Sigma: Towards a Graphical Architecture for
Integrated Cognition
Paul S. Rosenbloom
7/27/2012
The projects or efforts depicted were or are sponsored by the U.S.
Army, AFOSR and ONR. The content or information presented
does not necessarily reflect the position or the policy of the
Government, and no official endorsement should be inferred.
The Goal of this Work

A new cognitive architecture – Sigma (𝚺) – based on
– The broad yet theoretically elegant power of graphical models
– The unifying potential of piecewise continuous functions

As an approach towards integrated cognition
– Consolidating the functionality and phenomena implicated in
natural minds/brains and/or artificial cognitive systems

That meets two general desiderata
– Grand unified
– Functionally elegant

In support of developing functional and robust
virtual humans (and intelligent agents/robots)
– And ultimately relating to a new unified theory of cognition
2
Example Virtual Humans (USC/ICT)
Ada & Grace
Gunslinger
INOTS
3
SASO
Cognitive Architecture

Fixed 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
 Symbolic working memory


A Unified Theory of Cognition
(x1 ^next x2)(x2 ^next x3)
 Virtual humans, intelligent agents and robots
 Long-term memory
of rules
Induces a language, but not just
language
toolkit)
(a a
^next
b)(b ^next(or
c)(a
^next c)
– Embodies theory of, and constraints on, parts and their combination

Decide what to do next
 Overlaps in aims with what are variously
called AGI
based on preferences
generatedarchitectures
by rules
architectures and intelligent agent/robot

Examples include ACT-R, AuRA,
Clarion,
Companions,
 Reflect
when
can’t decide
Epic, Icarus, MicroPsi, OpenCog,
Polyscheme,
RCS,
 Learn
results of reflection
Soar, and TCA
USC/ICT – SASO
Soar 3-8 (CMU/UM/USC)
4

Interact with world
USC/ISI & UM – IFOR
Outline of Talk

Desiderata

Sigma’s core

Progress

Wrap up
5
DESIDERATA
6
Desideratum I: Grand Unified

Unified: Cognitive mechanisms work well together
– Share knowledge, skills and uncertainty
– Provide complementary functionality

Grand Unified: Extend to non-cognitive aspects
– Perception, motor control, emotion, personality, …
– Needed for virtual humans, intelligent robots, etc.

Forces important breadth up front
– Mixed: General symbolic reasoning with pervasive uncertainty
– Hybrid: Discrete and continuous
Expansive base for
 Towards synergistic robustness
mechanism development
– General combinatoric models
and integration
– Statistics over large bodies of data
7
Desideratum II: Functionally Elegant

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
Hybrid Mixed Long-Term Memory
Learning
Hybrid Mixed Short-Term Memory
8
Sigma
Soar
3-8
D
e
c
i
s
i
o
n
Soar 9 (UM)
Candidate Bases for Satisfying Desiderata

Programming languages (C, C++, Java, …)
– Little direct support for capability implementation or integration

AI languages (Lisp, Prolog, …)
– Neither hybrid nor mixed, nor supportive of integration

Architecture specification languages (Sceptic, …)
– Neither hybrid nor mixed, nor sufficiently efficient

Integration frameworks (Storm, …)
– Nothing to say about capability implementation

Neural networks
– Symbols still difficult, as is achieving necessary capability breadth

Statistical relational languages (Alchemy, BLOG, …)
– Exploring a variant tuned to architecture implementation and integration

9
Based on graphical models with piecewise continuous functions
SIGMA’S CORE
10
Graphical Models

Enable efficient computation over multivariate functions by
decomposing them into products of subfunctions
– Bayesian/Markov networks, Markov/conditional random fields, factor graphs
p(u,w,x,y,z) = p(u)p(w)p(x|u,w)p(y|x)p(z|x)
u
w

x
f(u,w,x,y,z) = f1(u,w,x)f2(x,y,z)f3(z)
w
y
u
z
y
x
f1
z
f2
f3
p(u)
y
Yield broad
capability
from a uniform base
– Stateuof the art performance across symbols, probabilities and signals via
p(y|x)
uniform representation and reasoning algorithm
 (Loopy) belief propagation,
p(x|u,w)
x forward-backward algorithm, Kalman filters, Viterbi algorithm, FFT,
turbo decoding, arc-consistency, production match, …
w
Can support
mixedp(z|x)
and hybrid processing
 Several
models map onto them
z
p(w)neural network

