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.

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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 #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 #1152714 has the title `nan` and the 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
`.
Question: Which category should Paper #1152714 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1152714 has the title `nan` and the 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
`.
Question: Which category should Paper #1152714 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