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17
Analog Computation via Neural Networks
 THEORETICAL COMPUTER SCIENCE
, 1994
"... We pursue a particular approach to analog computation, based on dynamical systems of the type used in neural networks research. Our systems have a fixed structure, invariant in time, corresponding to an unchanging number of "neurons". If allowed exponential time for computation, they turn out to ha ..."
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Cited by 87 (8 self)
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We pursue a particular approach to analog computation, based on dynamical systems of the type used in neural networks research. Our systems have a fixed structure, invariant in time, corresponding to an unchanging number of "neurons". If allowed exponential time for computation, they turn out to have unbounded power. However, under polynomialtime constraints there are limits on their capabilities, though being more powerful than Turing Machines. (A similar but more restricted model was shown to be polynomialtime equivalent to classical digital computation in the previous work [20].) Moreover, there is a precise correspondence between nets and standard nonuniform circuits with equivalent resources, and as a consequence one has lower bound constraints on what they can compute. This relationship is perhaps surprising since our analog devices do not change in any manner with input size. We note that these networks are not likely to solve polynomially NPhard problems, as the equality ...
Synthetic Ethology and the Evolution of Cooperative Communication
, 1993
"... . Synthetic ethology is proposed as a means of conducting controlled experiments investigating the mechanisms and evolution of communication. After a discussion of the goals and methods of synthetic ethology, two series of experiments are described based on at least 5000 breeding cycles. The first d ..."
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Cited by 64 (5 self)
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. Synthetic ethology is proposed as a means of conducting controlled experiments investigating the mechanisms and evolution of communication. After a discussion of the goals and methods of synthetic ethology, two series of experiments are described based on at least 5000 breeding cycles. The first demonstrates the evolution of cooperative communication in a population of simple machines. The average fitness of the population and the organization of its use of signals are compared under three conditions: communication suppressed, communication permitted, and communication permitted in the presence of learning. Where communication is permitted the fitness increases about 26 times faster than when communication is suppressed; with communication and learning the rate of fitness increase is about 100 fold. The second series of experiments illustrates the evolution of a syntactically simple language, in which a pair of signals is required for effective communication. Keywords: artificial lif...
Beyond The Universal Turing Machine
, 1998
"... We describe an emerging field, that of nonclassical computability and nonclassical computing machinery. According to the nonclassicist, the set of welldefined computations is not exhausted by the computations that can be carried out by a Turing machine. We provide an overview of the field and a phi ..."
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Cited by 31 (1 self)
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We describe an emerging field, that of nonclassical computability and nonclassical computing machinery. According to the nonclassicist, the set of welldefined computations is not exhausted by the computations that can be carried out by a Turing machine. We provide an overview of the field and a philosophical defence of its foundations.
Natural computation and nonTuring models of computation
 Theoretical Computer Science
, 2004
"... We propose certain nonTuring models of computation, but our intent is not to advocate models that surpass the power of Turing Machines (TMs), but to defend the need for models with orthogonal notions of power. We review the nature of models and argue that they are relative to a domain of applicatio ..."
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Cited by 18 (9 self)
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We propose certain nonTuring models of computation, but our intent is not to advocate models that surpass the power of Turing Machines (TMs), but to defend the need for models with orthogonal notions of power. We review the nature of models and argue that they are relative to a domain of application and are illsuited to use outside that domain. Hence we review the presuppositions and context of the TM model and show that it is unsuited to natural computation (computation occurring in or inspired by nature). Therefore we must consider an expanded definition of computation that includes alternative (especially analog) models as well as the TM. Finally we present an alternative model, of continuous computation, more suited to natural computation. We conclude with remarks on the expressivity of formal mathematics. Key words: analog computation, analog computer, biocomputation, computability, computation on reals, continuous computation, formal system, hypercomputation,
Characteristics of Connectionist Knowledge Representation
 Information Sciences
, 1994
"... Connectionism the use of neural networks for knowledge representation and inference has profound implications for the representation and processing of information because it provides a fundamentally new view of knowledge. However, its progress is impeded by the lack of a unifying theoretical constru ..."
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Cited by 17 (8 self)
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Connectionism the use of neural networks for knowledge representation and inference has profound implications for the representation and processing of information because it provides a fundamentally new view of knowledge. However, its progress is impeded by the lack of a unifying theoretical construct corresponding to the idea of a calculus (or formal system) in traditional ap proaches to knowledge representation. Such a construct, called a simulacrum, is proposed here, and its basic properties are explored. We find that although exact classification is impossible, several other useful, robust kinds of classification are permitted. The representation of structured information and constituent structure are considered, and we find a basis for more flexible rulelike processing than that permitted by conventional methods. We discuss briefly logical issues such as decidability and computability and show that they require reformulation in this new context. Throughout we discuss the implications for artificial intelligence and cognitive science of this new theoretical framework.
