Results 1  10
of
19
Computing with Truly Asynchronous Threshold Logic Networks
 THEORETICAL COMPUTER SCIENCE
, 1995
"... We present simulation mechanisms by which any network of threshold logic units with either symmetric or asymmetric interunit connections (i.e., a symmetric or asymmetric "Hopfield net") can be simulated on a network of the same type, but without any a priori constraints on the order of upd ..."
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Cited by 19 (7 self)
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We present simulation mechanisms by which any network of threshold logic units with either symmetric or asymmetric interunit connections (i.e., a symmetric or asymmetric "Hopfield net") can be simulated on a network of the same type, but without any a priori constraints on the order of updates of the units. Together with earlier constructions, the results show that the truly asynchronous network model is computationally equivalent to the seemingly more powerful models with either ordered sequential or fully parallel updates.
Complexity Issues in Discrete Hopfield Networks
, 1994
"... We survey some aspects of the computational complexity theory of discretetime and discretestate Hopfield networks. The emphasis is on topics that are not adequately covered by the existing survey literature, most significantly: 1. the known upper and lower bounds for the convergence times of Hopfi ..."
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Cited by 18 (4 self)
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We survey some aspects of the computational complexity theory of discretetime and discretestate Hopfield networks. The emphasis is on topics that are not adequately covered by the existing survey literature, most significantly: 1. the known upper and lower bounds for the convergence times of Hopfield nets (here we consider mainly worstcase results); 2. the power of Hopfield nets as general computing devices (as opposed to their applications to associative memory and optimization); 3. the complexity of the synthesis ("learning") and analysis problems related to Hopfield nets as associative memories. Draft chapter for the forthcoming book The Computational and Learning Complexity of Neural Networks: Advanced Topics (ed. Ian Parberry).
The Computational Power of Discrete Hopfield Nets with Hidden Units
 Neural Computation
, 1996
"... We prove that polynomial size discrete Hopfield networks with hidden units compute exactly the class of Boolean functions PSPACE/poly, i.e., the same functions as are computed by polynomial spacebounded nonuniform Turing machines. As a corollary to the construction, we observe also that networks wi ..."
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Cited by 11 (6 self)
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We prove that polynomial size discrete Hopfield networks with hidden units compute exactly the class of Boolean functions PSPACE/poly, i.e., the same functions as are computed by polynomial spacebounded nonuniform Turing machines. As a corollary to the construction, we observe also that networks with polynomially bounded interconnection weights compute exactly the class of functions P/poly, i.e., the class computed by polynomial timebounded nonuniform Turing machines.
EnergyBased Computation with Symmetric Hopfield Nets
"... We propose a unifying approach to the analysis of computational aspects of symmetric Hopfield nets which is based on the concept of "energy source". Within this framework we present different results concerning the computational power of various Hopfield model classes. It is shown that ..."
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Cited by 2 (0 self)
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We propose a unifying approach to the analysis of computational aspects of symmetric Hopfield nets which is based on the concept of "energy source". Within this framework we present different results concerning the computational power of various Hopfield model classes. It is shown that polynomialtime computations by nondeterministic Turing machines can be reduced to the process of minimizing the energy in Hopfield nets (the MIN ENERGY problem). Furthermore, external and internal sources of energy are distinguished. The external sources include e.g. energizing inputs from socalled Hopfield languages, and also certain external oscillators that prove finite analog Hopfield nets to be computationally Turing universal. On the other hand, the internal source of energy can be implemented by a symmetric clock subnetwork producing an exponential number of oscillations which are used to energize the simulation of convergent asymmetric networks by Hopfield nets. This shows that infinite families of polynomialsize Hopfield nets compute the complexity class PSPACE/poly. A special attention is paid to generalizing these results for analog states and continuous time to point out alternative sources of efficient computation. 1
Scalability of a neural network for the knight’s tour problem
 Neurocomputing
, 1996
"... The e ectiveness and e ciency of a Hop eldstyle neural network recently proposed by Takefuji and Lee for the knight's tour problem on an n n board are compared and contrasted with standard algorithmic techniques using a combination of experimental and theoretical analysis. Experiments indicate ..."
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Cited by 2 (1 self)
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The e ectiveness and e ciency of a Hop eldstyle neural network recently proposed by Takefuji and Lee for the knight's tour problem on an n n board are compared and contrasted with standard algorithmic techniques using a combination of experimental and theoretical analysis. Experiments indicate that the neural network has poor performance when implemented on a conventional computer, and it is further argued that it is unlikely to improve signi cantly when implemented in parallel. Keywords: Knight's tour problem, neural network, parallel algorithm, Hamiltonian cycle problem.
A Computational Taxonomy and Survey of Neural Network Models
 of Numbers and Symbols. (BS 1749:1985) London: British Standards Institution
, 2001
"... We survey and summarize the existing literature on the computational aspects of neural network models, by presenting a detailed taxonomy of the various models according to their computational characteristics. The criteria of classification include e.g. the architecture of the network (feedforward vs ..."
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We survey and summarize the existing literature on the computational aspects of neural network models, by presenting a detailed taxonomy of the various models according to their computational characteristics. The criteria of classification include e.g. the architecture of the network (feedforward vs. recurrent), time model (discrete vs. continuous), state type (binary vs. analog), weight constraints (symmetric vs. asymmetric), network size (finite nets vs. infinite families), computation type (deterministic vs. probabilistic), etc. The underlying results concerning the computational power of perceptron, RBF, winnertakeall, and spiking neural networks are briey surveyed, with pointers to the relevant literature.
General Purpose Computation with Neural Networks: A Survey of Complexity Theoretic Results
, 2003
"... We survey and summarize the existing literature on the computational aspects of neural network models, by presenting a detailed taxonomy of the various models according to their complexity theoretic characteristics. The criteria of classi cation include e.g. the architecture of the network (fee ..."
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Cited by 2 (0 self)
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We survey and summarize the existing literature on the computational aspects of neural network models, by presenting a detailed taxonomy of the various models according to their complexity theoretic characteristics. The criteria of classi cation include e.g. the architecture of the network (feedforward vs. recurrent), time model (discrete vs. continuous), state type (binary vs. analog), weight constraints (symmetric vs. asymmetric), network size ( nite nets vs. in  nite families), computation type (deterministic vs. probabilistic), etc.
Are Hopfield Networks Faster Than Conventional Computers?
"... It is shown that conventional computers can be exponentially faster than planar Hopfield networks: although there are planar Hopfield networks that take exponential time to converge, a stable state of an arbitrary planar Hopfield network can be found by a conventional computer in polynomial time. Th ..."
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It is shown that conventional computers can be exponentially faster than planar Hopfield networks: although there are planar Hopfield networks that take exponential time to converge, a stable state of an arbitrary planar Hopfield network can be found by a conventional computer in polynomial time. The theory of PLScompleteness gives strong evidence that such a separation is unlikely for nonplanar Hopfield networks, and it is demonstrated that this is also the case for several restricted classes of nonplanar Hopfield networks, including those who interconnection graphs are the class of bipartite graphs, graphs of degree 3, the dual of the knight’s graph, the 8neighbor mesh, the hypercube, the butterfly, the cubeconnected cycles, and the shuffleexchange graph. 1