition map onto
factor nodes
Bidirectional links
connect factors with their variables
Summary product alg. processes messages on links
Messages are distributions
over
link variables (starting w/
evidence
)
At variable nodes messages are combined via
pointwise product
At factor nodes do products, and summarize out unneeded variables:
12
21
32
...
y
z
x
f
1
=
0 2 4 6 …
1 3 5 7 …
2 4 6 8 …
…
f
2
=
0 1 2 …
1 2 3 …
2 3 4 …
…
Factor Graphs and the Summary Product Algorithm
A
single settling
can
efficiently yield:
Marginals
on all
variables (
integral
/
sum
)
Maximum
a
posterior – MAP (
max
)
Can mix across segments of graph
2
3
4
...
6
7
8
...
[0
0
0
1
0
…]
[0
0
1
0
0
…]
“3”
“2”
Based on Kschischang, Frey & Loeliger, 1998Slide13
Multidimensional continuous functions
One dimension per variableApproximated as piecewise linear over arrays of rectilinear (orthotopic) regionsDiscretize domain for discrete distributions & symbols [1,2)=.2, [2,3)=.5, [3,4)=.3Booleanize
range (and add symbol table) for symbols[
0,1)=1
Color(
x
,
Red
)=
True
,
[1,2)
=
0
Color(
x
,
Green
)=
False
Mixed Hybrid Representation for Functions/Messages
.7
x
+.3
y
+.1
.6
x
-.2
y
1
0
1
1
x
+y
.5x+.2
0
x
y
0
.2
.5
.3
Analogous to implementing digital circuits by restricting an inherently continuous underlying technologySlide14
Object:
WM
Concept:
Join
Pattern
Function
Constant
Constructing Sigma
Defining Long-Term and Working Memories
Walker
Table
Dog
Human
.1
.3
.5
.1
CONDITIONAL
Concept-Prior
Conditions
:
Object(
s
,O1)
Condacts
:
Concept(O1,
c
)
Predicate-based representation
E.g.,
Object(
s
,O1)
,
Concept(O1,
c
)
Arguments are constants in WM but may be variables in LTM
LTM is composed of
conditionals
(generalized rules)
A conditional is a set of
patterns
joined
with an
optional
function
Conditionals compile
into graph
structures
WM
comprises
n
D
continuous
functions for predicates
C
ompile to
evidence
at peripheral factor nodes
LTM Access: Message Passing until
Quiescence and then Modify WM
Slide15
Patterns can be
conditions, actions or condactsConditions and actions embody normal rule semanticsConditions: Messages flow from WMActions: Messages flow towards WMCondacts embody (bidirectional) constraint/probability semanticsMessages flow in both directions: local match + global influencePattern networks connect via join nodesProduct (
≈ AND for 0/1) enforces variable binding equality
Functions are defined over pattern variables
Object:
WM
Concept:
Join
Pattern
Function
Constant
Walker
Table
Dog
Human
.1
.3
.5
.1
The Structure of Conditionals
CONDITIONAL
Concept-Prior
Conditions
:
Object(
s
,O1)
Condacts
:
Concept(O1,
c
)Slide16
Some More Detail on Predicates and Patterns
May be closed world or open worldDo unspecified WM regions default to unknown (1) or false (0)?Arguments/variables may be unique or universalUnique act like random variables: P(a)Distribution over values: [.1 .5 .4]Basis for rating and choice
Universal act like rule variables: (
a ^next b
)(
b
^next
c
)
(
a
^next
c
)
Any/all elements can be
true/1
: [1 1 0 0 1]
Work with all
matching
values
Key distinctions between
Procedural and Declarative MemoriesSlide17
Key Questions to be Answered
To what extent can the full range of mechanisms required for intelligent behavior be implemented in this manner?Can the requisite range of mechanisms all be sufficiently efficient for real time behavior on the part of the whole system?What are the functional gains from such a uniform implementation and integration?To what extent can the human mind and brain be modeled via such an approach?Slide18
PROGRESSSlide19
Mental imagery [BICA 11a]*
2D continuous imagery bufferTransformations on objectsPerceptionEdge detectionObject recognition (CRFs) [BICA 11b]Localization (of self) [BICA 11b]