11
Based on Kschischang, Frey & Loeliger, 1998
Factor Graphs and the Summary Product Algorithm
 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:
m(y) = ò m(x) ´ f1 (x, y)
x
f (x,y,z)= y2 +yz+2yx+2xz
=(2x+y)(y+z)= f1(x,y) f2(y,z)
x [0 0“3”
0 1 0 …]
A single settling can efficiently yield:
Marginals on all variables (integral/sum)
Maximum a posterior – MAP (max)
Can
mix across segments of graph
12
f1 =
6
7
8
...
0246…
1357…
2468…
…
2x+ y
y
12
21
32
...
2
3
4
...
f2 =
“2”
[0 0 1 0 0 …]
012…
123…
234…
…
y+z
z
Mixed Hybrid Representation for Functions/Messages

Multidimensional continuous functions
– One dimension per variable

Approximated as piecewise linear over arrays of
x
rectilinear (orthotopic) regions
Analogous to implementing
digital circuits by restricting
an inherently continuous
underlying technology

y
.7x+.3y+.1
1
.5x+.
2
.6x-.2y
0
x+y
1
1
0
Discretize domain for discrete distributions & symbols
[1,2)=.2, [2,3)=.5, [3,4)=.3
0
.2
.5
.3
0.6
0.4
0.2
0

Booleanize range (and add symbol table) for symbols
[0,1)=1  Color(x, Red)=True,
13
[1,2)=0  Color(x, Green)=False
Constructing Sigma
Defining Long-Term and Working

CONDITIONAL Concept-Prior
Conditions:
MemoriesObject(s,O1)
Condacts:
Walker
TableConcept(O1,c)
Dog
Human
Predicate-based representation
.1
.3
.5
.1
– 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 nD continuous functions for predicates
– Compile to evidence at peripheral factor nodes
WM
Object:
Constant
Pattern
Join
Function
Concept:
LTM Access: Message Passing until Quiescence and then Modify WM
14
The Structure of Conditionals
CONDITIONAL Concept-Prior
Conditions:
Object(s,O1)
Condacts:
Walker
TableConcept(O1,c)
Dog
Human
.1

.3
.5
Patterns can be conditions, actions or condacts
– Conditions and actions embody normal rule semantics

Conditions: Messages flow from WM
 Actions: Messages flow towards WM
– Condacts embody (bidirectional) constraint/probability semantics


Messages flow in both directions: local match + global influence
Pattern networks connect via join nodes
– Product (≈ AND for 0/1) enforces variable binding equality

Functions are defined over pattern variables
WM
Object:
Concept:
15
Constant
Pattern
Join
Function
.1
Some More Detail on Predicates and Patterns

May be closed world or open world
– Do unspecified WM regions default to unknown (1) or false (0)?

Arguments/variables may be unique or universal
– Unique 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 Memories
16
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?
17
PROGRESS
18
Progress

Memory [ICCM 10]
– Procedural (rule)
– Declarative (semantic, episodic)
– Constraint


Preference based decisions [AGI 11]
Impasse-driven reflection
Decision-theoretic (POMDP) [BICA 11b] 
Theory of Mind
Learning
– Episodic
– Gradient descent
– Reinforcement
Mental imagery [BICA 11a]*
– 2D continuous imagery buffer
– Transformations on objects
Problem solving
–
–
–
–



Perception
– Edge detection
– Object recognition (CRFs) [BICA 11b]
– Localization (of self) [BICA 11b]
Statistical natural language
– Question answering (selection)
– Word sense disambiguation
Graph integration
– CRF + Localization + POMDP
Some of these are very much just beginnings!
19
[BICA 11b]
CONDITIONAL Transitive
Conditions: Next(a,b)
Next(b,c)
Actions: Next(a,c)
Memory (Rules)
Pattern
Join
– CW and universal variables
X1
20
X1 0
X2 1
X3 0
0
0
0
0
X1
1
0
X1 0
X2 1
X3 0
c
second
X1 0
X2 1
X3 10
b
Next(X1,X2)
Next(X2,X3)
first
X1 X2 X3
WM
a
X2 X3
0
0
0
0
X1
1
0
X1
0
X2
X3 1
b
X2 X3
0
0
0
0
1
0
1
a
c

Procedural if-then Structures
Just conditions and actions
b

a
X2 X3
0
0
(type ’X :constants ‘(X1 X2 X3))
(predicate ‘Next ‘((first X) (second X)) :world ‘closed)
Memory (Semantic)
Given cues, retrieve (predict) object category and missing attributes
E.g., Given Color=Silver, Retrieve Category=Walker, Legs=4, Mobile=T, Alive=F, Weight=10


