Above are papers related to the following paper: [Paper_ID] Paper #217984. 	[Title] Analyzing Phase Transitions in High-Dimensional Self-Organizing Maps [Abstract] The Self-Organizing Map (SOM), a widely used algorithm for the unsupervised learning of neural maps, can be formulated in a low-dimensional "feature map" variant which requires prespecified parameters ("features") for the description of receptive fields, or in a more general high-dimensional variant which allows to self-organize the structure of individual receptive fields as well as their arrangement in a map. We present here a new analytical method to derive conditions for the emergence of structure in SOMs which is particularly suited for the as yet inaccessible high-dimensional SOM variant. Our approach is based on an evaluation of a map distortion function. It involves only an ansatz for the way stimuli are distributed among map neurons; the receptive fields of the map need not be known explicitely. Using this method we first calculate regions of stability for four possible states of SOMs projecting from a rectangular input space to a ring of neurons. We then analyze the transition from non-oriented to oriented receptive fields in a SOM-based model for the development of orientation maps. In both cases, the analytical results are well corroborated by the results of computer simulations. submitted to Biological Cybernetics, December 14, 1995 revised version, July 14, 1996 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #7297. 	[Title] Self-Organization and Functional Role of Lateral Connections and Multisize Receptive Fields in the Primary Visual Cortex [Abstract] Cells in the visual cortex are selective not only to ocular dominance and orientation of the input, but also to its size and spatial frequency. The simulations reported in this paper show how size selectivity could develop through Hebbian self-organization, and how receptive fields of different sizes could organize into columns like those for orientation and ocular dominance. The lateral connections in the network self-organize cooperatively and simultaneously with the receptive field sizes, and produce patterns of lateral connectivity that closely follow the receptive field organization. Together with our previous work on ocular dominance and orientation selectivity, these results suggest that a single Hebbian self-organizing process can give rise to all the major receptive field properties in the visual cortex, and also to structured patterns of lateral interactions, some of which have been verified experimentally and others predicted by the model. The model also suggests a functional role for the self-organized structures: The afferent receptive fields develop a sparse coding of the visual input, and the recurrent lateral interactions eliminate redundancies in cortical activity patterns, allowing the cortex to efficiently process massive amounts of visual 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 #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 #1112369. 	[Title] Breaking Rotational Symmetry in a Self-Organizing Map-Model for Orientation Map Development [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1365. 	[Title] Cholinergic suppression of transmission may allow combined associative memory function and self-organization in the neocortex. [Abstract] Selective suppression of transmission at feedback synapses during learning is proposed as a mechanism for combining associative feedback with self-organization of feedforward synapses. Experimental data demonstrates cholinergic suppression of synaptic transmission in layer I (feedback synapses), and a lack of suppression in layer IV (feed-forward synapses). A network with this feature uses local rules to learn mappings which are not linearly separable. During learning, sensory stimuli and desired response are simultaneously presented as input. Feedforward connections form self-organized representations of input, while suppressed feedback connections learn the transpose of feedfor-ward connectivity. During recall, suppression is removed, sensory input activates the self-organized representation, and activity generates the learned response. 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 #217984 has the title `Analyzing Phase Transitions in High-Dimensional Self-Organizing Maps  
` and the abstract `The Self-Organizing Map (SOM), a widely used algorithm for the unsupervised learning of neural maps, can be formulated in a low-dimensional "feature map" variant which requires prespecified parameters ("features") for the description of receptive fields, or in a more general high-dimensional variant which allows to self-organize the structure of individual receptive fields as well as their arrangement in a map. We present here a new analytical method to derive conditions for the emergence of structure in SOMs which is particularly suited for the as yet inaccessible high-dimensional SOM variant. Our approach is based on an evaluation of a map distortion function. It involves only an ansatz for the way stimuli are distributed among map neurons; the receptive fields of the map need not be known explicitely. Using this method we first calculate regions of stability for four possible states of SOMs projecting from a rectangular input space to a ring of neurons. We then analyze the transition from non-oriented to oriented receptive fields in a SOM-based model for the development of orientation maps. In both cases, the analytical results are well corroborated by the results of computer simulations. submitted to Biological Cybernetics, December 14, 1995 revised version, July 14, 1996
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Question: Which category should Paper #217984 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #217984 has the title `Analyzing Phase Transitions in High-Dimensional Self-Organizing Maps  
` and the abstract `The Self-Organizing Map (SOM), a widely used algorithm for the unsupervised learning of neural maps, can be formulated in a low-dimensional "feature map" variant which requires prespecified parameters ("features") for the description of receptive fields, or in a more general high-dimensional variant which allows to self-organize the structure of individual receptive fields as well as their arrangement in a map. We present here a new analytical method to derive conditions for the emergence of structure in SOMs which is particularly suited for the as yet inaccessible high-dimensional SOM variant. Our approach is based on an evaluation of a map distortion function. It involves only an ansatz for the way stimuli are distributed among map neurons; the receptive fields of the map need not be known explicitely. Using this method we first calculate regions of stability for four possible states of SOMs projecting from a rectangular input space to a ring of neurons. We then analyze the transition from non-oriented to oriented receptive fields in a SOM-based model for the development of orientation maps. In both cases, the analytical results are well corroborated by the results of computer simulations. submitted to Biological Cybernetics, December 14, 1995 revised version, July 14, 1996
`.
Question: Which category should Paper #217984 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