Representational Systems

                                David W. Croft
          Internet CroftDW@Portia.Caltech.Edu, CompuServe [76600,102]

                                Philosophy 131
                       Philosophy of Mind and Psychology
                             Professor Fiona Cowie

                      California Institute of Technology
                             Pasadena, California

                            1994 March 19 Saturday

     Abstract.  This paper seeks to define a representational system in
     such a manner as to be capable of implementation in a connectionist,
     or neural, network.  A representational system is defined and
     demonstrated to possess the ability to produce outputs which achieve
     global minima.  The paper concludes by showing that, while a
     feed-forward neural network is incapable of representation,
     representation may be implemented in a recurrent, or internal
     feedback, connectionist network.

          Representational systems are commonly in the Artificial
     Intelligence (AI) domain of symbolic logic.  Expert Systems are
     programmed into computer systems by recording the step-by-step
     logical methodology of experts to minimize the costs or maximize the
     utility of their decisions.  Logical statements, or beliefs, be they
     fuzzy or hard, are established as "rules".  Another branch of AI,
     Connectionism, attempts to build systems, often in artificial neural
     networks (ANNs), that implement the methodologies of the illogical,
     inexplicable, or intuitive capabilities of distributed systems such
     as pattern recognition systems.  Here, it is not some logical mapping
     of input to output, but rather a holistic host of inputs which
     indicate micro-features which may or may not synergistically produce
     a desired output.
          While connectionist systems are recognized as being capable of
     distributed, non-representational processing, they may also possess
     the capability to additionally perform the rule-based logic of
     representational systems.  As will be shown, not all connectionist
     networks possess the appropriate architecture for this task.  Thus, a
     neural network, depending upon its architecture, may possess the
     capability to perform representational processing, connectionist
     processing, or both.  This conclusion has a logical and intuitive
     appeal in that human thought processes, which are determined by
     biological neural networks, are expert at both symbolic logic and
     distributed processing.
     SysOp-In-A-Box (SIAB)
          As examples of non-representational and representational
     connectionist finite state-machine, consider the following story.  A
     Computer System Operator by the name of Al is hired to provide
     on-line help to networked users of a computer system.  Unfortunately,
     many of the users write on-line, or "chat", only in Japanese text
     which Al does not understand.  Fortunately, Jan, his bilingual friend
     who recommended Al as a replacement for herself in the role as a
     system operator (SysOp), is kind enough to provide Al with her manual
     of common user questions and standard solutions flowchart written in
     Japanese.  Al, concerned that he might lose his job if it is
     discovered that he is not bilingual, attempts to satisfy the demands
     of his Japanese users by simply typing in the suggested responses
     given in the manual for the common questions that most resemble the
     queries appearing in Japanese on his computer terminal. 
     Additionally, he cleverly attempts to appear to be following the
     conversation by tracking his responses through the manual as he sees
     Japanese user text given to him at various points in his flowchart
          After some time at this, Al decides to minimize his effort by
     incorporating his methodology into software.  Using a connectionist
     pattern recognition system to target Japanese user queries to their
     most similar counterparts in his manual and then a logical branching
     assignment of those queries to suggested outputs, he does so and his
     computer program adequately responds to Japanese user queries using
     the same "rules" that he himself would use given the manual and the
     fact that he does not understand one word of Japanese.  Al is so
     delighted with his program that he writes a similar program in his
     native tongue based upon common technical questions of his
     English-speaking users, which he understood, based upon his given
     answers as preserved in his chat log.  After spending some time
     monitoring and enhancing the performance of his SysOp-In-A-Box (SIAB)
     program, he then approaches his employers with his accomplishment
     before they can question him about his seeming inability to respond
     to problems not stored in the database of his program due to
     deficiencies in the Japanese manual or his failure to predict, for
     the English queries, uncommon or unique problems.  His employers are
     impressed and proceed to replace their bilingual SysOps with the SIAB
     computer program in order to minimize salary costs.  Al is promoted
     to Chief Artificial Intelligence (AI) Expert despite the fact that he
     never truly understood one Japanese user query.
          Al, concerned that his career may be terminated when his SIAB
     program becomes obsoleted by changes in the technical nature of his
     Japanese users' queries, attempts to contract Jan to provide updates
     to the Japanese manual.  Jan, as one of the SysOps who was replaced
     by the SIAB program shortly after arriving at her new position,
     quotes a compensatory estimate for her proposed contractual work that
     is unusually high given that she was Al's friend.  Al decides,
     instead, to hire a subordinate whose name he abbreviates as Bo since
     Bo's real name is difficult to pronounce for an English-speaker.  Now
     Bo only speaks English and Hindi but he is well-qualified for his
     position under Al in that he is willing to work cheaply.  While Al
     maintains the English-database of the SIAB, he tasks Bo to help him