Statistical natural languageQuestion answering (selection)
Word sense disambiguationGraph integration [BICA 11b]
CRF + Localization +
POMDP
Progress
Memory
[ICCM 10]
Procedural (rule)
Declarative (semantic
,
episodic
)
Constraint
Problem solving
Preference based decisions
[AGI 11]
Impasse-driven reflection
Decision-theoretic (POMDP)
[BICA 11b]
Theory of Mind
Learning
Episodic
Gradient
descent
Reinforcement
Some of these are very much just beginnings!Slide20
CONDITIONAL
Transitive
Conditions
:
Next(
a
,
b
)
Next
(
b
,
c
)
Actions
:
Next(
a
,
c
)
(type
’X
:constants
‘(
X
1
X
2
X
3))(predicate
‘Next ‘((first X) (second X)) :world ‘closed)
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
Procedural
if-then
Structures
Just conditions and actions
CW and universal variables
Memory (Rules)
WM
Pattern
Join
X
2
second
first
X
1
X
2
X
3
X
1
X
3
WM
Next(X
1
,X
2
)
Next(
X
2
,X
3
)
Next(
a
,
b
)
Next(
b
,
c
)
X
2
c
b
X
1
X
2
X
3
X
1
X
3
X
2
b
a
X
1
X
2
X
3
X
1
X
3
a
b
c
X
2
c
a
X
1
X
2
X
3
X
1
X
3
1
1Slide21
CONDITIONAL
Concept-Prior Conditions: Object(s,O1) Condacts: Concept(O1,c)
Naïve Bayes classifierPrior on concept + CPs on attributes
Just condacts (in pure form)OW and unique variables
Memory (Semantic)
CONDITIONAL
Concept-Weight
Conditions
:
Object(
s
,O1
)
Condacts
:
Concept(O1,
c
)
Weight
(O1,
w
)
w
\
c
Walker
Table
…[1,10>.01
w.001w
…[10,20>.2-.01w“
…[20,50>0
.025-.00025w
…[50,100>““
…
WalkerTable
Dog
Human
.1
.3
.5
.1
Object:
WM
Concept:
Join
Pattern
Function
Constant
Given
cues,
retrieve (predict)
object category and missing attributes
E.g.,
Given
Color
=
Silver,
Retrieve
Category
=Walker,
Legs
=4,
Mobile
=T,
Alive
=F,
Weight
=
10Slide22
Example Semantic Memory Graph
Concept (S)
Legs (D)
Mobile (B)
Weight (C)
Color (S)
Alive (B)
Just a subset of factor nodes (and no variable nodes)
B: Boolean
S: Symbolic
D: Discrete
C:
Continuous
Function
WM
Join
T
4
Dog=.21
F=.01, T=.2
Silver=.01, Brown=.14,
White=.05
[1,50)=.00006
w
-.
00006,
[50,150)=.004-.00003wSlide23
Local, Incremental, Gradient Descent Learning
(w/ Abram Demski & Teawon Han)
Concept (S)
Legs (D)
Mobile (B)
Weight (C)
Color (S)
Alive (B)
T
4
Based on Russell et al., 1995
Gradient defined by feedback to function node
Normalize (and subtract out average)
Multiply by learning rate
Add to function, (shift positive,) and normalizeSlide24
Procedural vs. Declarative Memories
SimilaritiesAll based on WM and LTMAll LTM based on conditionalsAll conditionals map to graphProcessing by summary productDifferencesProcedural vs. declarativeConditions+actions
vs. condactsDirectionality of message flow
Closed vs. open worldUniversal vs. unique variables
Constraints are actually hybrid:
condacts, OW, universal
Other variations also possibleSlide25
Mental Imagery
How is spatial information represented and processed in minds?Add and delete objects from imagesTranslate, scale and rotate objectsExtract implied properties for further reasoningIn a symbolic architecture either need toRepresent and reason about images symbolicallyConnect to an imagery component (as in Soar 9)Here goal is to use same mechanismsRepresentation: Piecewise continuous functionsReasoning: Conditionals (FGs + SP)Slide26
2D Imagery Buffer in the Eight Puzzle
The Eight Puzzle is a classic sliding tile puzzleRepresented symbolically in typical AI systemsLeftOf(cell11, cell21
), At(tile1,
cell11), etc.Instead represent as a 3D functionC
ontinuous spatial
x
&
y
dimensions
(type
'dimension
:
min 0 :max 3
)
Discrete
tile
dimension (an
xy
plane)
(type
'tile :discrete t :min 0 :max 9)
Region of plane with tile has value 1
All other regions have value 0
(
predicate 'board
’((
x dimension) (y dimension) (tile tile !))