CONDITIONAL Concept-Weight
Naïve Bayes classifier
Conditions: Object(s,O1)
Condacts: Concept(O1,c)
– Prior on concept + CPs on attributes
Weight(O1,w)
Just condacts (in pure form)
– OW and unique variables
CONDITIONAL Concept-Prior
Conditions: Object(s,O1)
Condacts: Concept(O1,c)
WM
Object:
Concept:
21
Walker
Table
Dog
Human
.1
.3
.5
.1
Constant
Pattern
w\c
Walker
Table
…
[1,10>
.01w
.001w
…
[10,20>
.2-.01w
“
…
[20,50>
0
.025.00025w
…
[50,100>
“
“
…
Join
Function
Example Semantic Memory Graph
Concept (S)
Silver=.01,
Brown=.14,
White=.05
[1,50)=.00006w-.00006,
[50,150)=.004-.00003w
Weight (C)
Dog=.21
Color (S)
Function
WM
Join
Mobile (B)
Legs (D)
T
Alive (B)
Just a subset of factor nodes (and no variable nodes)
22
B: Boolean
S: Symbolic
D: Discrete
C: Continuous
Based on Russell et al., 1995
Local, Incremental, Gradient Descent Learning
(w/ Abram Demski & Teawon Han)
Concept (S)
Color (S)
Weight (C)
Mobile (B)
Legs (D)
T
Alive (B)
23
Gradient defined by feedback to function node
Normalize (and subtract out average)
Multiply by learning rate
Add to function, (shift positive,) and normalize
Procedural vs. Declarative Memories
Similarities
Differences

All based on WM and LTM

All LTM based on conditionals

All conditionals map to graph

Processing by summary product

Procedural vs. declarative
– Conditions+actions vs. condacts

Directionality of message flow
– Closed vs. open world
– Universal vs. unique variables
Constraints are actually hybrid:
condacts, OW, universal
Other variations also possible
24
Mental Imagery

How is spatial information represented
and processed in minds?
– Add and delete objects from images
– Translate, scale and rotate objects
– Extract implied properties for further reasoning

In a symbolic architecture either need to
– Represent and reason about images symbolically
– Connect to an imagery component (as in Soar 9)

Here goal is to use same mechanisms
– Representation: Piecewise continuous functions
– Reasoning: Conditionals (FGs + SP)
25
2D Imagery Buffer in the Eight Puzzle

The Eight Puzzle is a classic sliding tile puzzle

Represented symbolically in typical AI systems
– LeftOf(cell11, cell21), At(tile1, cell11), etc.

Instead represent as a 3D function
– Continuous 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
26

All other regions have value 0

(predicate 'board ’((x dimension) (y dimension) (tile tile !)))
Affine Transformations

Translation: Addition (offset)
– Negative (e.g., y + -3.1 or y − 3.1): Shift to the left
– Positive (e.g., y + 1.5): Shift to the right

Scaling: 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 center
Rotation (by multiples of 90°): Swap dimensions
– x ⇄y
– In general also requires reflections and translations
27
Translate a Tile
Offset boundaries of regions along a dimensions

28
CROP
CONDITIONAL 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)
PAD

Special purpose optimization of a delta function
Transform a Z Tetromino
CONDITIONAL Rotate-90-Right
Conditions: (tetromino x:x y:y)
Actions: (tetromino x:4-y y:x)
CONDITIONAL Reflect-Horizontal
Conditions: (tetromino x:x y:y)
Actions: (tetromino x:4-x y:y)
CONDITIONAL Scale-Half-Horizontal
Conditions: (tetromino x:x y:y)
Actions: (tetromino x:x/2+1 y:y)
29
Comments on Affine
Transformations

CONDITIONAL Edge-Detector-Left
Conditions: (tetromino x:x y:y)
(tetromino – x:x-.00001
y:y)
Actions: (edge x:x y:y)
Support feature extraction
– Edge detection with no fixed pixel size
×

Support symbolic reasoning
– Working across time slices in episodic memory
– Working across levels of reflection
– Asserting equality of different variables

30
Need polytopic regions for any-angle rotation
http://mathworld.wolfram.com/
ConvexPolyhedron.html
Problem Solving

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
1 2 3
based on associative
(rule-driven) retrieval of preferences
4 5

7 8 move
6
E.g., operators that
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 integratesU the latter
intoUthe former
U
1
2
1
4
5
3
4
7
8
6
7
1
8
3
1
2
3
5
4
5
6
8
6
7
8
2
3
2
41
2
3
7 6 5
– While exploring (aspect
of) grand unification with perception
Pr
X0
XT1
X
XT2
X2
XT3
1
A0
31
A1
A2
X3
Standard (Soar-like) Problem Solving

Base level: Generate, evaluate, select, apply operators
– Generate (retractable): OW actions – LTM(WM)  WM
– Evaluate (retractable): OW actions + fns – LTM(WM)  LM