     maintain the Japanese-database by responding to Japanese users by
     following the "rules" of Jan's original Japanese manual in the same
     manner that Al did before he wrote SIAB.  Additionally, however, Bo
     is empowered to update the "rules" to ensure that the changing needs
     of the Japanese users are met based upon an ingenious performance
     feedback system devised by Al:  Bo works on a percentage commission
     determined by a simple numerical user satisfaction survey ranging
     from 0 to 100%.  Initially Bo follows the "rules" without deviation
     and earns a commission with which he is content.  However, as time
     proceeds and the information in Jan's manual gradually becomes
     obsolete, his income begins to drop.  Bo, concerned that he will not
     be able to pay his rent at some point in the future, for the first
     time actually begins to compare the user surveys to their related
     transactions in the chat log.  He then marks in the manual where a
     given response for a given query generally produced a low survey
     rating.  For future similar situations, he resolves to echo back to
     the user something different, so long as it is different.  He then
     tries a combination of suggested responses to other common questions
     with a mix of Japanese text that he read in the queries that seems
     somewhat common and an occasional random string of text.  In studying
     the results of his attempts, he finds that the user evaluations were
     either lower, the same, or higher for the given common query.  Bo
     then records in the margins of the manual those answers which gave
     better results and crosses out the obsoleted answers.
          After some time, Al asks Bo to re-write the manual afresh.  Bo
     does so and Al asks him to explain why he believes his changes were
     appropriate where he made them.  Bo responds by showing Al the
     history of his attempted answers and that, through his testing of his
     hypotheses, why he believes that the answers in the new manual will
     produce a higher commission.  Al tests Bo on his knowledge of the
     nature of the technical problems related in the updated Japanese
     manual.  Bo explains that he still has no insight into the Japanese
     language and that for all he knows he may be succeeding in earning
     his commission by responding to the user queries with well-received
     humorous Japanese proverbs.  Simply put, Bo knows commissions.  Al
     then takes Bo's new manual and updates the SIAB Japanese-database.
          A strictly feed-forward system is a function.  For example, a
     layered feed-forward connectionist neural network with an input
     layer, a hidden layer, and an output layer simply maps a set of
     inputs to a set of outputs.  At any point in time, presentation of a
     particular input will always give the same output.  A state-machine,
     on the other hand, will provide different outputs for a given input
     depending on what state it is in when the input arrives.  It has an
     internal, stored state.  Since the number of possible states is any
     real state-machine is limited, or finite, the number of possible of
     outputs for a given input is also limited.
          A feedback system is a state-machine.  A feedback system is
     capable of determining its output from both past and present inputs. 
     It is a state-machine in that previous inputs determine the state the
     system will be in upon arrival of subsequent inputs.  Assuming that
     system has a non-infinitesimal resolution in its parameters, it is
     also a finite state-machine, although the number of states may be
     extremely large.
          A layered feed-forward connectionist network combined with a
     training algorithm is a state-machine.  The training algorithm
     provides performance feedback which is then used to modify the
     plastic, adaptable components of the network; it is a feedback
     system.  Upon repetition of input presentation, the outputs will vary
     as the state of the system has changed during the training process.
          Since a plastic connectionist network is a state-machine, one
     can replace the network with a fixed state-machine that emulates it. 
     For example, we could label a plastic connectionist network and the
     present state of its adaptable components as Network A.  The networks
     that could be possibly generated after training with the plastic
     weights changed for any of many possible inputs and update
     corrections we could label as Networks B, C, D, etc.  This whole
     system of labeled networks can be emulated by a fixed state-machine
     wherein the possible states are the possible networks of the plastic
     system, Network A, B, C, D, etc.  The "plasticity" in such a fixed
     system is stored in the internal present state of the machine. 
     Initially it may be in any state, thereupon transitioning to state
     Network A or B or C, etc. depending on its current state, the inputs,
     and the update correction input.
          Plasticity and the use of internal states are identical.  The
     states of a fixed state-machine emulation may or may not represent
     the entire span of possible networks generated by the training
     process of a plastic connectionist network.  If such is the case,
     since all of the possible states are pre-defined in the fixed
     components of the machine, there will be some network states that the
     fixed state-machine cannot learn.  However, it may be said that the
     limited fixed state-machine adequately represents a more limited
     plastic connectionist network.  The key idea is that both prior and
     present inputs, including update corrections, determine the outputs. 
     Thus, when we talk about plasticity or internal state, we are
     referring to the same concept:  an external feedback system.
     Representational Systems
          A representational system is a state-machine, or feedback
     system, with the ability to hypothesize, or imagine, different
     performance results for a variety of possible outputs and select the
