Above are papers related to the following paper: [Paper_ID] Paper #631015. 	[Title] Theory of Correlations in Stochastic Neural Networks [Abstract] One of the main experimental tools in probing the interactions between neurons has been the measurement of the correlations in their activity. In general, however the interpretation of the observed correlations is difficult, since the correlation between a pair of neurons is influenced not only by the direct interaction between them but also by the dynamic state of the entire network to which they belong. Thus, a comparison between the observed correlations and the predictions from specific model networks is needed. In this paper we develop the theory of neuronal correlation functions in large networks comprising of several highly connected subpopulations, and obeying stochastic dynamic rules. When the networks are in asynchronous states, the cross-correlations are relatively weak, i.e., their amplitude relative to that of the auto-correlations is of order of 1=N , N being the size of the interacting populations. Using the weakness of the cross-correlations, general equations which express the matrix of cross-correlations in terms of the mean neuronal activities, and the effective interaction matrix are presented. The effective interactions are the synaptic efficacies multiplied by the the gain of the postsynaptic neurons. The time-delayed cross-correlation matrix can be expressed as a sum of exponentially decaying modes that correspond to the (non-orthogonal) eigenvectors of the effective interaction matrix. The theory is extended to networks with random connectivity, such as randomly dilute networks. This allows for the comparison between the contribution from the internal common input and that from the direct Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #30817. 	[Title] Analysis of Linsker's application of Hebbian rules to Linear Networks [Abstract] Linsker has reported the development of structured receptive fields in simulations using a Hebb-type synaptic plasticity rule in a feed-forward linear network. The synapses develop under dynamics determined by a matrix that is closely related to the covariance matrix of input cell activities. We analyse the dynamics of the learning rule in terms of the eigenvectors of this matrix. These eigenvectors represent independently evolving weight structures. Some general theorems are presented regarding the properties of these eigenvectors and their eigenvalues. For a general covariance matrix four principal parameter regimes are predicted. We concentrate on the gaussian covariances at layer B ! C of Linsker's network. Analytic and numerical solutions for the eigenvectors at this layer are presented. Three eigenvectors dominate the dynamics: a DC eigenvector, in which all synapses have the same sign; a bi-lobed, oriented eigenvector; and a circularly symmetric, centre-surround eigenvector. Analysis of the circumstances in which each of these vectors dominates yields an explanation of the emergence of centre-surround structures and symmetry-breaking bi-lobed structures. Criteria are developed estimating the boundary of the parameter regime in which centre-surround structures emerge. The application of our analysis to Linsker's higher layers, at which the covariance functions were oscillatory, is briefly discussed. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #50337. 	[Title] Recursive algorithms for approximating probabilities in graphical models [Abstract] MIT Computational Cognitive Science Technical Report 9604 Abstract We develop a recursive node-elimination formalism for efficiently approximating large probabilistic networks. No constraints are set on the network topologies. Yet the formalism can be straightforwardly integrated with exact methods whenever they are/become applicable. The approximations we use are controlled: they maintain consistently upper and lower bounds on the desired quantities at all times. We show that Boltzmann machines, sigmoid belief networks, or any combination (i.e., chain graphs) can be handled within the same framework. The accuracy of the methods is verified exper imentally. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #19621. 	[Title] References "Using Neural Networks to Identify Jets", Kohonen, "Self Organized Formation of Topologically Correct Feature [Abstract] 2] D. E. Rumelhart, G. E. Hinton and R. J. Williams, "Learning Internal Representations by Error Propagation", in D. E. Rumelhart and J. L. McClelland (eds.) Parallel Distributed Processing: Explorations in the Microstructure of Cognition (Vol. 1), MIT Press (1986). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #300806. 	[Title] Learning in Boltzmann Trees [Abstract] We introduce a large family of Boltzmann machines that can be trained using standard gradient descent. The networks can have one or more layers of hidden units, with tree-like connectivity. We show how to implement the supervised learning algorithm for these Boltzmann machines exactly, without resort to simulated or mean-field annealing. The stochastic averages that yield the gradients in weight space are computed by the technique of decimation. We present results on the problems of N -bit parity and the detection of hidden symmetries. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #2665. 	[Title] An information-maximisation approach to blind separation and blind deconvolution [Abstract] We derive a new self-organising learning algorithm which maximises the information transferred in a network of non-linear units. The algorithm does not assume any knowledge of the input distributions, and is defined here for the zero-noise limit. Under these conditions, information maximisation has extra properties not found in the linear case (Linsker 1989). The non-linearities in the transfer function are able to pick up higher-order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation. This enables the network to separate statistically independent components in the inputs: a higher-order generalisation of Principal Components Analysis. We apply the network to the source separation (or cocktail party) problem, successfully separating unknown mixtures of up to ten speakers. We also show that a variant on the network architecture is able to perform blind deconvolution (cancellation of unknown echoes and reverberation in a speech signal). Finally, we derive dependencies of information transfer on time delays. We suggest that information max-imisation provides a unifying framework for problems in `blind' signal processing. fl Please send comments to tony@salk.edu. This paper will appear as Neural Computation, 7, 6, 1004-1034 (1995). The reference for this version is: Technical Report no. INC-9501, February 1995, Institute for Neural Computation, UCSD, San Diego, CA 92093-0523. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #49482. 	