)Slide27
Affine Transformations
Translation: Addition (offset)Negative (e.g., y + -3.1 or y − 3.1): Shift to the leftPositive (e.g., y + 1.5): Shift to the rightScaling: Multiplication (coefficient)<1 (e.g. ¼ × y): Shrink>1 (e.g. 4.37 × y): Enlarge-1 (e.g., -1 × y or -y): Reflect
Requires translation as well to scale around object centerRotation (by multiples of 90°): Swap dimensionsx
⇄ yIn general also requires reflections and translationsSlide28
Offset boundaries of regions along a dimensionsSpecial purpose optimization of a
delta functionCONDITIONAL Move-Right
Conditions:
(selected
state:
s
operator:
o
)
(operator
id:
o
state:
s
x:
x
y:
y
)
(board
state:
s
x:
x
y:y tile:t) (board state:s x:x+1 y:y tile:0)
Actions:
(board state:s x:
x+1 y:y
tile:t) (board –
state:s x:x
y:y tile:t
) (board state:s
x:x
y:
y
tile:0)
(board –
state:
s
x:
x
+1
y:
y
tile:0)
CROP
PAD
Translate a TileSlide29
Transform a Z Tetromino
CONDITIONAL
Rotate-90-Right
C
onditions:
(
tetromino
x:
x
y:
y
)
A
ctions:
(
tetromino
x
:
4-
y
y:
x
)
CONDITIONAL
Reflect-Horizontal
C
onditions:
(
tetromino
x:
x
y:
y
)
A
ctions:
(
tetromino
x:4-
x
y:
y
)
CONDITIONAL
Scale-Half-Horizontal
C
onditions:
(
tetromino
x:
x
y:
y
)
A
ctions:
(
tetromino
x:
x
/2+1
y:
y
)Slide30
Comments on Affine Transformations
Support feature extractionEdge detection with no fixed pixel sizeSupport symbolic reasoningWorking across time slices in episodic memoryWorking across levels of reflectionAsserting equality of different variablesNeed polytopic regions for any-angle rotation
CONDITIONAL
Edge-Detector-Left
C
onditions:
(
tetromino
x:
x
y:
y
)
(
tetromino
– x:
x
-.00001
y:
y
)
A
ctions:
(edge
x:x y:y)
×
http://
mathworld.wolfram.com
/
ConvexPolyhedron.htmlSlide31
X
1
X
2
XT
2
A
1
U
2
A
2
XT
3
X
3
U
3
U
1
X
0
XT
1
A
0
Pr
Problem Solving
1
2
3
4
5
7
8
6
1
2
3
4
5
7
8
6
1
2
4
5
3
7
8
6
1
2
3
4
5
6
7
8
1
2
3
8
4
7
6
5
…
In cognitive architectures, the standard approach is combinatoric search for a goal over sequences of operator applications to symbolic states
Architectures like Soar also add control knowledge for decisions based on associative (rule-driven) retrieval of preferences
E.g., operators that move tiles into position are best
Decision-theoretic approach maximizes utility over sequences of operators with uncertain outcomes
E.g., via a partially observable Markov decision process (POMDP)
This work integrates the latter into the former
While exploring (aspect of) grand unification with perceptionSlide32
Standard (Soar-like) Problem Solving
Base level: Generate, evaluate, select, apply operatorsGenerate (retractable): OW actions – LTM(WM) WMEvaluate (retractable): OW actions + fns – LTM(WM) LMLink memory (LM) caches last message in both directionsSubsumes Soar’s alpha, beta and preference memoriesSelect: Unique variables – LM(WM) WM
Apply (latched): CW actions – LTM(WM)
WMMeta level: Reflect on impasse (not focus here)
Selection
Application
LTM
WM
Generation
L
M
Evaluation
–
–
Join
Negate
WM
Changes
+
Decision subgraph
ChoiceSlide33
All knowledge encoded as conditionals
Total of 17 conditionals to solve simple problems667 nodes (359 variable, 308 factor) and 732 linksSample problem takes 5541 messages over 7 decisions792 messages per graph cycle, and .8 msec per message (on iMac)CONDITIONAL Move-Left
; Move tile left (and blank right) Conditions:
(selected state:
s
