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.

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 #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 #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 #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.

Paper #133567 has the title `Complete Controllability of Continuous-Time Recurrent Neural Networks  
` and the 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.
`.
Question: Which category should Paper #133567 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #133567 has the title `Complete Controllability of Continuous-Time Recurrent Neural Networks  
` and the 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.
`.
Question: Which category should Paper #133567 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