     globally optimizing output, or behavior, for a given input.  Suppose
     a driver with a full tank of gasoline wishes to go from point A to
     point B and arrive with as much gasoline in his tank as possible. 
     The driver is told that to go from A directly to B will reduce the
     contents of the tank by five gallons.  The driver is also told that
     to go from A to point C will reduce his tank by 6 gallons. 
     Furthermore, to go from C to A will allow him to replenish his tank
     to full as there is a gas station enroute just before point B. 
     Clearly the driver possesses an input-output mapping where the input,
     origination and destination, relates to the output, which is the
     remaining gas in the tank after the trip.  Because the driver
     possesses a representational mind, and not just an input to output
     mapping, the driver believes that his optimal path is to take the
     indirect route from A to B through C.  The driver has formed a belief
     or hypothesis about an optimal trip despite never having been told
     that to go from A to B via C is the best route.  To do this, the
     driver must have imagined and compared going from A to B directly and
     going from A to C then to B.
          A representational system is not simply a state-machine.  A
     state-machine is a internal feedback system in which the inputs
     include the present inputs and a parameter defining the history of
     the prior inputs, the present state of the system.  Although a
     state-machine may be designed to perform a task and thus meet the
     definitional requirement of a system, which has a purpose, it cannot
     believe its rules because it has no mechanism to determine whether or
     not its transition rules are producing an output which achieves its
     purpose.  The state-machine does not believe its state transition
     rules; it simply executes them.  In our story about Al, he was
     initially performing as a simple state-machine by taking in the
     Japanese queries as input and his current location in the flowchart
     as the present state.  His software implementation of his methodology
     in the instantiation of the SIAB program was simply an identical
     state-machine.  Neither he nor the SIAB program would have any
     greater or lesser belief in the transition rules if someone, such as
     Jan, replaced his database of standard Japanese technical responses
     with a list of insults highly offensive to the Japanese users. 
     Without some form of performance feedback, Al and SIAB have no
     capability of hypothesizing and testing a belief that a particular
     response is producing the desired purpose.  Using a neural network
     term, the system lacks a cost function.
          Upon presentation of an input to a representational system, the
     system will produce a possible output.  This represents the current
     belief of the system as to the appropriate response to a particular
     input to minimize costs.  The system will then produce additional
     possible outputs and compare their expected costs to the costs of its
     present belief, that is, it tests its hypothesis.  If it projects, or
     imagines, that an alternate output will produce further minimize
     costs, it updates its belief.  In doing so, it converts stored
     mappings of possible inputs and outputs to a global representation of
     its possible cost space from which it can extract the global minimum
     or minima.  In the story, Bo formed conjectures or hypotheses as to
     appropriate responses for a given Japanese input.  He considered both
     past and present answers, or hypotheses, along with their expected,
     or previously recorded, survey results and selected the answer which
     he believed would minimize the number of sub-standard survey results.
          While it might be argued that Bo lacks true understanding or
     representation of the Japanese queries since his purpose is to
     optimize commissions and not answer technical questions, it should be
     recognized that this is a touchy-feely qualia argument without much
     substance.  Bo has constructed in his mind and in his new manual a
     new language space for a problem that is logically identical to the
     original problem.  The symbol "technical solution" has been replaced
     by "high commission" without any change in the logic space required
     to achieve it.  If one were to argue that Bo lacks true
     understanding, one should be prepared to argue that Bo would lack
     true understanding even if the Japanese queries were translated into
     his native tongue of Hindi.  That is, there is no additional
     information to be gained in the assignment of a particular label to a
     known symbol whose logical relationships and manipulations are
          A feed-forward connectionist network, unlike a recurrent
     connectionist network, is not capable of representation.  The inputs
     to a feed-forward network include sensory inputs, performance
     feedback inputs, and its current state which is the current setting
     of its plastic weights which encompass its input to output mappings,
     or "rules".  A recurrent network, however, possesses the additional
     input of possible, or hypothesized, outputs which are fed back to the
     system for comparison and selection.  This input may even be used as
     additional, reinforcing, or a competing performance feedback input. 
     A recurrent connectionist network is capable of "imagining" the
     short- and long-term consequences of its actions before actually
     performing the behaviors.
          A representational system requires the ability to form
     hypotheses from a stored mapping of inputs and outputs, the ability
     to select a hypothesis for output by contrasting expected results,
     the ability to tests its hypotheses through performance feedback, and
     the ability to revise its stored mappings of inputs and outputs. 
     This may be implemented in a connectionist recurrent network but not
     in a connectionist feed-forward network which lacks the ability to
     search for the global minima.

Transcribed to HTML on 1997-10-27 by David Wallace Croft.