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 #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 #105865. 	[Title] Statistical Ideas for Selecting Network Architectures [Abstract] Choosing the architecture of a neural network is one of the most important problems in making neural networks practically useful, but accounts of applications usually sweep these details under the carpet. How many hidden units are needed? Should weight decay be used, and if so how much? What type of output units should be chosen? And so on. We address these issues within the framework of statistical theory for model This paper is principally concerned with architecture selection issues for feed-forward neural networks (also known as multi-layer perceptrons). Many of the same issues arise in selecting radial basis function networks, recurrent networks and more widely. These problems occur in a much wider context within statistics, and applied statisticians have been selecting and combining models for decades. Two recent discussions are [4, 5]. References [3, 20, 21, 22] discuss neural networks from a statistical perspective. choice, which provides a number of workable approximate answers. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #193932. 	[Title] Lessons in Neural Network Training: Overfitting Lessons in Neural Network Training: Overfitting May be Harder [Abstract] For many reasons, neural networks have become very popular AI machine learning models. Two of the most important aspects of machine learning models are how well the model generalizes to unseen data, and how well the model scales with problem complexity. Using a controlled task with known optimal training error, we investigate the convergence of the backpropagation (BP) algorithm. We find that the optimal solution is typically not found. Furthermore, we observe that networks larger than might be expected can result in lower training and generalization error. This result is supported by another real world example. We further investigate the training behavior by analyzing the weights in trained networks (excess degrees of freedom are seen to do little harm and to aid convergence), and contrasting the interpolation characteristics of multi-layer perceptron neural networks (MLPs) and polynomial models (overfitting behavior is very different the MLP is often biased towards smoother solutions). Finally, we analyze relevant theory outlining the reasons for significant practical differences. These results bring into question common beliefs about neural network training regarding convergence and optimal network size, suggest alternate guidelines for practical use (lower fear of excess degrees of freedom), and help to direct future work (e.g. methods for creation of more parsimonious solutions, importance of the MLP/BP bias and possibly worse performance of improved training algorithms). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #447250. 	[Title] Introduction to Radial Basis Function Networks [Abstract] This document is an introduction to radial basis function (RBF) networks, a type of artificial neural network for application to problems of supervised learning (e.g. regression, classification and time series prediction). It is available in either PostScript or hyper-text 2 . Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3229. 	[Title] Book Review  Introduction to the Theory of Neural Computation Reviewed by: 2 [Abstract] Neural computation, also called connectionism, parallel distributed processing, neural network modeling or brain-style computation, has grown rapidly in the last decade. Despite this explosion, and ultimately because of impressive applications, there has been a dire need for a concise introduction from a theoretical perspective, analyzing the strengths and weaknesses of connectionist approaches and establishing links to other disciplines, such as statistics or control theory. The Introduction to the Theory of Neural Computation by Hertz, Krogh and Palmer (subsequently referred to as HKP) is written from the perspective of physics, the home discipline of the authors. The book fulfills its mission as an introduction for neural network novices, provided that they have some background in calculus, linear algebra, and statistics. It covers a number of models that are often viewed as disjoint. Critical analyses and fruitful comparisons between these models 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.

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 #3191. 	[Title] Model Selection and Accounting for Model Uncertainty in Linear Regression Models [Abstract] 1 Adrian E. Raftery is Professor of Statistics and Sociology, David Madigan is Assistant Professor of Statistics, and Jennifer Hoeting is a Ph.D. Candidate, all at the Department of Statistics, GN-22, University of Washington, Seattle, WA 98195. The research of Raftery and Hoeting was supported by ONR Contract N-00014-91-J-1074. Madigan's research was partially supported by NSF grant no. DMS 92111627. The authors are grateful to Danika Lew for research assistance. 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.

