Above are papers related to the following paper: [Paper_ID] Paper #687401. 	[Title] TURING COMPUTABILITY WITH NEURAL NETS [Abstract] This paper shows the existence of a finite neural network, made up of sigmoidal neurons, which simulates a universal Turing machine. It is composed of less than 10 5 synchronously evolving processors, interconnected linearly. High-order connections are not required. 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 #1114992. 	[Title] Analog Neural Nets with Gaussian or other Common Noise Distributions cannot Recognize Arbitrary Regular Languages [Abstract] We consider recurrent analog neural nets where the output of each gate is subject to Gaussian noise, or any other common noise distribution that is nonzero on a large set. We show that many regular languages cannot be recognized by networks of this type, and we give a precise characterization of those languages which can be recognized. This result implies severe constraints on possibilities for constructing recurrent analog neural nets that are robust against realistic types of analog noise. On the other hand we present a method for constructing feedforward analog neural nets that are robust with regard to analog noise of this type. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #16471. 	[Title] Constructing Deterministic Finite-State Automata in Recurrent Neural Networks [Abstract] Recurrent neural networks that are trained to behave like deterministic finite-state automata (DFAs) can show deteriorating performance when tested on long strings. This deteriorating performance can be attributed to the instability of the internal representation of the learned DFA states. The use of a sigmoidal discriminant function together with the recurrent structure contribute to this instability. We prove that a simple algorithm can construct second-order recurrent neural networks with a sparse interconnection topology and sigmoidal discriminant function such that the internal DFA state representations are stable, i.e. the constructed network correctly classifies strings of arbitrary length. The algorithm is based on encoding strengths of weights directly into the neural network. We derive a relationship between the weight strength and the number of DFA states for robust string classification. For a DFA with n states and m input alphabet symbols, the constructive algorithm generates a "programmed" neural network with O(n) neurons and O(mn) weights. We compare our algorithm to other methods proposed in the literature. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #273949. 	[Title] On the Effect of Analog Noise in Discrete-Time Analog Computations [Abstract] We introduce a model for analog computation with discrete time in the presence of analog noise that is flexible enough to cover the most important concrete cases, such as noisy analog neural nets and networks of spiking neurons. This model subsumes the classical model for digital computation in the presence of noise. We show that the presence of arbitrarily small amounts of analog noise reduces the power of analog computational models to that of finite automata, and we also prove a new type of upper bound for the Please summarise all the given information.

Paper #687401 has the title `TURING COMPUTABILITY WITH NEURAL NETS  
` and the abstract `This paper shows the existence of a finite neural network, made up of sigmoidal neurons, which simulates a universal Turing machine. It is composed of less than 10 5 synchronously evolving processors, interconnected linearly. High-order connections are not required.
`.
Question: Which category should Paper #687401 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #687401 has the title `TURING COMPUTABILITY WITH NEURAL NETS  
` and the abstract `This paper shows the existence of a finite neural network, made up of sigmoidal neurons, which simulates a universal Turing machine. It is composed of less than 10 5 synchronously evolving processors, interconnected linearly. High-order connections are not required.
`.
Question: Which category should Paper #687401 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