Above are papers related to the following paper: [Paper_ID] Paper #39210. 	[Title] Pattern analysis and synthesis in attractor neural networks [Abstract] The representation of hidden variable models by attractor neural networks is studied. Memories are stored in a dynamical attractor that is a continuous manifold of fixed points, as illustrated by linear and nonlinear networks with hidden neurons. Pattern analysis and synthesis are forms of pattern completion by recall of a stored memory. Analysis and synthesis in the linear network are performed by bottom-up and top-down connections. In the nonlinear network, the analysis computation additionally requires rectification nonlinearity and inner product inhibition between hidden neurons. One popular approach to sensory processing is based on generative models, which assume that sensory input patterns are synthesized from some underlying hidden variables. For example, the sounds of speech can be synthesized from a sequence of phonemes, and images of a face can be synthesized from pose and lighting variables. Hidden variables are useful because they constitute a simpler representation of the variables that are visible in the sensory input. Using a generative model for sensory processing requires a method of pattern analysis. Given a sensory input pattern, analysis is the recovery of the hidden variables from which it was synthesized. In other words, analysis and synthesis are inverses of each other. There are a number of approaches to pattern analysis. In analysis-by-synthesis, the synthetic model is embedded inside a negative feedback loop[1]. Another approach is to construct a separate analysis model[2]. This paper explores a third approach, in which visible-hidden pairs are embedded as attractive fixed points, or attractors, in the state space of a recurrent neural network. The attractors can be regarded as memories stored in the network, and analysis and synthesis as forms of pattern completion by recall of a memory. The approach is illustrated with linear and nonlinear network architectures. In both networks, the synthetic model is linear, as in principal Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #126912. 	[Title] Continuous sigmoidal belief networks trained using slice sampling [Abstract] Real-valued random hidden variables can be useful for modelling latent structure that explains correlations among observed variables. I propose a simple unit that adds zero-mean Gaussian noise to its input before passing it through a sigmoidal squashing function. Such units can produce a variety of useful behaviors, ranging from deterministic to binary stochastic to continuous stochastic. I show how "slice sampling" can be used for inference and learning in top-down networks of these units and demonstrate learning on two simple problems. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #52515. 	[Title] Unsupervised learning of distributions on binary vectors using two layer networks [Abstract] We present a distribution model for binary vectors, called the influence combination model and show how this model can be used as the basis for unsupervised learning algorithms for feature selection. The model is closely related to the Harmonium model defined by Smolensky [RM86][Ch.6]. In the first part of the paper we analyze properties of this distribution representation scheme. We show that arbitrary distributions of binary vectors can be approximated by the combination model. We show how the weight vectors in the model can be interpreted as high order correlation patterns among the input bits. We compare the combination model with the mixture model and with principle component analysis. In the second part of the paper we present two algorithms for learning the combination model from examples. The first algorithm is based on gradient ascent. Here we give a closed form for this gradient that is significantly easier to compute than the corresponding gradient for the general Boltzmann machine. The second learning algorithm is a greedy method that creates the hidden units and computes their weights one at a time. This method is a variant of projection pursuit density estimation. In the third part of the paper we give experimental results for these learning methods on synthetic data and on natural data of handwritten digit images. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #400356. 	[Title] Factor Analysis Using Delta-Rule Wake-Sleep Learning [Abstract] Technical Report No. 9607, Department of Statistics, University of Toronto We describe a linear network that models correlations between real-valued visible variables using one or more real-valued hidden variables a factor analysis model. This model can be seen as a linear version of the Helmholtz machine, and its parameters can be learned using the wake-sleep method, in which learning of the primary generative model is assisted by a recognition model, whose role is to fill in the values of hidden variables based on the values of visible variables. The generative and recognition models are jointly learned in wake and sleep phases, using just the delta rule. This learning procedure is comparable in simplicity to Oja's version of Hebbian learning, which produces a somewhat different representation of correlations in terms of principal components. We argue that the simplicity of wake-sleep learning makes factor analysis a plau sible alternative to Hebbian learning as a model of activity-dependent cortical plasticity. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1153861. 	[Title] Data Mining for Association Rules with Unsupervised Neural Networks [Abstract] results for Gaussian mixture models and factor analysis are discussed. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #66982. 	[Title] Learning Generative Models with the Up-Propagation Algorithm [Abstract] Up-propagation is an algorithm for inverting and learning neural network generative models. Sensory input is processed by inverting a model that generates patterns from hidden variables using top-down connections. The inversion process is iterative, utilizing a negative feedback loop that depends on an error signal propagated by bottom-up connections. The error signal is also used to learn the generative model from examples. The algorithm is benchmarked against principal component analysis in In his doctrine of unconscious inference, Helmholtz argued that perceptions are formed by the interaction of bottom-up sensory data with top-down expectations. According to one interpretation of this doctrine, perception is a procedure of sequential hypothesis testing. We propose a new algorithm, called up-propagation, that realizes this interpretation in layered neural networks. It uses top-down connections to generate hypotheses, and bottom-up connections to revise them. It is important to understand the difference between up-propagation and its ancestor, the backpropagation algorithm[1]. Backpropagation is a learning algorithm for recognition models. As shown in Figure 1a, bottom-up connections recognize patterns, while top-down connections propagate an error signal that is used to learn the recognition model. In contrast, up-propagation is an algorithm for inverting and learning generative models, as shown in Figure 1b. Top-down connections generate patterns from a set of hidden variables. Sensory input is processed by inverting the generative model, recovering hidden variables that could have generated the sensory data. This operation is called either pattern recognition or pattern analysis, depending on the meaning of the hidden variables. Inversion of the generative model is done iteratively, through a negative feedback loop driven by an error signal from the bottom-up connections. The error signal is also used for learning the connections experiments on images of handwritten digits. