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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.
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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 worldSoar 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
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Hybrid Short-Term Memory
Prediction-Based Learning
Hybrid Mixed Long-Term Memory
Graphical Architecture
Decision
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 9Soar 3-8
4
Goals of This 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
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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 WMSelection
ApplicationGenerationEvaluation
Decision Cycle
Elaboration Cycle
Match Cycle
Elaboration cycles + decision
Parallel rule match + firing
Pass token within Rete rule-match network
D
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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
yx
z
u
p(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)
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The Graphical ArchitectureFactor 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
f1
w
f3f2
y
x zu
f(u,w,x,y,z) = f1(u,w,x)f2(x,y,z)f3(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.
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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 .2y 0
[5,15> .5x 1 .1+.2x+.4y
Series10
0.2
0.4
0.6
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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
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Conditionals
CONDITIONAL Transitive conditions: (Next ob1:a ob2:b) (Next ob1:b ob2:c) actions: (Next ob1:a ob2:c)
WM
Pattern
Join
w\c Walker Table …
[1,10> .01w .001w …
[10,20> .2-.01w “ …
[20,50> 0 .025-.00025w …
[50,100> “ “ …
CONDITIONAL Concept-Weight condacts: (concept object:O1 class:c) (weight object:O1 value:w)
function:
WM PatternJoin Function
Conditions test WM
Actions propose changes to WM
Condacts test and change WM
Functions modulate variables
All four can be freely mixed
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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> .01w .001w …
[10,20> .2-.01w “ …
[20,50> 0 .025-.00025w …
[50,100>
“ “ …
Function:
CONDITIONAL ConceptWeight Condacts: Concept(O1,c) Weight(O1,w)
Concept (S)
Legs (D)Mobile (B)
Weight (C) Color (S)
Alive (B)
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Additional Aspects Relevant to Problem SolvingOpen World versus Closed World 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
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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 SolvingUniversal versus Unique Variables
Join Negate WMChanges
+
–
Action combination subgraph:
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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 SolvingLink Memory
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Problem Solving in theGraphical 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
LM WMSelection
ApplicationGenerationEvaluation
Graph Cycle
Message Cycle
Message cycles + WM change
Process message within factor graph
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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 states operator:ct) :function 10
CONDITIONAL previous-reject ; Reject previously moved operator :conditions (acceptable state:s operator:ct) (previous state:s operator:ct) :actions (selected - state:s operator:ct)
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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)
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