Above are papers related to the following paper: [Paper_ID] Paper #1111240. 	[Title] On the Distribution of Performance from Multiple Neural Network Trials, On the Distribution of Performance [Abstract] Andrew D. Back was with the Department of Electrical and Computer Engineering, University of Queensland. St. Lucia, Australia. He is now with the Brain Information Processing Group, Frontier Research Program, RIKEN, The Institute of Physical and Chemical Research, 2-1 Hirosawa, Wako-shi, Saitama 351-01, Japan Abstract The performance of neural network simulations is often reported in terms of the mean and standard deviation of a number of simulations performed with different starting conditions. However, in many cases, the distribution of the individual results does not approximate a Gaussian distribution, may not be symmetric, and may be multimodal. We present the distribution of results for practical problems and show that assuming Gaussian distributions can significantly affect the interpretation of results, especially those of comparison studies. For a controlled task which we consider, we find that the distribution of performance is skewed towards better performance for smoother target functions and skewed towards worse performance Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #14807. 	[Title] Exponentially many local minima for single neurons [Abstract] We show that for a single neuron with the logistic function as the transfer function the number of local minima of the error function based on the square loss can grow exponentially in the dimension. 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 #100197. 	[Title] Neural Networks and Statistical Models Proceedings of the Nineteenth Annual SAS Users Group International Conference, [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #688361. 	[Title] Neural Network Implementation in SAS R Software [Abstract] The estimation or training methods in the neural network literature are usually some simple form of gradient descent algorithm suitable for implementation in hardware using massively parallel computations. For ordinary computers that are not massively parallel, optimization algorithms such as those in several SAS procedures are usually far more efficient. This talk shows how to fit neural networks using SAS/OR R fl , SAS/ETS R fl , and SAS/STAT R fl software. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #350319. 	[Title] Averaging and Data Snooping [Abstract] Presenting and Analyzing the Results of AI Experiments: Data Averaging and Data Snooping, Proceedings of the Fourteenth National Conference on Artificial Intelligence, AAAI-97, AAAI Press, Menlo Park, California, pp. 362367, 1997. Copyright AAAI. Presenting and Analyzing the Results of AI Experiments: Abstract Experimental results reported in the machine learning AI literature can be misleading. This paper investigates the common processes of data averaging (reporting results in terms of the mean and standard deviation of the results from multiple trials) and data snooping in the context of neural networks, one of the most popular AI machine learning models. Both of these processes can result in misleading results and inaccurate conclusions. We demonstrate how easily this can happen and propose techniques for avoiding these very important problems. For data averaging, common presentation assumes that the distribution of individual results is Gaussian. However, we investigate the distribution for common problems and find that it often does not approximate the Gaussian distribution, may not be symmetric, and may be multimodal. We show that assuming Gaussian distributions can significantly affect the interpretation of results, especially those of comparison studies. For a controlled task, we find that the distribution of performance is skewed towards better performance for smoother target functions and skewed towards worse performance for more complex target functions. We propose new guidelines for reporting performance which provide more information about the actual distribution (e.g. box-whiskers plots). For data snooping, we demonstrate that optimization of performance via experimentation with multiple parameters can lead to significance being assigned to results which are due to chance. We suggest that precise descriptions of experimental techniques can be very important to the evaluation of results, and that we need to be aware of potential data snooping biases when formulating these experimental techniques (e.g. selecting the test procedure). Additionally, it is important to only rely on appropriate statistical tests and to ensure that any assumptions made in the tests are valid (e.g. normality of the distribution). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6775. 	[Title] Statistical Evaluation of Neural Network Experiments: Minimum Requirements and Current Practice [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #3192. 	[Title] Bayesian Graphical Models for Discrete Data [Abstract] z York's research was supported by a NSF graduate fellowship. The authors are grateful to Julian Besag, David Bradshaw, Jeff Bradshaw, James Carlsen, David Draper, Ivar Heuch, Robert Kass, Augustine Kong, Steffen Lauritzen, Adrian Raftery, and James Zidek for helpful comments and discussions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #193918. 	[Title] A Unifying View of Some Training Algorithms for Multilayer Perceptrons with FIR Filter Synapses [Abstract] Recent interest has come about in deriving various neural network architectures for modelling time-dependent signals. A number of algorithms have been published for multilayer perceptrons with synapses described by finite impulse response (FIR) and infinite impulse response (IIR) filters (the latter case is also known as Locally Recurrent Globally Feedforward Networks). The derivations of these algorithms have used different approaches in calculating the gradients, and in this note, we present a short, but unifying account of how these different algorithms compare for the FIR case, both in derivation, and performance. New algorithms are subsequently presented. Simulation results have been performed to benchmark these algorithms. In this note, results are compared for the Mackey-Glass chaotic time series against a number of other methods including a standard multilayer perceptron, and a local approximation method. Please summarise all the given information.

Paper #193931 has the title `What Size Neural Network Gives Optimal Generalization? Convergence Properties of Backpropagation  
` and the 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. 
`.
Question: Which category should Paper #193931 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #193931 has the title `What Size Neural Network Gives Optimal Generalization? Convergence Properties of Backpropagation  
` and the 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. 
`.
Question: Which category should Paper #193931 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