Link memory (LM) caches last message in both directions
– Subsumes Soar’s alpha, beta and preference memories
– Select: Unique variables – LM(WM)  WM
– Apply (latched): CW actions – LTM(WM)  WM

Meta level: Reflect on impasse (not focus here)
Decision subgraph
LTM
Join Negate Changes WM
–
–
Choice
+
32
LM
Selection
WM
Eight Puzzle Problem Solving

All knowledge encoded as conditionals
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

Total of 17 conditionals to solve simple problems
– 667 nodes (359 variable, 308 factor) and 732 links
– Sample problem takes 5541 messages over 7 decisions

33
792 messages per graph cycle, and .8 msec per message (on iMac)
Decision Theoretic Problem Solving + Perception
G
I
Door 1

Wall
Wall
Challenge problem
Door 3
Find way in corridor from
Door 2
to G
– Locations are discrete, and a map is provided
– Vision is local, and feature based rather than object based


Can detect walls (rectangles) and doors (rectangles + circles, colors)
Integrates perception, localization, decisions & action
– Both perception and action introduce uncertainty

Yielding distributions over objects, locations and action effects
W
0
34
D1
G
1
2
3
D2
4
5
6
D3
7
8
I
9
W
10
11
Integrated Graph for Challenge Problem
W
D1
0
G
1
2
D2
3
4
5
D3
6
7
SLAM
X-2
XT-3
I
U1
Teawon Han (USC)
X-3
8
X-1
XT-2
X0
XT-1
XT1
X
W
9
10
11
U2
XT2
X2
U3
XT3
X3
1
Pr
A-
A-
M-2
3
Abram Demski (USC/ICT)
O-2
P1-2
O-1
OT-2
P3-2
S1
S2-2
-2
A0
A1
P1-1
O0
OT-1
P3-1
P 10
P 2-1
S3
-2
M0
A2
1
P 2-2
35
A-
M-1
2
S1
S2-1
P 30
P 20
S3
-1
POMDP
-1
S1
S3
0
0
Nicole Rafidi (Princeton)
David Pynadath (USC/ICT)
CRF
Junda Chen (USC)
Louis-Philippe Morency (USC/ICT)
S20
Yields distribution over
A0 from which best
action can be selected
Comments on Problem Solving & Integrated Graph

Shows decision-theoretic problem solving within
same architecture as symbolic problem solving
– Ultimately using same preference-based choice mechanism
– Capable of reflecting on impasses in decision making

Implemented within graphical architecture without
adding CRF, localization and POMDP modules to it
– Instead, knowledge is added to LTM and evidence to WM

Distribution on A0 defines operator selection preferences
– Just as when solve the Eight Puzzle in standard manner

Total of 25 conditionals
– 293 nodes (132 variable, 161 factor) and 289 links
– Sample problem takes 7837 messages over 20 decisions

36
392 messages per graph cycle, and .5 msec per message (on iMac)
Reinforcement Learning

Learn values of actions for states from rewards
– SARSA: Q(st, at) ← Q(st, at) + α[rt + γQ(st+1, at+1) - Q(st, at)]

Deconstruct in terms of:
– Gradient-descent learning
– Schematic knowledge for prediction

Rt
Current reward (R)
Discounted future reward (P)
Q values (Q)
Learn given an action model
Q(A)t
Rt+1
At
Pt+1
St+1
St
St+1
R
Rt
Pt
Q(A)t
Rt+1
Pt+1
Diachronic learning/prediction of:
– Action model (transition function) (SN)
– Requires addition of intervening decision cycle
37
Pt
Synchronic learning/prediction of:
–
–
–
–

R
At
St
St+1
SNt
St+1
RL in 1D Grid
0
1
2
3
Sampling of conditionals
CONDITIONAL Reward
Condacts: (Reward x:x value:r)
Function<x,r>: .1:<[1,6)>,*> …
G
4
5
6
7
10
Reward
5
0
0
1
2
3
4
5
6
7
10
CONDITIONAL Backup
5
Conditions: (Location state:s x:x)
(Selected state:s operator:o)
0
(Location*Next state:s x:nx)
(Reward x:nx value:r)
10
(Projected x:nx value:p)
Actions: (Q x:x operator:o value:.95*(p+r))
5
(Projected x:x value:.95*(p+r))
Q
Left
Right
0
1
2
3
4
5
6
7
2
3
4
5
6
7
Projected
0
0
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 * * *)
38
1
0
1
2
Graphs are of expected values,
but learning is of full distributions
3
4
5
6
7
Theory of Mind (ToM)
(w/ David Pynadath & Stacy Marsella)

