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

1. 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: 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 aUnified Theory of Cognition the core of virtual humans and intelligent agents or robots the basis for artificial general intelligence 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 ICT 2010

3. Diversity Dilemma • 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, … Hybrid Mixed Long-Term Memory Decision Prediction-Based Learning Hybrid Short-Term Memory Soar 9 Soar 3-8 Graphical Architecture

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

5. LTM Problem Solving in Soar Evaluation Application Generation PM WM • 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) Selection D Decision Cycle Elaboration cycles + decision Elaboration Cycle Parallel rule match + firing Match Cycle Pass token within Rete rule-match network

6. u y x w z Graphical Models • 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 • f(u,w,x,y,z) = f1(u,w,x)f2(x,y,z)f3(z) • p(u,w,x,y,z) = p(u)p(w)p(x|u,w)p(y|x)p(z|x) w y u x z f1 f2 f3

7. 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 • f(u,w,x,y,z) = f1(u,w,x)f2(x,y,z)f3(z) w y u x z f1 f2 f3 A single settling of the graph can efficiently compute: Variable marginals Maximum a posterior (MAP) probs. .2 .4 .1 .3 .2 .1 .06 .08 .01

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

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 predicatepatterns and functions • Patterns define conditions, actionsand condacts (a neologism) • Functions are mixed hybrid over pattern variables in conditionals • Each predicate induces own working memory node WM

10. Conditionals CONDITIONALConcept-Weight condacts: (concept object:O1class:c) (weightobject:O1value:w) function: Conditions test WM Actions propose changes to WM Condacts test and change WM Functions modulate variables CONDITIONAL Transitive conditions: (Next ob1:aob2:b) (Nextob1:bob2:c) actions: (Nextob1:aob2:c) Pattern Join WM Pattern WM Join Function All four can be freely mixed

11. Memory Capabilities Implemented Concept (S) • 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 Color (S) Weight (C) CONDITIONAL Transitive Conditions: Next(a,b) Next(b,c) Actions: Next(a,c) CONDITIONAL ConceptWeight Condacts: Concept(O1,c) Weight(O1,w) Pattern Function: Join Mobile (B) Legs (D) WM Alive (B)

12. 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

13. Additional Aspects Relevant to Problem SolvingUniversal versus Unique Variables • 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 Join Negate Changes WM – + Action combination subgraph:

14. Additional Aspects Relevant to Problem SolvingLink Memory • 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

15. LTM Problem Solving in theGraphical Architecture Evaluation Application Generation LM WM • 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) Selection Graph Cycle Message cycles + WM change Message Cycle 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) CONDITIONALgoal-best; Prefer operator that moves a tile into its desired location :conditions (blank state:scell:cb) (acceptable state:soperator:ct) (location cell:cttile:t) (goal cell:cbtile:t) :actions (selected statesoperator:ct) :function 10 CONDITIONALprevious-reject; Reject previously moved operator :conditions (acceptable state:soperator:ct) (previous state:soperator:ct) :actions (selected -state:soperator: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)