Above are papers related to the following paper: [Paper_ID] Paper #253971. 	[Title] Fools Gold: Extracting Finite State Machines From Recurrent Network Dynamics [Abstract] Several recurrent networks have been proposed as representations for the task of formal language learning. After training a recurrent network, the next step is to understand the information processing carried out by the network. Some researchers (Giles et al., 1992; Watrous & Kuhn, 1992; Cleeremans et al., 1989) have resorted to extracting finite state machines from the internal state trajectories of their recurrent networks. This paper describes two conditions, sensitivity to initial conditions and frivolous computational explanations due to discrete measurements (Kolen & Pollack, 1993), which allow these extraction methods to return illusionary finite state descriptions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #44514. 	[Title] The Observers Paradox: Apparent Computational Complexity in Physical Systems [Abstract]  Please summarise all the given information.

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Above are papers related to the following paper: [Paper_ID] Paper #1129621. 	[Title] Analysis of Dynamical Recognizers [Abstract] Pollack (1991) demonstrated that second-order recurrent neural networks can act as dynamical recognizers for formal languages when trained on positive and negative examples, and observed both phase transitions in learning and IFS-like fractal state sets. Follow-on work focused mainly on the extraction and minimization of a finite state automaton (FSA) from the trained network. However, such networks are capable of inducing languages which are not regular, and therefore not equivalent to any FSA. Indeed, it may be simpler for a small network to fit its training data by inducing such a non-regular language. But when is the network's language not regular? In this paper, using a low dimensional network capable of learning all the Tomita data sets, we present an empirical method for testing whether the language induced by the network is regular or not. We also provide a detailed "-machine analysis of trained networks for both regular and non-regular languages. Please summarise all the given information.

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Above are papers related to the following paper: [Paper_ID] Paper #16476. 	[Title] Extraction of Rules from Discrete-Time Recurrent Neural Networks [Abstract] The extraction of symbolic knowledge from trained neural networks and the direct encoding of (partial) knowledge into networks prior to training are important issues. They allow the exchange of information between symbolic and connectionist knowledge representations. The focus of this paper is on the quality of the rules that are extracted from recurrent neural networks. Discrete-time recurrent neural networks can be trained to correctly classify strings of a regular language. Rules defining the learned grammar can be extracted from networks in the form of deterministic finite-state automata (DFA's) by applying clustering algorithms in the output space of recurrent state neurons. Our algorithm can extract different finite-state automata that are consistent with a training set from the same network. We compare the generalization performances of these different models and the trained network and we introduce a heuristic that permits us to choose among the consistent DFA's the model which best approximates the learned regular grammar. Keywords: Recurrent Neural Networks, Grammatical Inference, Regular Languages, Deterministic Finite-State Automata, Rule Extraction, Generalization Performance, Model Selection, Occam's Razor. fl Technical Report CS-TR-3465 and UMIACS-TR-95-54, University of Maryland, College Park, MD 20742. Ac cepted for publication in Neural Networks. Please summarise all the given information.

Paper #253971 has the title `Fools Gold: Extracting Finite State Machines From Recurrent Network Dynamics  
` and the abstract `Several recurrent networks have been proposed as representations for the task of formal language learning. After training a recurrent network, the next step is to understand the information processing carried out by the network. Some researchers (Giles et al., 1992; Watrous & Kuhn, 1992; Cleeremans et al., 1989) have resorted to extracting finite state machines from the internal state trajectories of their recurrent networks. This paper describes two conditions, sensitivity to initial conditions and frivolous computational explanations due to discrete measurements (Kolen & Pollack, 1993), which allow these extraction methods to return illusionary finite state descriptions.
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Question: Which category should Paper #253971 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #253971 has the title `Fools Gold: Extracting Finite State Machines From Recurrent Network Dynamics  
` and the abstract `Several recurrent networks have been proposed as representations for the task of formal language learning. After training a recurrent network, the next step is to understand the information processing carried out by the network. Some researchers (Giles et al., 1992; Watrous & Kuhn, 1992; Cleeremans et al., 1989) have resorted to extracting finite state machines from the internal state trajectories of their recurrent networks. This paper describes two conditions, sensitivity to initial conditions and frivolous computational explanations due to discrete measurements (Kolen & Pollack, 1993), which allow these extraction methods to return illusionary finite state descriptions.
`.
Question: Which category should Paper #253971 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