Modeling the minds of others
– Assessing and predicting complex multiparty situations

My model of her model of …
– Building social agents and virtual humans

Can Sigma (elegantly) extend to ToM?
– Based on PscyhSim (Pynadath & Marsella)

Decision theoretic problem solving based on POMDPs
 Recursive 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 games
– Cooperate vs. defect
39
One-Shot, Two-Person Games


B
Two players
Played only once (not repeated)
A
Prisoner’s
Dilemma
Cooperat
e
Defect
Cooperate
.3
.1(,.4)
.4(,.1)
.2
Defect
– So do not need to look beyond current decision

Symmetric: Players have same payoff matrix

Asymmetric: Players have distinct payoff matrices

A
Cooperat
Defect
Cooperat
Defect
Socially
preferred
outcome:B optimum
in
some sense
e

e
Cooperate
.1
.2
Cooperate
.1
.1
Nash
equilibrium:
No player
can increase
their
Defect
.4
.4
Defect
.3
.1
payoff by changing their choice if others stay fixed
– Sigma is finding the best Nash equilibrium
40
Symmetric, One-Shot, Two-Person Games
Agent A
Agent B
CONDITIONAL Payoff-A-A
Conditions: Choice(A,B,op-b)
Actions:
Choice(A,A,op-a)
Function:
payoff(op-a,op-b)
CONDITIONAL Payoff-B-B
Conditions: Choice(B,A,op-a) [B’s model of A]
Actions:
Choice(B,B,op-b) [B’s model of B]
Function:
payoff(op-b,op-a)
CONDITIONAL Payoff-A-B
Conditions: Choice(A,A,op-a)
Actions:
Choice(A,B,op-b)
Function:
payoff(op-b,op-a)
CONDITIONAL Payoff-B-A
Conditions: Choice(B,B,op-b)
Actions:
Choice(B,A,op-a)
Function:
payoff(op-a,op-b)
CONDITIONAL Select-Own-Op
Conditions: Choice(ag,ag,op)
Actions:
Selected(ag,op)
Prisoner’s
Dilemma
Cooperat
e
Defect
A
Result
B
Result
Stag
Hunt
Cooperat
e
Defect
A
Result
B
Result
Cooperate
.3
.1
.43
.43
Cooperate
.25
0
.54
.54
Defect
.4
.2
.57
.57
Defect
.1
.1
.46
.46
602 Messages
41
962 Messages
Graph Structure
Nominal
Agent A
Select
PBA
AA
AB
PAB
Actual (Abstracted)
Agent B
Select
PAB
BB
BA
PBA
PBA
PAB
Select
PO
R
**
PAB
All one predicate
42
PBA
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)
Correct
Other
A
Result
B
Result
Other as
Self
A
Result
B
Result
Cooperate
.51
.29
Cooperate
.47
.29
Defect
.49
.71
Defect
.53
.71
374 Messages
43
636 Messages
A
Cooperat
e
Defect
Cooperate
.1
.2
Defect
.3
.1
B
Cooperat
e
Defect
Cooperate
.1
.1
Defect
.4
.4
WRAP UP
44
Broad Set of Capabilities from Space of Variations
Highlighting Functional Elegance and Grand Unification
➤ Rule memory
➤ Episodic memory
➤ Semantic memory
➤ Mental imagery
➤ Edge detectors
➤ Preference-based decisions
➤ POMDP-based decisions
➤ Localization
…
Uni- vs. bi-directional links
Max vs. sum summarization
Long- vs. short-term memory
Product vs. affine factors
Closed vs. open world functions
Universal vs. unique variables
Discrete vs. continuous variables
Boolean vs. numeric function values

.5y
0
x+.3y
1
x-y
1
f(u,w,x,y,z) = f1(u,w,x)f2(x,y,z)f3(z)
w
u
y
x
Knowledge above architecture also involved
– Conditionals
that are compiled into subgraphs
f
0
6x
f2
f3
Factor graphs w/ Summary Product
1
Piecewise Continuous Functions
45
z
Conclusion

Sigma is a novel graphical architecture
– With 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 cognition


However, makes interesting points of contact with existing theories
Grand unification
– Demonstrated mixed processing

Both general symbolic problem solving and probabilistic reasoning
– Demonstrated hybrid processing

Including forms of perception integrated directly with cognition
– Need much more on perception, plus action, emotion, …

Functional elegance
– Demonstrated aspects of memory, learning, problem solving,
perception, imagery, Theory of Mind [and natural language]
– Based on factor graphs and piecewise continuous functions
46
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 MultiRepresentational 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 10th 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).
47