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State observability in recurrent neural networks
Full text linkWe obtain a characterization of observability for a class of nonlinear systems which appear in neural networks research
State Observability In Recurrent Neural Networks
No full textWe obtain a characterization of observability for a class of nonlinear systems which appear in neural networks research. Keywords: Recurrent neural networks, observability. This research was supported in part by US Air Force Grant AFOSR-91-0346, and also by an INDAM (Istituto Nazionale di Alta Matematica Francesco Severi, Italy) fellowship. Rutgers Center for Systems and Control December 1992, rev May 1993 3 Also: Universita' di Padova, Dipartimento di Matematica, Via Belzoni 7, 35100 Padova, Italy. STATE OBSERVABILITY IN RECURRENT NEURAL NETWORKS y Francesca Albertini z Eduardo D. Sontag Department of Mathematics Rutgers University, New Brunswick, NJ 08903 E-mail: [email protected], [email protected] Key words: Recurrent neural networks, observability ABSTRACT We obtain a characterization of observability for a class of nonlinear systems which appear in neural networks research. 1 Introduction Systems consisting of a large number of interconnected "neurons..
For Neural Networks, Function Determines Form
No full textThis paper shows that the weights of continuous-time feedback neural networks are uniquely identifiable from input/output measurements. Under very weak genericity assumptions, the following is true: Assume given two nets, whose neurons all have the same nonlinear activation function oe; if the two nets have equal behaviors as "black boxes" then necessarily they must have the same number of neurons and ---except at most for sign reversals at each node--- the same weights. Key words: Neural networks, realization from input/output data, control systems Research supported in part by US Air Force Grant AFOSR-91-0343. Rutgers Center for Systems and Control May FOR NEURAL NETWORKS, FUNCTION DETERMINES FORM 1 Francesca Albertini Eduardo D. Sontag SYCON - Rutgers Center for Systems and Control Department of Mathematics, Rutgers University, New Brunswick, NJ 08903 (908) 932-3072, E-mail: [email protected], [email protected] ABSTRACT This paper shows that the weights of ..
Discrete-Time Transitivity and Accessibility: Analytic Systems
Full text linkA basic open question for discrete-time nonlinear systems is that of determining when, in analogy with the classical continuous-time ''positive form of Chow's Lemma,'' accessibility follows from transitivity of a natural group action.
This paper studies the problem and establishes the desired implication for analytic systems in several cases: (i) compact state space, (ii) under a Poisson stability condition, and (iii) in a generic sense. In addition, the paper studies accessibility properties of the ''controllability sets'' recently introduced in the context of dynamical systems studies. Finally, various examples and counterexamples are provided relating the various Lie algebras introduced in past work
Further Results on Controllability Properties of Discrete-Time Nonlinear Systems
Full text linkControllability questions for discrete-time nonlinear systems are addressed in this paper. In particular, we continue the search for conditions under which the group-like notion of transitivity implies the stronger and semigroup-like property of forward accessibility. We show that this implication holds, pointwise, for states which have a weak Poisson stability property, and globally, if there exists a global "attractor" for the system. 1 Introduction This paper continues the study, initiated in [4] and then developed in [1], of some controllability properties of discrete-time nonlinear systems, of the type: x(t + 1) = f(x(t); u(t)); t = 0; 1; 2; : : : ; (1) where x(t) 2 X and u(t) 2 U . We will deal, as in the above-mentioned papers, with the class of invertible systems, that is with those systems for which the function f(1; u) is a diffeomorphism. Such systems arise, for instance, when dealing with continuous-time models under digital controls via sampling. For futher motivations o..
On The Computational Power Of Neural Nets
No full textThis paper deals with the simulation of Turing machines by neural networks. Such networks are made up of interconnections of synchronously evolving processors, each of which updates its state according to a "sigmoidal" linear combination of the previous states of all units. The main result states that one may simulate all Turing machines by nets, in linear time. In particular, it is possible to give a net made up of about 1,000 processors which computes a universal partial-recursive function. (This is an update of Report SYCON-91-08; new results include the simulation in linear time of binary-tape machines, as opposed to the unary alphabets used in the previous version.) Key words: neural networks, Turing machines Research supported in part by US Air Force Grant AFOSR-91-0343. Rutgers Center for Systems and Control November ON THE COMPUTATIONAL POWER OF NEURAL NETS 3 Hava T. Siegelmann, Department of Computer Science Eduardo D. Sontag, Department of Mathematics Rutgers University..
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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