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Neural networks and analog computation
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As a mathematical object, an automaton is simply the quintuple because the automaton of LaSalle's inequality is the inequality of the following type: For α ≥ 1, β ≥ 1 using LaShelle's inequality.Abstract:
ly, an automaton is defined by the above data. Thus, as a mathematical object, an automaton is simply the quintupleread more
Citations
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Survey A survey of computational complexity results in systems and control
TL;DR: This paper considers problems related to stability or stabilizability of linear systems with parametric uncertainty, robust control, time-varying linear systems, nonlinear and hybrid systems, and stochastic optimal control.
Neurons withgraded response havecollective computational properties likethoseoftwo-state neurons
TL;DR: This paper shows that the important properties of the earlier stochastic model based on McCulloch-Pitts neurons remain intact and are one of thesimplest collective properties of such a system.
Journal ArticleDOI
Significance of Models of Computation, from Turing Model to Natural Computation
TL;DR: Present account of models of computation highlights several topics of importance for the development of new understanding of computing and its role: natural computation and the relationship between the model and physical implementation, interactivity as fundamental for computational modelling of concurrent information processing systems such as living organisms and their networks, and the new developments in logic needed to support this generalized framework.
Posted Content
On the Practical Computational Power of Finite Precision RNNs for Language Recognition
TL;DR: In particular, this article showed that the LSTM and the Elman-RNN with ReLU activation are strictly stronger than the RNN with a squashing activation and the GRU.
Journal Article
Evolution in Materio: Exploiting the Physics of Materials for Computation
TL;DR: In this article, the authors describe several techniques for using bulk matter for special purpose computation, using an evolutionary algorithm to program the substrate on which the computation is to take place, and the computation comes about as a result of nearest neighbour interactions at the nano- micro- and meso-scale.
References
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Journal ArticleDOI
A logical calculus of the ideas immanent in nervous activity
Warren S. McCulloch,Walter Pitts +1 more
TL;DR: In this article, it is shown that many particular choices among possible neurophysiological assumptions are equivalent, in the sense that for every net behaving under one assumption, there exists another net which behaves under another and gives the same results, although perhaps not in the same time.
A Reflection on Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
J. Guckenheimer,P. J. Holmes +1 more
TL;DR: In this paper, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
Journal ArticleDOI
Approximation by superpositions of a sigmoidal function
TL;DR: It is demonstrated that finite linear combinations of compositions of a fixed, univariate function and a set of affine functionals can uniformly approximate any continuous function ofn real variables with support in the unit hypercube.
Book
Introduction To The Theory Of Neural Computation
TL;DR: This book is a detailed, logically-developed treatment that covers the theory and uses of collective computational networks, including associative memory, feed forward networks, and unsupervised learning.