Continuous Formal Systems: A Unifying Model in Language and Cognition
 In Proceedings of the IEEE Workshop on Architectures for Semiotic Modeling and Situation Analysis in Large Complex Systems
, 1995
"... this paper we outline the general characteristics of continuous formal systems ..."
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Cited by 15 (10 self)
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this paper we outline the general characteristics of continuous formal systems
Neural Networks with Real Weights: Analog Computational Complexity
, 1992
"... We pursue a particular approach to analog computation, based on dynamical systems of the type used in neural networks research. Our systems have a fixed structure, invariant in time, corresponding to an unchanging number of "neurons". If allowed exponential time for computation, they turn out to hav ..."
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Cited by 15 (3 self)
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We pursue a particular approach to analog computation, based on dynamical systems of the type used in neural networks research. Our systems have a fixed structure, invariant in time, corresponding to an unchanging number of "neurons". If allowed exponential time for computation, they turn out to have unbounded power. However, under polynomialtime constraints there are limits on their capabilities, though being more powerful than Turing Machines. (A similar but more restricted model was shown to be polynomialtime equivalent to classical digital computation in the previous work [17].) Moreover, there is a precise correspondence between nets and standard nonuniform circuits with equivalent resources, and as a consequence one has lower bound constraints on what they can compute. This relationship is perhaps surprising since our analog devices do not change in any manner with input size. We note that these networks are not likely to solve polynomially NPhard problems, as the equality "p...
Foundations Of Recurrent Neural Networks
, 1993
"... "Artificial neural networks" provide an appealing model of computation. Such networks consist of an interconnection of a number of parallel agents, or "neurons." Each of these receives certain signals as inputs, computes some simple function, and produces a signal as output, which is in turn broadca ..."
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Cited by 14 (6 self)
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"Artificial neural networks" provide an appealing model of computation. Such networks consist of an interconnection of a number of parallel agents, or "neurons." Each of these receives certain signals as inputs, computes some simple function, and produces a signal as output, which is in turn broadcast to the successive neurons involved in a given computation. Some of the signals originate from outside the network, and act as inputs to the whole system, while some of the output signals are communicated back to the environment and are used to encode the end result of computation. In this dissertation we focus on the "recurrent network" model, in which the underlying graph is not subject to any constraints. We investigate the computational power of neural nets, taking a classical computer science point of view. We characterize the language re...
Transcending Turing Computability
 Minds and Machines
, 2001
"... It has been argued that neural networks and other forms of analog computation may transcend the limits of Turing computation; proofs have been oered on both sides, subject to diering assumptions. In this report I argue that the important comparisons between the two models of computation are not so m ..."
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Cited by 12 (8 self)
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It has been argued that neural networks and other forms of analog computation may transcend the limits of Turing computation; proofs have been oered on both sides, subject to diering assumptions. In this report I argue that the important comparisons between the two models of computation are not so much mathematical as epistemological. The Turing machine model makes assumptions about information representation and processing that are badly matched to the realities of natural computation (information representation and processing in or inspired by natural systems). This points to the need for new models of computation addressing issues orthogonal to those that have occupied the traditional theory of computation. Keywords: computability, Turing machine, hypercomputation, natural computation, biocomputation, analog computer, analog computation, continuous computation 1.
The Broad Conception Of Computation
 American Behavioral Scientist
, 1997
"... A myth has arisen concerning Turing's paper of 1936, namely that Turing set forth a fundamental principle concerning the limits of what can be computed by machine  a myth that has passed into cognitive science and the philosophy of mind, to wide and pernicious effect. This supposed principle, somet ..."
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Cited by 11 (2 self)
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A myth has arisen concerning Turing's paper of 1936, namely that Turing set forth a fundamental principle concerning the limits of what can be computed by machine  a myth that has passed into cognitive science and the philosophy of mind, to wide and pernicious effect. This supposed principle, sometimes incorrectly termed the 'ChurchTuring thesis', is the claim that the class of functions that can be computed by machines is identical to the class of functions that can be computed by Turing machines. In point of fact Turing himself nowhere endorses, nor even states, this claim (nor does Church). I describe a number of notional machines, both analogue and digital, that can compute more than a universal Turing machine. These machines are exemplars of the class of nonclassical computing machines. Nothing known at present rules out the possibility that machines in this class will one day be built, nor that the brain itself is such a machine. These theoretical considerations undercut a numb...