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The Interactive Search Optimization Algorithm February 2008

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2 AGI: Dealing with New Situations But, if target not-well defined, can ’ t decide which algorithm to use (creativity, intuition). a, b, c,. A, B, C,. F A, B, C,. ? F, F’, F’’,.

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3 AGI Needs Non-Turing Computation Deal effectively with new situations Directly implies At the outset, no well-defined target result If well-defined, must have seen this before Contradicts assumption that situation is “ new ” Turing machine, by definition, has well-defined target result At minimum, description of this result is algorithm itself Exception: randomized algorithms (later) Universal TM allows handling any algorithm; not any situation

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4 Plan / Results Focus on a common process where target not known Participate in this process with computation Use Distributed Cognition Isolate 1 component of Cognitive Process Replace/Enhance with our own computation Describe implementation experiment Show results: Effective; w/out knowledge of target Derive consequence: non-Turing computation Discuss how may be used

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5 Construct a Non-Turing Instance E-Mail Search Can ’ t remember the sender ’ s name Was it “ Jason ” ? “ Jackson ” ? “ Hampton ” ? In the end it turned out to be “ Erlang ” !! The long “ a ” sound in [Ja]son, [Jack]son, [Hamp]ton came from the 2 nd syllable in Er[lang] The Danish sound of “ Erlang ” was transformed into more familiar (to me) American name forms The brain has creative labyrinths! User bangs around the search space, modifying keywords based on what the search engine presents.

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6 Distributed Cognition (Hutchins 1995 etc.) Cognition is distributed over dimensions beyond the physical individual Over groups of people (social dimension) Over physical artifacts in the environment where cognition takes place Over time: Earlier cognition events influence later ones, and possibly vice versa Embodiment: Physical, Cultural and Language substrates that carry the cognition, directly influence what is possible to “ think ”. Substrates matter.

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7 ISO as an Element in Distributed Cog(1) Without ISO Search Engine Language/Word-sounds substrate User ’ s Intuition keywords results (Embodiment)

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8 ISO as an Element in Distributed Cog(2) With ISO Search Engine Language/Word Sounds substrate User ’ s Intuition keywords results (Embodiment) ISO Algorithm

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9 Change of Perspective Conventional view: Provide user with tools Tool is oblivious to the overall user process Tools map known input space to known target space ISO view: Participate in the Cognitive process Aware (??) of the user ’ s overall goal Unknown mapping; synthetic target space

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10 Initial Position Letter groupings follow associations between letter sounds (a e h o u), (b d), (c s x) (g j), (i y), (k q), (m n), (p t), (v w) Other letters are singletons Groups and Singletons ordered approx. as in alphabet. Letters assigned positions on the 360 0 of a circle. User “ navigates ” the space of word possibilities by pointing a joystick in angular directions. m joysticks for m letters

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11 User Response Grade (Joystick) User Response Grade urg ( ): +1, -1, 0 135° 45° -135° -45° We ’ re headed in right direction Definitely going the wrong way Neutral (+/-)

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12 ISO as an Element in Distributed Cog With ISO Substrate matters So, can also infer from substrate Search Engine Language/Word Sounds substrate User ’ s Intuition keywords results (Embodiment) ISO Algorithm

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13 ISO Action Two basic support actions Remind user what they ’ ve done in similar situations Avoid backward steps Abbreviate multiple steps into one, if sequence useful repeatedly in the past Speed up progress “ Useful ” means: Our metric for “ direction ” shows progress (+1) Does not required knowledge of target goal! Other metrics possible, hybrid metrics

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14 User Interface No actual Joystick (conceptual). Each triple of letters is small arc of circle. User points joystick with the slider; sees relative motion of circle in the triple.