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #83847. 	[Title] Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: A theory [Abstract] The head-direction (HD) cells found in the limbic system in freely moving rats represent the instantaneous head direction of the animal in the horizontal plane regardless of the location of the animal. The internal direction represented by these cells uses both self-motion information for inertially based updating and familiar visual landmarks for calibration. Here, a model of the dynamics of the HD cell ensemble is presented. The stability of a localized static activity profile in the network and a dynamic shift mechanism are explained naturally by synaptic weight distribution components with even and odd symmetry, respectively. Under symmetric weights or symmetric reciprocal connections, a stable activity profile close to the known directional tuning curves will emerge. By adding a slight asymmetry to the weights, the activity profile will shift continuously without disturbances to its shape, and the shift speed can be accurately controlled by the strength of the odd-weight component. The generic formulation of the shift mechanism is determined uniquely within the current theoretical framework. The attractor dynamics of the system ensures modality-independence of the internal representation and facilitates the correction for cumulative error by the putative local-view detectors. The model offers a specific one-dimensional example of a computational mechanism in which a truly world-centered representation can be derived from observer-centered sensory inputs by integrating self-motion information. 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 #390889. 	[Title] A HIERARCHICAL COMMUNITY OF EXPERTS [Abstract] We describe a directed acyclic graphical model that contains a hierarchy of linear units and a mechanism for dynamically selecting an appropriate subset of these units to model each observation. The non-linear selection mechanism is a hierarchy of binary units each of which gates the output of one of the linear units. There are no connections from linear units to binary units, so the generative model can be viewed as a logistic belief net (Neal 1992) which selects a skeleton linear model from among the available linear units. We show that Gibbs sampling can be used to learn the parameters of the linear and binary units even when the sampling is so brief that the Markov chain is far from equilibrium. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #66986. 	[Title] Learning Continuous Attractors in Recurrent Networks [Abstract] One approach to invariant object recognition employs a recurrent neural network as an associative memory. In the standard depiction of the network's state space, memories of objects are stored as attractive fixed points of the dynamics. I argue for a modification of this picture: if an object has a continuous family of instantiations, it should be represented by a continuous attractor. This idea is illustrated with a network that learns to complete patterns. To perform the task of filling in missing information, the network develops a continuous attractor that models the manifold from which the patterns are drawn. From a statistical viewpoint, the pattern completion task allows a formulation of unsupervised A classic approach to invariant object recognition is to use a recurrent neural network as an associative memory[1]. In spite of the intuitive appeal and biological plausibility of this approach, it has largely been abandoned in practical applications. This paper introduces two new concepts that could help resurrect it: object representation by continuous attractors, and learning attractors by pattern completion. In most models of associative memory, memories are stored as attractive fixed points at discrete locations in state space[1]. Discrete attractors may not be appropriate for patterns with continuous variability, like the images of a three-dimensional object from different viewpoints. When the instantiations of an object lie on a continuous pattern manifold, it is more appropriate to represent objects by attractive manifolds of fixed points, or continuous attractors. To make this idea practical, it is important to find methods for learning attractors from examples. A naive method is to train the network to retain examples in short-term memory. This method is deficient because it does not prevent the network from storing spurious fixed points that are unrelated to the examples. A superior method is to train the network to restore examples that have been corrupted, so that it learns to complete patterns by filling in missing information. learning in terms of regression rather than density estimation. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1152490. 	[Title] Data Mining for Association Rules with Unsupervised Neural Networks [Abstract] results for Gaussian mixture models and factor analysis are discussed. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #66990. 	[Title] Generative Models for Discovering Sparse Distributed Representations [Abstract] We describe a hierarchical, generative model that can be viewed as a non-linear generalization of factor analysis and can be implemented in a neural network. The model uses bottom-up, top-down and lateral connections to perform Bayesian perceptual inference correctly. Once perceptual inference has been performed the connection strengths can be updated using a very simple learning rule that only requires locally available information. We demon strate that the network learns to extract sparse, distributed, hierarchical representations. 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 #32276. 	[Title] Extracting Support Data for a Given Task [Abstract] We report a novel possibility for extracting a small subset of a data base which contains all the information necessary to solve a given classification task: using the Support Vector Algorithm to train three different types of handwritten digit classifiers, we observed that these types of classifiers construct their decision surface from strongly overlapping small ( 4%) subsets of the data base. This finding opens up the possibility of compressing data bases significantly by disposing of the data which is not important for the solution of a given task. In addition, we show that the theory allows us to predict the classifier that will have the best generalization ability, based solely on performance on the training set and characteristics of the learning machines. This finding is important for cases where the amount of available data is limited. