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.

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 #1126044. 	[Title] A Brief History of Connectionism [Abstract] Connectionist research is firmly established within the scientific community, especially within the multi-disciplinary field of cognitive science. This diversity, however, has created an environment which makes it difficult for connectionist researchers to remain aware of recent advances in the field, let alone understand how the field has developed. This paper attempts to address this problem by providing a brief guide to connectionist research. The paper begins by defining the basic tenets of connectionism. Next, the development of connectionist research is traced, commencing with connectionism's philosophical predecessors, moving to early psychological and neuropsychological influences, followed by the mathematical and computing contributions to connectionist research. Current research is then reviewed, focusing specifically on the different types of network architectures and learning rules in use. The paper concludes by suggesting that neural network research|at least in cognitive science|should move towards models that incorporate the relevant functional principles inherent in neurobiological systems. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #16485. 	[Title] POWER OF NEURAL NETS [Abstract] Report SYCON-91-11 ABSTRACT This paper deals with the simulation of Turing machines by neural networks. Such networks are made up of interconnections of synchronously evolving processors, each of which updates its state according to a "sigmoidal" linear combination of the previous states of all units. The main result states that one may simulate all Turing machines by nets, in linear time. In particular, it is possible to give a net made up of about 1,000 processors which computes a universal partial-recursive function. (This is an update of Report SYCON-91-08; new results include the simulation in linear time of binary-tape machines, as opposed to the unary alphabets used in the previous version.) Please summarise all the given information.

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 #193931. 	[Title] What Size Neural Network Gives Optimal Generalization? Convergence Properties of Backpropagation [Abstract] Technical Report UMIACS-TR-96-22 and CS-TR-3617 Institute for Advanced Computer Studies University of Maryland College Park, MD 20742 Abstract One of the most important aspects of any machine learning paradigm is how it scales according to problem size and complexity. Using a task with known optimal training error, and a pre-specified maximum number of training updates, we investigate the convergence of the backpropagation algorithm with respect to a) the complexity of the required function approximation, b) the size of the network in relation to the size required for an optimal solution, and c) the degree of noise in the training data. In general, for a) the solution found is worse when the function to be approximated is more complex, for b) oversized networks can result in lower training and generalization error in certain cases, and for c) the use of committee or ensemble techniques can be more beneficial as the level of noise in the training data is increased. For the experiments we performed, we do not obtain the optimal solution in any case. We further support the observation that larger networks can produce better training and generalization error using a face recognition example where a network with many more parameters than training points generalizes better than smaller networks. 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 #133553. 	[Title] Sample Complexity for Learning Recurrent Perceptron Mappings [Abstract] Recurrent perceptron classifiers generalize the classical perceptron model. They take into account those correlations and dependences among input coordinates which arise from linear digital filtering. This paper provides tight bounds on sample complexity associated to the fitting of such models to experimental data. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1104787. 	[Title] Fault-Tolerant Implementation of Finite-State Automata in Recurrent Neural Networks [Abstract] Recently, we have proven that the dynamics of any deterministic finite-state automata (DFA) with n states and m input symbols can be implemented in a sparse second-order recurrent neural network (SORNN) with n + 1 state neurons and O(mn) second-order weights and sigmoidal discriminant functions [5]. We investigate how that constructive algorithm can be extended to fault-tolerant neural DFA implementations where faults in an analog implementation of neurons or weights do not affect the desired network performance. We show that tolerance to weight perturbation can be achieved easily; tolerance to weight and/or neuron stuck-at-zero faults, however, requires duplication of the network resources. This result has an impact on the construction of neural DFAs with a dense internal representation of DFA states. 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 #16474. 	[Title] Rule Revision with Recurrent Neural Networks [Abstract] Recurrent neural networks readily process, recognize and generate temporal sequences. By encoding grammatical strings as temporal sequences, recurrent neural networks can be trained to behave like deterministic sequential finite-state automata. Algorithms have been developed for extracting grammatical rules from trained networks. Using a simple method for inserting prior knowledge (or rules) into recurrent neural networks, we show that recurrent neural networks are able to perform rule revision. Rule revision is performed by comparing the inserted rules with the rules in the finite-state automata extracted from trained networks. The results from training a recurrent neural network to recognize a known non-trivial, randomly generated regular grammar show that not only do the networks preserve correct rules but that they are able to correct through training inserted rules which were initially incorrect. (By incorrect, we mean that the rules were not the ones in the randomly generated grammar.) 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 #175548. 	[Title] Neural Networks with Quadratic VC Dimension [Abstract] This paper shows that neural networks which use continuous activation functions have VC dimension at least as large as the square of the number of weights w. This result settles a long-standing open question, namely whether the well-known O(w log w) bound, known for hard-threshold nets, also held for more general sigmoidal nets. Implications for the number of samples needed for valid generalization are discussed. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #289085. 	[Title] Networks of Spiking Neurons: The Third Generation of Neural Network Models [Abstract] The computational power of formal models for networks of spiking neurons is compared with that of other neural network models based on McCulloch Pitts neurons (i.e. threshold gates) respectively sigmoidal gates. In particular it is shown that networks of spiking neurons are computationally more powerful than these other neural network models. A concrete biologically relevant function is exhibited which can be computed by a single spiking neuron (for biologically reasonable values of its parameters), but which requires hundreds of hidden units on a sigmoidal neural net. This article does not assume prior knowledge about spiking neurons, and it contains an extensive list of references to the currently available literature on computations in networks of spiking neurons and relevant results from neuro biology. Please summarise all the given information.

Paper #273949 has the title `On the Effect of Analog Noise in Discrete-Time Analog Computations  
` and the 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 
`.
Question: Which category should Paper #273949 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #273949 has the title `On the Effect of Analog Noise in Discrete-Time Analog Computations  
` and the 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 
`.
Question: Which category should Paper #273949 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: Theory