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