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #11093. 	[Title] Factorial Learning and the EM Algorithm [Abstract] Many real world learning problems are best characterized by an interaction of multiple independent causes or factors. Discovering such causal structure from the data is the focus of this paper. Based on Zemel and Hinton's cooperative vector quantizer (CVQ) architecture, an unsupervised learning algorithm is derived from the Expectation-Maximization (EM) framework. Due to the combinatorial nature of the data generation process, the exact E-step is computationally intractable. Two alternative methods for computing the E-step are proposed: Gibbs sampling and mean-field approximation, and some promising empirical results are presented. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1117501. 	[Title] The Rectified Gaussian Distribution [Abstract] A simple but powerful modification of the standard Gaussian distribution is studied. The variables of the rectified Gaussian are constrained to be nonnegative, enabling the use of nonconvex energy functions. Two multimodal examples, the competitive and cooperative distributions, illustrate the representational power of the rectified Gaussian. Since the cooperative distribution can represent the translations of a pattern, it demonstrates the potential of the rectified Gaussian for modeling pattern manifolds. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #39199. 	[Title] Unsupervised Learning by Convex and Conic Coding [Abstract] Unsupervised learning algorithms based on convex and conic encoders are proposed. The encoders find the closest convex or conic combination of basis vectors to the input. The learning algorithms produce basis vectors that minimize the reconstruction error of the encoders. The convex algorithm develops locally linear models of the input, while the conic algorithm discovers features. Both algorithms are used to model handwritten digits and compared with vector quantization and principal component analysis. The neural network implementations involve feedback connections that project a reconstruction back to the input layer. Please summarise all the given information.

Paper #39210 has the title `Pattern analysis and synthesis in attractor neural networks  
` and the abstract `The representation of hidden variable models by attractor neural networks is studied. Memories are stored in a dynamical attractor that is a continuous manifold of fixed points, as illustrated by linear and nonlinear networks with hidden neurons. Pattern analysis and synthesis are forms of pattern completion by recall of a stored memory. Analysis and synthesis in the linear network are performed by bottom-up and top-down connections. In the nonlinear network, the analysis computation additionally requires rectification nonlinearity and inner product inhibition between hidden neurons. One popular approach to sensory processing is based on generative models, which assume that sensory input patterns are synthesized from some underlying hidden variables. For example, the sounds of speech can be synthesized from a sequence of phonemes, and images of a face can be synthesized from pose and lighting variables. Hidden variables are useful because they constitute a simpler representation of the variables that are visible in the sensory input. Using a generative model for sensory processing requires a method of pattern analysis. Given a sensory input pattern, analysis is the recovery of the hidden variables from which it was synthesized. In other words, analysis and synthesis are inverses of each other. There are a number of approaches to pattern analysis. In analysis-by-synthesis, the synthetic model is embedded inside a negative feedback loop[1]. Another approach is to construct a separate analysis model[2]. This paper explores a third approach, in which visible-hidden pairs are embedded as attractive fixed points, or attractors, in the state space of a recurrent neural network. The attractors can be regarded as memories stored in the network, and analysis and synthesis as forms of pattern completion by recall of a memory. The approach is illustrated with linear and nonlinear network architectures. In both networks, the synthetic model is linear, as in principal 
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Question: Which category should Paper #39210 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #39210 has the title `Pattern analysis and synthesis in attractor neural networks  
` and the abstract `The representation of hidden variable models by attractor neural networks is studied. Memories are stored in a dynamical attractor that is a continuous manifold of fixed points, as illustrated by linear and nonlinear networks with hidden neurons. Pattern analysis and synthesis are forms of pattern completion by recall of a stored memory. Analysis and synthesis in the linear network are performed by bottom-up and top-down connections. In the nonlinear network, the analysis computation additionally requires rectification nonlinearity and inner product inhibition between hidden neurons. One popular approach to sensory processing is based on generative models, which assume that sensory input patterns are synthesized from some underlying hidden variables. For example, the sounds of speech can be synthesized from a sequence of phonemes, and images of a face can be synthesized from pose and lighting variables. Hidden variables are useful because they constitute a simpler representation of the variables that are visible in the sensory input. Using a generative model for sensory processing requires a method of pattern analysis. Given a sensory input pattern, analysis is the recovery of the hidden variables from which it was synthesized. In other words, analysis and synthesis are inverses of each other. There are a number of approaches to pattern analysis. In analysis-by-synthesis, the synthetic model is embedded inside a negative feedback loop[1]. Another approach is to construct a separate analysis model[2]. This paper explores a third approach, in which visible-hidden pairs are embedded as attractive fixed points, or attractors, in the state space of a recurrent neural network. The attractors can be regarded as memories stored in the network, and analysis and synthesis as forms of pattern completion by recall of a memory. The approach is illustrated with linear and nonlinear network architectures. In both networks, the synthetic model is linear, as in principal 
`.
Question: Which category should Paper #39210 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