[Title] Topography And Ocular Dominance: A Model Exploring Positive Correlations [Abstract] The map from eye to brain in vertebrates is topographic, i.e. neighbouring points in the eye map to neighbouring points in the brain. In addition, when two eyes innervate the same target structure, the two sets of fibres segregate to form ocular dominance stripes. Experimental evidence from the frog and goldfish suggests that these two phenomena may be subserved by the same mechanisms. We present a computational model that addresses the formation of both topography and ocular dominance. The model is based on a form of competitive learning with subtractive enforcement of a weight normalization rule. Inputs to the model are distributed patterns of activity presented simultaneously in both eyes. An important aspect of this model is that ocular dominance segregation can occur when the two eyes are positively correlated, whereas previous models have tended to assume zero or negative correlations between the eyes. This allows investigation of the dependence of the pattern of stripes on the degree of correlation between the eyes: we find that increasing correlation leads to narrower stripes. Experiments are suggested to test this prediction. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #631052. 	[Title] Constrained Optimization for Neural Map Formation: A Unifying Framework for Weight Growth and Normalization [Abstract] Computational models of neural map formation can be considered on at least three different levels of abstraction: detailed models including neural activity dynamics, weight dynamics that abstract from the neural activity dynamics by an adiabatic approximation, and constrained optimization from which equations governing weight dynamics can be derived. Constrained optimization uses an objective function, from which a weight growth rule can be derived as a gradient flow, and some constraints, from which normalization rules are derived. In this paper we present an example of how an optimization problem can be derived from detailed non-linear neural dynamics. A systematic investigation reveals how different weight dynamics introduced previously can be derived from two types of objective function terms and two types of constraints. This includes dynamic link matching as a special case of neural map formation. We focus in particular on the role of coordinate transformations to derive different weight dynamics from the same optimization problem. Several examples illustrate how the constrained optimization framework can help in understanding, generating, and comparing different models of neural map formation. The techniques used in this analysis may also be useful in investigating other types of neural dynamics. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #35922. 	[Title] Mean Field Theory for Sigmoid Belief Networks [Abstract] We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics. Our mean field theory provides a tractable approximation to the true probability distribution in these networks; it also yields a lower bound on the likelihood of evidence. We demonstrate the utility of this framework on a benchmark problem in statistical pattern recognition|the classification of handwritten digits. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #396412. 	[Title] Boltzmann Machine learning using mean field theory and linear response correction [Abstract] We present a new approximate learning algorithm for Boltzmann Machines, using a systematic expansion of the Gibbs free energy to second order in the weights. The linear response correction to the correlations is given by the Hessian of the Gibbs free energy. The computational complexity of the algorithm is cubic in the number of neurons. We compare the performance of the exact BM learning algorithm with first order (Weiss) mean field theory and second order (TAP) mean field theory. The learning task consists of a fully connected Ising spin glass model on 10 neurons. We conclude that 1) the method works well for paramagnetic problems 2) the TAP correction gives a significant improvement over the Weiss mean field theory, both for paramagnetic and spin glass problems and 3) that the inclusion of diagonal weights improves the Weiss approximation for paramagnetic problems, but not for spin glass problems. 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.

Paper #631015 has the title `Theory of Correlations in Stochastic Neural Networks  
` and the abstract `One of the main experimental tools in probing the interactions between neurons has been the measurement of the correlations in their activity. In general, however the interpretation of the observed correlations is difficult, since the correlation between a pair of neurons is influenced not only by the direct interaction between them but also by the dynamic state of the entire network to which they belong. Thus, a comparison between the observed correlations and the predictions from specific model networks is needed. In this paper we develop the theory of neuronal correlation functions in large networks comprising of several highly connected subpopulations, and obeying stochastic dynamic rules. When the networks are in asynchronous states, the cross-correlations are relatively weak, i.e., their amplitude relative to that of the auto-correlations is of order of 1=N , N being the size of the interacting populations. Using the weakness of the cross-correlations, general equations which express the matrix of cross-correlations in terms of the mean neuronal activities, and the effective interaction matrix are presented. The effective interactions are the synaptic efficacies multiplied by the the gain of the postsynaptic neurons. The time-delayed cross-correlation matrix can be expressed as a sum of exponentially decaying modes that correspond to the (non-orthogonal) eigenvectors of the effective interaction matrix. The theory is extended to networks with random connectivity, such as randomly dilute networks. This allows for the comparison between the contribution from the internal common input and that from the direct 
`.
Question: Which category should Paper #631015 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #631015 has the title `Theory of Correlations in Stochastic Neural Networks  
` and the abstract `One of the main experimental tools in probing the interactions between neurons has been the measurement of the correlations in their activity. In general, however the interpretation of the observed correlations is difficult, since the correlation between a pair of neurons is influenced not only by the direct interaction between them but also by the dynamic state of the entire network to which they belong. Thus, a comparison between the observed correlations and the predictions from specific model networks is needed. In this paper we develop the theory of neuronal correlation functions in large networks comprising of several highly connected subpopulations, and obeying stochastic dynamic rules. When the networks are in asynchronous states, the cross-correlations are relatively weak, i.e., their amplitude relative to that of the auto-correlations is of order of 1=N , N being the size of the interacting populations. Using the weakness of the cross-correlations, general equations which express the matrix of cross-correlations in terms of the mean neuronal activities, and the effective interaction matrix are presented. The effective interactions are the synaptic efficacies multiplied by the the gain of the postsynaptic neurons. The time-delayed cross-correlation matrix can be expressed as a sum of exponentially decaying modes that correspond to the (non-orthogonal) eigenvectors of the effective interaction matrix. The theory is extended to networks with random connectivity, such as randomly dilute networks. This allows for the comparison between the contribution from the internal common input and that from the direct 
`.
Question: Which category should Paper #631015 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