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 #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 #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 #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 #1106287. 	[Title] Separating hippocampal maps  Spatial Functions of the Hippocampal Formation and the [Abstract] The place fields of hippocampal cells in old animals sometimes change when an animal is removed from and then returned to an environment [ Barnes et al., 1997 ] . The ensemble correlation between two sequential visits to the same environment shows a strong bimodality for old animals (near 0, indicative of remapping, and greater than 0.7, indicative of a similar representation between experiences), but a strong unimodality for young animals (greater than 0.7, indicative of a similar representation between experiences). One explanation for this is the multi-map hypothesis in which multiple maps are encoded in the hippocampus: old animals may sometimes be returning to the wrong map. A theory proposed by Samsonovich and McNaughton (1997) suggests that the Barnes et al. experiment implies that the maps are pre-wired in the CA3 region of hippocampus. Here, we offer an alternative explanation in which orthogonalization properties in the dentate gyrus (DG) region of hippocampus interact with errors in self-localization (reset of the path integrator on re-entry into the environment) to produce the bimodality. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1130678. 	[Title] Interpreting neuronal population activity by reconstruction: A unified framework with application to hippocampal place cells [Abstract] Physical variables such as the orientation of a line in the visual field or the location of the body in space are coded as activity levels in populations of neurons. Reconstruction or decoding is an inverse problem in which the physical variables are estimated from observed neural activity. Reconstruction is useful first in quantifying how much information about the physical variables is present in the population, and second, in providing insight into how the brain might use distributed representations in solving related computational problems such as visual object recognition and spatial navigation. Two classes of reconstruction methods, namely, probabilistic or Bayesian methods and basis function methods, are discussed. They include important existing methods as special cases, such as population vector coding, optimal linear estimation and template matching. As a representative example for the reconstruction problem, different methods were applied to multi-electrode spike train data from hippocampal place cells in freely moving rats. The reconstruction accuracy of the trajectories of the rats was compared for the different methods. Bayesian methods were especially accurate when a continuity constraint was enforced, and the best errors were within a factor of two of the the information-theoretic limit on how accurate any reconstruction can be, which were comparable with the intrinsic experimental errors in position tracking. In addition, the reconstruction analysis uncovered some interesting aspects of place cell activity, such as the tendency for erratic jumps of the reconstructed trajectory when the animal stopped running. In general, the theoretical values of the minimal achievable reconstruction errors quantify how accurately a physical variable is encoded in the neuronal population in the sense of mean square error, regardless of the method used for reading out the information. One related result is that the theoretical accuracy is independent of the width of the Gaussian tuning function only in two dimensions. Finally, all the reconstruction methods considered in this paper can be implemented by a unified neural network architecture, which the brain could feasibly use to solve related problems. 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 #66986 has the title `Learning Continuous Attractors in Recurrent Networks  
` and the 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.
`.
Question: Which category should Paper #66986 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #66986 has the title `Learning Continuous Attractors in Recurrent Networks  
` and the 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.
`.
Question: Which category should Paper #66986 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