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. Introduction 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 tree. 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. State-Machines 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 well-established. 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. Conclusion 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.