Above are papers related to the following paper: [Paper_ID] Paper #133566. 	[Title] Recurrent Neural Networks: Some Systems-Theoretic Aspects [Abstract] This paper provides an exposition of some recent research regarding system-theoretic aspects of continuous-time recurrent (dynamic) neural networks with sigmoidal activation functions. The class of systems is introduced and discussed, and a result is cited regarding their universal approximation properties. Known characterizations of controllability, ob-servability, and parameter identifiability are reviewed, as well as a result on minimality. Facts regarding the computational power of recurrent nets are also mentioned. fl Supported in part by US Air Force Grant AFOSR-94-0293 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #105856. 	[Title] Vapnik-Chervonenkis Dimension of Recurrent Neural Networks [Abstract] Most of the work on the Vapnik-Chervonenkis dimension of neural networks has been focused on feedforward networks. However, recurrent networks are also widely used in learning applications, in particular when time is a relevant parameter. This paper provides lower and upper bounds for the VC dimension of such networks. Several types of activation functions are discussed, including threshold, polynomial, piecewise-polynomial and sigmoidal functions. The bounds depend on two independent parameters: the number w of weights in the network, and the length k of the input sequence. In contrast, for feedforward networks, VC dimension bounds can be expressed as a function of w only. An important difference between recurrent and feedforward nets is that a fixed recurrent net can receive inputs of arbitrary length. Therefore we are particularly interested in the case k w. Ignoring multiplicative constants, the main results say roughly the following: * For architectures with activation = any fixed nonlinear polynomial, the VC dimension is wk. * For architectures with activation = any fixed piecewise polynomial, the VC dimension is between wk and w 2 k. * For architectures with activation = H (threshold nets), the VC dimension is between w log(k=w) and minfwk log wk; w 2 + w log wkg. * For the standard sigmoid (x) = 1=(1 + e x ), the VC dimension is between wk and w 4 k 2 . An earlier version of this paper has appeared in Proc. 3rd European Workshop on Computational Learning Theory, LNCS 1208, pages 223-237, Springer, 1997. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1109891. 	[Title] Interconnected Automata and Linear Systems: A Theoretical Framework in Discrete-Time In Hybrid Systems III: Verification [Abstract] This paper summarizes the definitions and several of the main results of an approach to hybrid systems, which combines finite automata and linear systems, developed by the author in the early 1980s. Some related more recent results are briefly mentioned as well. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #48550. 	[Title] Identification and Control of Nonlinear Systems Using Neural Network Models: Design and Stability Analysis [Abstract] Report 91-09-01 September 1991 (revised) May 1994 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1152714. 	[Title]  [Abstract] Further Results on Controllability Abstract This paper studies controllability properties of recurrent neural networks. The new contributions are: (1) an extension of a previous result to a slightly different model, (2) a formulation and proof of a necessary and sufficient condition, and (3) an analysis of a low-dimensional case for which the of Recurrent Neural Networks fl Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #48555. 	[Title] FEEDBACK STABILIZATION USING TWO-HIDDEN-LAYER NETS [Abstract] This paper compares the representational capabilities of one hidden layer and two hidden layer nets consisting of feedforward interconnections of linear threshold units. It is remarked that for certain problems two hidden layers are required, contrary to what might be in principle expected from the known approximation theorems. The differences are not based on numerical accuracy or number of units needed, nor on capabilities for feature extraction, but rather on a much more basic classification into "direct" and "inverse" problems. The former correspond to the approximation of continuous functions, while the latter are concerned with approximating one-sided inverses of continuous functions |and are often encountered in the context of inverse kinematics determination or in control questions. A general result is given showing that nonlinear control systems can be stabilized using two hidden layers, but not in general using just one. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #5194. 	[Title] NETWORKS, FUNCTION DETERMINES FORM [Abstract] Report SYCON-92-03 ABSTRACT This 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 ; 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. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #133550. 	[Title] OBSERVABILITY IN RECURRENT NEURAL NETWORKS [Abstract] Report SYCON-92-07rev ABSTRACT We obtain a characterization of observability for a class of nonlinear systems which appear in neural networks research. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1120049. 	[Title] Dimension of Recurrent Neural Networks [Abstract] DIMACS Technical Report 96-56 December 1996 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #140569. 	[Title] Using Fourier-Neural Recurrent Networks to Fit Sequential Input/Output Data [Abstract] This paper suggests the use of Fourier-type activation functions in fully recurrent neural networks. The main theoretical advantage is that, in principle, the problem of recovering internal coefficients from input/output data is solvable in closed form. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #133563. 	[Title] NEURAL NETS AS SYSTEMS MODELS AND CONTROLLERS suitability of "neural nets" as models for dynamical [Abstract] This paper briefly surveys some recent results relevant Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3229. 	[Title] Book Review  Introduction to the Theory of Neural Computation Reviewed by: 2 [Abstract] Neural computation, also called connectionism, parallel distributed processing, neural network modeling or brain-style computation, has grown rapidly in the last decade. Despite this explosion, and ultimately because of impressive applications, there has been a dire need for a concise introduction from a theoretical perspective, analyzing the strengths and weaknesses of connectionist approaches and establishing links to other disciplines, such as statistics or control theory. The Introduction to the Theory of Neural Computation by Hertz, Krogh and Palmer (subsequently referred to as HKP) is written from the perspective of physics, the home discipline of the authors. The book fulfills its mission as an introduction for neural network novices, provided that they have some background in calculus, linear algebra, and statistics. It covers a number of models that are often viewed as disjoint. Critical analyses and fruitful comparisons between these models Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #133567. 	[Title] Complete Controllability of Continuous-Time Recurrent Neural Networks [Abstract] This paper presents a characterization of controllability for the class of control systems commonly called (continuous-time) recurrent neural networks. The characterization involves a simple condition on the input matrix, and is proved when the activation function is the hyperbolic tangent. Please summarise all the given information.

Paper #133566 has the title `Recurrent Neural Networks: Some Systems-Theoretic Aspects  
` and the abstract `This paper provides an exposition of some recent research regarding system-theoretic aspects of continuous-time recurrent (dynamic) neural networks with sigmoidal activation functions. The class of systems is introduced and discussed, and a result is cited regarding their universal approximation properties. Known characterizations of controllability, ob-servability, and parameter identifiability are reviewed, as well as a result on minimality. Facts regarding the computational power of recurrent nets are also mentioned. fl Supported in part by US Air Force Grant AFOSR-94-0293
`.
Question: Which category should Paper #133566 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #133566 has the title `Recurrent Neural Networks: Some Systems-Theoretic Aspects  
` and the abstract `This paper provides an exposition of some recent research regarding system-theoretic aspects of continuous-time recurrent (dynamic) neural networks with sigmoidal activation functions. The class of systems is introduced and discussed, and a result is cited regarding their universal approximation properties. Known characterizations of controllability, ob-servability, and parameter identifiability are reviewed, as well as a result on minimality. Facts regarding the computational power of recurrent nets are also mentioned. fl Supported in part by US Air Force Grant AFOSR-94-0293
`.
Question: Which category should Paper #133566 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Neural_Networks