operator:left
)
(
operator
id:left
state:
s
x:
x
y:
y
)
(
board
state:
s
x:
x
y:y tile:t) (board state:s x:x-1 y:y tile:0)Actions: (board state:s x:x y:y tile:0) (board – state:s x:x-1 y:
y tile:0)
(board state:s x:x-1 y:
y tile:t) (
board – state:s x:x
y:y tile:t)
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:
1
Eight Puzzle Problem SolvingSlide34
Find way in corridor from to GLocations are discrete, and a map is provided
Vision is local, and feature based rather than object basedCan detect walls (rectangles) and doors (rectangles + circles, colors)Integrates perception, localization, decisions & actionBoth perception and action introduce uncertaintyYielding distributions over objects, locations and action effects
Decision Theoretic Problem Solving + Perception
Challenge problem
Door 1
Door 3
Door 2
Wall
Wall
I
GSlide35
Integrated Graph for Challenge Problem
O
0
X
0
XT
-1
A
-1
O
-1
X
-1
XT
-2
A
-2
O
-2
X
-2
XT
-3
A
-3
X
-3
M
0
M
-1
M
-2
Pr
O
0
O
-1
O
-2
OT
-2
OT
-1
P
1
-2
S
1
-2
P
2
-2
S
2
-2
P
3
-2
S
3
-2
P
1
-1
S
1
-1
P
2
-1
S
2
-1
P
3
-1
S
3
-1
P
1
0
S
1
0
P
2
0
S
2
0
P
3
0
S
3
0
X
1
X
2
XT
2
A
1
U
2
A
2
XT
3
X
3
U
3
U
1
XT
1
A
0
CRF
POMDP
SLAM
Yields distribution over
A
0
from which best action can be selected
Teawon Han (USC)
Junda Chen (USC)
Louis-Philippe Morency (USC/ICT)
Nicole Rafidi (Princeton)
David Pynadath (USC/ICT)
Abram Demski (USC/ICT)Slide36
Comments on Problem Solving & Integrated Graph
Shows decision-theoretic problem solving within same architecture as symbolic problem solvingUltimately using same preference-based choice mechanismCapable of reflecting on impasses in decision makingImplemented within graphical architecture without adding CRF, localization and POMDP modules to itInstead, knowledge is added to LTM and evidence to WMDistribution on A0 defines operator selection preferencesJust as when solve the Eight Puzzle in standard mannerTotal of 25 conditionals
293 nodes (132 variable, 161 factor) and 289 links
Sample problem takes 7837 messages over 20 decisions392 messages per graph cycle, and .5 msec per
message (on iMac)Slide37
Reinforcement Learning
Learn values of actions for states from rewardsSARSA: Q(st, at) ← Q(st, at) + α[rt + γQ(st+1, at+1
) - Q(st, a
t)] Deconstruct in terms of:Gradient-descent learning
Schematic knowledge for prediction
Synchronic learning/prediction
of:
Current
reward (
R
)
Discounted future
reward (
P
)
Q
values (
Q
)Learn given an action model
Diachronic learning/prediction of:
Action model (transition function
) (
SN
)
Requires addition of intervening decision cycle
A
t
P
t+1
S
t+1Rt+1Q(A)tP
t
Rt
St
S
t+1
R
A
t
P
t+1
S
t+1
R
t+1
Q
(
A
)
t
P
t
R
t
S
t
SN
t
R
S
t+1Slide38
RL in 1D Grid
CONDITIONAL Reward Condacts: (Reward x:x value:r) Function<
x,r
>: .1:<[1,6)>,*> …
CONDITIONAL
Backup
Conditions: (Location
state:
s
x:
x
)
(Selected
state:
s
operator:
o
)
(Location*Next
state:
s
x:
nx
)
(Reward
x:
nx value:r) (Projected x:nx value:p) Actions: (Q x:x operator:o value:.95*(p+r)) (Projected x:x value:.95*(p+r))
CONDITIONAL
Transition Conditions: (Location state:s x:x
) (Selected state:s operator:o
) Condacts: (Location*Next state:s x:nx)
Function<x,o,nx>: (.125 * * *)
0
1
2
3
4
5
6
7
G
0
1
2
3
4
5
6
7
Reward
Projected
Q
Graphs are of expected values, but learning is of full distributions
Sampling of conditionalsSlide39
Theory of Mind (ToM)(w/
