sigma: towards a graphical architecture for integrated cognition
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Sigma: Towards a Graphical Architecture for Integrated Cognition. Paul S. Rosenbloom | 7/27/2012. The Goal of this Work. A new cognitive architecture – Sigma ( 𝚺 ) – based on The broad yet theoretically elegant power of graphical models - PowerPoint PPT PresentationTRANSCRIPT
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Sigma: Towards a Graphical Architecture for Integrated Cognition
Paul S. Rosenbloom | 7/27/2012
2
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
3
Example Virtual Humans (USC/ICT)
Ada & Grace
SASO
Gunslinger
INOTS
4
USC/ICT – SASO USC/ISI & UM – IFOR
Cognitive Architecture
Symbolic working memory (x1 ^next x2)(x2 ^next x3)
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 reflection Interact with worldSoar 3-8 (CMU/UM/USC)
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
A Unified Theory of Cognition Virtual 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 TCA
5
Outline of Talk
Desiderata
Sigma’s core
Progress
Wrap up
6
DESIDERATA
7
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
Towards synergistic robustness– General combinatoric models– Statistics over large bodies of data
Desideratum I: Grand Unified
Expansive base for mechanism
development and integration
8
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 Elegant
9
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
Based on graphical models with piecewise continuous functions
10
SIGMA’S CORE
11
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, production match, …
Can support mixed and hybrid processing Several neural network models map onto them
Graphical Models
w
yx
z
up(u,w,x,y,z) = p(u)p(w)p(x|u,w)p(y|x)p(z|x)
f1
w
f3f2
y
x zu
f(u,w,x,y,z) = f1(u,w,x)f2(x,y,z)f3(z)
p(x|u,w)
w
y
x
z
u p(y|x)
p(z|x)
p(u)
p(w)
12
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:
122132 ...
y zx
f1 =0 2 4 6 …1 3 5 7 …2 4 6 8 … …
f2 =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
234...
678...[0 0 0 1 0 …] [0 0 1 0 0 …]
“3” “2”
Based on Kschischang, Frey & Loeliger, 1998
13
Multidimensional continuous functions– One dimension per variable
Approximated as piecewise linear over arrays of rectilinear (orthotopic) 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
Series10
0.2
0.4
0.6
Mixed Hybrid Representation for Functions/Messages
.7x+.3y+.1
.6x-.2y
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 technology
14
Object:
WM
Concept:
Join
Pattern
Function
Constant
Constructing SigmaDefining 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 nD continuous functions for predicates– Compile to evidence at peripheral factor nodes
LTM Access: Message Passing until Quiescence and then Modify WM
15
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
Object:
WM
Concept:
Join
Pattern
Function
Constant
Walker Table Dog Human
.1 .3 .5 .1
The Structure of ConditionalsCONDITIONAL Concept-Prior Conditions: Object(s,O1) Condacts: Concept(O1,c)
16
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
17
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?
18
PROGRESS
19
Mental imagery [BICA 11a]*– 2D continuous imagery buffer– Transformations on objects
Perception– Edge detection– Object recognition (CRFs) [BICA 11b]
– Localization (of self) [BICA 11b]
Statistical natural language– Question answering (selection)– Word sense disambiguation
Graph 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!
20
CONDITIONAL Transitive Conditions: Next(a,b) Next(b,c) Actions: Next(a,c)
(type ’X :constants ‘(X1 X2 X3))(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
X2
second
first
X1
X2 X3X1
X3
WM
Next(X1,X2)Next(X2,X3)
Next(a,b)
Next(b,c)X2c
b
X1
X2 X3X1
X3
X2ba
X1
X2 X3X1
X3
a
b
cX2c
a
X1
X2 X3X1
X3
1
1
21
CONDITIONAL Concept-Prior Conditions: Object(s,O1) Condacts: Concept(O1,c)
Naïve Bayes classifier– Prior 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> .01w .001w …
[10,20> .2-.01w “ …
[20,50> 0 .025-.00025w …
[50,100> “ “ …
Walker Table Dog Human
.1 .3 .5 .1
Object:
WM
Concept:
Join
Pattern
Function
Constant
Given cues, retrieve (predict) object category and missing attributesE.g., Given Color=Silver, Retrieve Category=Walker, Legs=4, Mobile=T, Alive=F, Weight=10
22
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: BooleanS: SymbolicD: DiscreteC: Continuous
FunctionWMJoin
T
4
Dog=.21
F=.01, T=.2
Silv
er=.
01,
Bro
wn=
.14,
Whi
te=.
05
[1,50)=.00006w-.00006,
[50,150)=.004-.00003w
23
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 rateAdd to function, (shift positive,) and normalize
24
Procedural vs. Declarative Memories
Similarities All based on WM and LTM All LTM based on conditionals All conditionals map to graph Processing by summary product
Differences 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, universalOther variations also possible
25
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)
26
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
All other regions have value 0 (predicate 'board ’((x dimension) (y dimension) (tile tile !)))