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15 The Delta Matrix: User Response For keyword(s) of m letters, user provides: An angle theta for each letter, indicating how it should be changed An indication w of the user ’ s confidence in the value

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16 Delta Matrix: Action Taken We take the user ’ s response as a probabilistic indication of the keyword for next input to the search engine With probability w the delta will be changed as specified With probability ( 1- w ) will not be changed The Normalized Scalar Response is a single value representing the entire delta matrix: is the expectation of the random variable

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17 Record of Progress Response DeltaAction Delta Normalized Scalar Response Compute: Dimensional Progress Index

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18 DPI Concept DPI = 1 DPI = 2 DPI = 3

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19 Record of Progress (cont ’ d) For a sequence of user search iterations, the computed Delta matrices yield: And for each k, we have the measures: and Each k is a generation, and the sequence of generations is the history, or more simply

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20 Unification: Short-cutting the History Go a step further with the R A Delta matrix transformation: Unification For X any Delta matrix, the Unification of the sequence abbreviates the effect of the sequence into a single Delta matrix X ’ Method: Take the sequence of weights w i, i = [k, k+l], as joint probabilities for the sequence of Bernoulli random variables : Do this for each of m positions in a Delta matrix with probability w i with probability (1-w i )

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21 Unification Synthetic User Response 1 When to apply Unification? Remind user what they ’ ve done in similar situations Synthetic Response unifies A k and A k+1 urg same user response dpi At same “place” in search space (fuzzy)

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22 Unification Synthetic User Response 2 When to apply Unification? Abbreviate multiple steps into one, if sequence useful repeatedly in the past urg = +1, - 1 getting off to a bad start urg= +1 urg = - 1 or 0 history shows got lost for a while dpi At same “place” in search space (fuzzy)

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23 Using Synthetic Delta Compute all unifications that qualify Rank them as a function of – Closest to current situation Number of instances found in history (fuzzy)

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24 Experiments (Automaton Users) Automaton 1: Advance 1/4 distance to target; get lost with probability Automaton 4: Advance to target, retreat, as terms in series,,..., etc.

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25 Experiments (Results 1) A4: Base = 80%; Error = 50% # Steps Winning Trials # Steps All Trials # steps Failed Trials # Steps Winning Trials # Steps All Trials # steps Failed Trials A1: Uniform Confidence: 100%

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26 Experiments (Results 2)

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27 Experiments (Results 3)

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28 Conclusion Is this plausible? The keyword produced by the user at each step is a prescient, transcendental insight, unrelated to previous More likely: The steps get incrementally closer Builds on previous in some way (but w/out constraining!) If ISO consistently reduces search time – Must be a correspondence between Keywords generated by ISO Overall User Cognitive Process – not just specific input at each step Otherwise, would follow, not enhance ISO “ synchronizes ” with the user Cognitive process Captures no-man ’ s-land between passive vs. knowledge of target

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29 A Non-Turing Computation (informal) TM ’ s Have a well-defined target The exception is the random component in randomized algorithms ISO : Has no well-defined target “ Synchronizes ” with overall user cognitive process But: A random process cannot synchronize with anything, by definition Conclusion: ISO represents a non-Turing, non- random, computation.

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30 Consequences of Conclusion Where target not known ( “ new situations ” ) Consider as legitimate indicators like “ close ” / ” far ” Based on partially successful attempts Departs from classical algorithmic view: each step fixed (deterministically or non-d) solely by specified final goal Participation in a Cognitive process may be a useful tool for Understanding the underlying mechanisms Implementing replicas of those mechanisms Pay attention to the substrate carrying the process Fix base metric structure (e.g. letter sounds) Learn additional structure layered on the base e.g. long a sound in 2 nd syllable in Danish (Erlang) becomes the 1 st syllable in English (Jackson) Additional structure may be discoverable in partial contexts

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31 Next Steps Try other metrics, hybrid metrics Test on humans Tighten up the non-Turing result to a formal one Generally, more theoretical basis needed Apply to other application areas Remembering a word in foreign language Making the right investment decision in given circumstances other Replace the human direction with precedent from other contexts

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