David Pynadath & Stacy Marsella)Modeling the minds of othersAssessing and predicting complex multiparty situationsMy model of her model of …Building social agents and virtual humansCan Sigma (elegantly) extend to ToM?Based on PscyhSim (Pynadath & Marsella)Decision theoretic problem solving based on POMDPsRecursive agent modeling
Preliminary work in Sigma on intertwined POMDPs (w/ Nicole Rafidi)Belief revision based on explaining past history
Can cost and quality of ToM be improved?Initial experiments with one-shot, two-person gamesCooperate vs. defectSlide40
One-Shot, Two-Person Games
Two playersPlayed only once (not repeated)So do not need to look beyond current decisionSymmetric: Players have same payoff matrixAsymmetric: Players have distinct payoff matricesSocially preferred outcome: optimum in some senseNash equilibrium: No player can increase their payoff by changing their choice if others stay fixedSigma is finding the best Nash equilibriumPrisoner’s Dilemma
Cooperate
DefectCooperate
.3
.1(,.4)
Defect
.4(,.1)
.2
A
B
A
Cooperate
Defect
Cooperate
.1
.2
Defect
.3
.1
B
Cooperate
Defect
Cooperate
.1
.1
Defect
.4
.4Slide41
Symmetric, One-Shot, Two-Person Games
CONDITIONAL Payoff-A-A CONDITIONAL Payoff-B-B Conditions: Choice(A,
B,op-b
) Conditions
:
Choice
(
B
,
A
,
op
-a
)
[B’s model of A]
Actions:
Choice(
A
,
A
,
op
-a
)
Actions:
Choice(
B
,
B
,op-b) [B’s model of B] Function: payoff(op-a,op-b) Function: payoff(op-b,op-a)CONDITIONAL Payoff-A-B CONDITIONAL Payoff-B-A Conditions: Choice(A,A
,op-a
) Conditions: Choice(B,B,
op-b) Actions: Choice(
A,B,op-b) Actions:
Choice(B,A,op-a
)
Function: payoff(op-b,
op-a) Function:
payoff(op-a,op
-b
)
CONDITIONAL
Select-Own-Op
Conditions
:
Choice(
ag
,
ag
,
op
)
Actions
:
Selected(
ag
,
op
)
Prisoner’s Dilemma
Cooperate
Defect
A
Result
B
Result
Cooperate
.3
.1
.43
.43
Defect
.4
.2
.57
.57
Stag
Hunt
Cooperate
Defect
A
Result
BResultCooperate
.25
0
.54
.54
Defect
.1
.1
.46
.46
602 Messages
962 Messages
Agent A
Agent BSlide42
Graph Structure
Select
**
P
BA
P
AB
P
AB
P
BA
POR
Actual (Abstracted)
All one predicate
Select
BB
BA
P
AB
P
BA
AA
AB
P
BA
P
AB
Select
Nominal
Agent A
Agent BSlide43
Asymmetric, One-Shot, Two-Person Games
CONDITIONAL Payoff-A-A CONDITIONAL Payoff-B-B Conditions: Choice(A,
B,op
-b)
Conditions
:
Choice
(
B
,
A
,
op
-a
)
Actions:
Choice(
A
,
A
,
op
-a
)
Actions:
Choice(
B
,
B
,op-b) Function: payoff(A,op-a,op-b) Function: payoff(B,op-b,op-a)CONDITIONAL Payoff-A-B CONDITIONAL Payoff-B-A Conditions: Choice(
A,A,
op-a) Conditions: Choice(B,
B,op-b)
Model(m) Model(m)
Actions: Choice(A,B,op
-b)
Actions: Choice(B,A
,op-a) Function:
payoff(m,
op
-
b,
op
-a
)
Function:
payoff
(
m
,
op
-
a,
op
-
b
)
CONDITIONAL
Select-Own-Op
Conditions
:
Choice(
ag
,
ag
,
op
)
Actions
:
Selected(
ag
,
op
)
A
Cooperate
DefectCooperate.1.2
Defect.3.1
BCooperateDefectCooperate
.1
.1
Defect
.4
.4
374 Messages
636 Messages
Correct
Other
A
Result
B
Result
Cooperate
.51
.29
Defect
.49
.71
Other as
Self
A
Result
B
Result
Cooperate
.47
.29
Defect
.53
.71Slide44
Wrap UPSlide45
Closed vs. open world functions
Universal vs. unique variablesDiscrete vs. continuous variablesBoolean vs. numeric function values
Uni
- vs. bi-directional linksMax vs. sum summarization
Long- vs. short-term memory
Product vs. affine factors
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
)
Factor graphs w/ Summary Product
0
x
+.