27
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
28
Offset boundaries of regions along a dimensions
Special purpose optimization of a delta function
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)
CR
OPPA
D
Translate a Tile
29
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)
30
Comments on Affine Transformations
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
Need polytopic regions for any-angle rotation
CONDITIONAL Edge-Detector-Left Conditions: (tetromino x:x y:y) (tetromino – x:x-.00001 y:y) Actions: (edge x:x y:y)
×
http://mathworld.wolfram.com/ConvexPolyhedron.html
31
X1 X2 XT2
A1
U2
A2
XT3 X3
U3U1
X0 XT1
A0
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 perception
32
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)
Selection
Application
LTM
WM
Generation
LMEvaluation
––
Join Negate WMChanges
+
Decision subgraph
Choice
33
All knowledge encoded as conditionals
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
792 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 Solving
34
Find way in corridor from 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
Decision Theoretic Problem Solving + PerceptionChallenge problem
Door 1 Door 3 Door 2
Wal
l WallIG
35
Integrated Graph for Challenge Problem
O0
X0 XT-1
A-1
O-1
X-1 XT-2
A-2
O-2
X-2 XT-3
A-3
X-3
M0M-1M-2 Pr
O0 O-1 O-2 OT-2 OT-1
P1-2
S1-2
P 2-2
S2-2
P3-2
S3-2
P1-1
S1-1
P 2-1
S2-1
P3-1
S3-1
P10
S10
P 20
S20
P30
S30
X1 X2 XT2
A1
U2
A2
XT3 X3
U3U1
XT1
A0
CRF
POMDP
SLAM
Yields distribution over A0 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)
36
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
392 messages per graph cycle, and .5 msec per message (on iMac)
37
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
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
At
Pt+1
St+1
Rt+1Q(A)tPtRt
St St+1
R
At
Pt+1
St+1
Rt+1Q(A)tPtRt
St SNt
R
St+1
38
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 7G
0 1 2 3 4 5 6 702468
LeftRight
0 1 2 3 4 5 6 70
5
10
0 1 2 3 4 5 6 702468
0 1 2 3 4 5 6 7
Reward
Projected
Q
Graphs are of expected values, but learning is of full distributions
Sampling of conditionals
39
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
40
One-Shot, Two-Person Games
Two players Played only once (not repeated)
– So do not need to look beyond current decision
Symmetric: Players have same payoff matrix Asymmetric: Players have distinct payoff matrices Socially preferred outcome: optimum in some sense Nash equilibrium: No player can increase their
payoff by changing their choice if others stay fixed– Sigma is finding the best Nash equilibrium
Prisoner’s Dilemma
Cooperate
Defect
Cooperate .3 .1(,.4)
Defect .4(,.1) .2A
B
A Cooperate
Defect
Cooperate .1 .2
Defect .3 .1
B Cooperate
Defect
Cooperate .1 .1
Defect .4 .4
41
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 AResult
BResult
Cooperate .3 .1 .43 .43
Defect .4 .2 .57 .57
StagHunt
Cooperate
Defect AResult
BResult
Cooperate .25 0 .54 .54
Defect .1 .1 .46 .46
602 Messages 962 Messages
Agent A Agent B
42
Graph Structure
Select **
PBA
PAB
PAB
PBA
POR
Actual (Abstracted)
All one predicate
Select BB BA
PAB
PBA
AA AB
PBA
PAB
Select
Nominal
Agent A
Agent B
43
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
Defect
Cooperate .1 .2
Defect .3 .1
B Cooperate
Defect
Cooperate .1 .1
Defect .4 .4374 Messages 636 Messages
CorrectOther
AResult
BResult
Cooperate .51 .29
Defect .49 .71
Other asSelf
AResult
BResult
Cooperate .47 .29
Defect .53 .71
44
WRAP UP
45
Closed vs. open world functionsUniversal vs. unique variablesDiscrete vs. continuous variablesBoolean vs. numeric function values
Uni- vs. bi-directional linksMax vs. sum summarizationLong- vs. short-term memoryProduct vs. affine factors
f1
w
f3f2
y
x zu
f(u,w,x,y,z) = f1(u,w,x)f2(x,y,z)f3(z)
Factor graphs w/ Summary Product
0
x+.3y
0
1
.5y
6x
x-y
1
Piecewise Continuous Functions
Rule memory Preference-based decisionsEpisodic memory POMDP-based decisionsSemantic memory LocalizationMental imagery …Edge detectors
➤➤➤➤➤
➤➤➤
Broad Set of Capabilities from Space of VariationsHighlighting Functional Elegance and Grand Unification
Knowledge above architecture also involved– Conditionals that are compiled into subgraphs
46
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
47
PublicationsRosenbloom, 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 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
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