3y
0
1
.5y
6
x
x
-
y
1
Piecewise Continuous Functions
Rule memory Preference-based decisions
Episodic memory POMDP-based decisions
Semantic memory Localization
Mental imagery …
Edge detectors
➤
➤
➤
➤
➤
➤
➤
➤
Broad Set of Capabilities from Space of Variations
Highlighting
Functional Elegance
and
Grand Unification
Knowledge above architecture also involved
Conditionals that are compiled into subgraphsSlide46
Conclusion
Sigma is a novel graphical architectureWith potential to support integrated cognition and the development of virtual humans (and intelligent agents/robots)Focus so far is not on a unified theory of human cognitionHowever, makes interesting points of contact with existing theoriesGrand unificationDemonstrated mixed processingBoth general symbolic problem solving and probabilistic reasoningDemonstrated hybrid
processingIncluding forms of perception integrated directly with cognitionNeed much more on perception, plus action, emotion, …
Functional eleganceDemonstrated aspects of memory,
learning, problem
solving, perception, imagery,
Theory of Mind [and natural language]
Based on factor
graphs
and piecewise continuous
functionsSlide47
Publications
Rosenbloom, P. S. (2009). Towards a new cognitive hourglass: Uniform implementation of cognitive architecture via factor graphs. Proceedings of the 9th International Conference on Cognitive Modeling.Rosenbloom, P. S. (2009). A graphical rethinking of the cognitive inner loop. Proceedings of the IJCAI International Workshop on Graphical Structures for Knowledge Representation and Reasoning.Rosenbloom, P. S. (2009). Towards uniform implementation of architectural diversity. Proceedings of the AAAI Fall Symposium on Multi-Representational Architectures for Human-Level
Intelligence.Rosenbloom, P. S. (2010). An architectural approach to statistical relational AI.
Proceedings of the AAAI Workshop on Statistical Relational AI.
Rosenbloom
, P. S. (2010). Speculations on leveraging graphical models for architectural integration of visual representation and reasoning.
Proceedings of the AAAI-10 Workshop on Visual Representations and Reasoning
.
Rosenbloom
, P. S. (2010). Combining procedural and declarative knowledge in a graphical architecture.
Proceedings of the
10
th
International Conference on Cognitive Modeling
.
Rosenbloom
, P. S. (2010). Implementing first-order variables in a graphical cognitive architecture.
Proceedings of the First International Conference on Biologically Inspired Cognitive Architectures
.
Rosenbloom
, P. S. (2011). Rethinking cognitive architecture via graphical models.
Cognitive Systems Research
, 12, 198-
209.
Rosenbloom, P. S. (2011). From memory to problem solving: Mechanism reuse in a graphical cognitive architecture.
Proceedings of the Fourth Conference on Artificial General
Intelligence
.
Winner of the
2011 Kurzweil Award for Best AGI Idea.Rosenbloom, P. S. (2011). Mental imagery in a graphical cognitive architecture. Proceedings of the Second International Conference on Biologically Inspired Cognitive Architectures.Chen, J., Demski, A., Han, T., Morency, L-P., Pynadath, P., Rafidi, N. & Rosenbloom, P. S. (2011). Fusing symbolic and decision-theoretic problem solving + perception in a graphical cognitive architecture. Proceedings of the Second International Conference on Biologically Inspired Cognitive Architectures.Rosenbloom, P. S. (2011). Bridging dichotomies in cognitive architectures for virtual humans. Proceedings of the AAAI Fall Symposium on Advances in Cognitive Systems.Rosenbloom, P. S. (2012). Graphical models for integrated intelligent robot architectures. Proceedings of the AAAI Spring Symposium on Designing Intelligent Robots: Reintegrating AI.Rosenbloom, P. S. (2012). Towards a 50 msec cognitive cycle in a graphical architecture. Proceedings of the 11th International Conference on Cognitive Modeling.Rosenbloom, P. S. (2012). Towards functionally elegant, grand unified architectures. Proceedings of the 21st Behavior Representation in Modeling & Simulation (BRIMS) Conference. Abstract for panel on “Accelerating the Evolution of Cognitive Architectures,” K. A. Gluck (organizer).