Mapping correlated Gaussian patterns in a perceptron
نویسندگان
چکیده
منابع مشابه
Mapping correlated Gaussian patterns in a perceptron
We study the performance of a single-layer perceptron in realising a binary mapping of Gaussian input patterns. By introducing non-trivial correlations among the patterns, we generate a family of mappings including easier ones where similar inputs are mapped into the same output, and more difficult ones where similar inputs are mapped into different classes. The difficulty of the problem is gau...
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We calculate the storage capacity of a perceptron for correlated Gaussian patterns. We find that the storage capacity αc can be less than 2 if similar patterns are mapped onto different outputs and vice versa. As long as the patterns are in a general position we obtain, in contrast to previous works, that αc ≥ 1 in agreement with Cover’s theorem. Numerical simulations confirm the results. The c...
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In this paper, we address the problem of how many randomly labeled patterns can be correctly classified by a single-layer perceptron when the patterns are correlated with each other. In order to solve this problem, two analytical schemes are developed based on the replica method and Thouless-Anderson-Palmer (TAP) approach by utilizing an integral formula concerning random rectangular matrices. ...
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In this paper we calculate the storage capacity of the perceptron for block-wise semantically correlated patterns. The set of patterns is divided into blocks, each block consisting of n binary patterns. The patterns in a block have the overlap R with each other and patterns in diierent blocks have overlap 0. Using a cavity method, which was recently developed by F. Gerl 1], we derive a general ...
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A framework to analyze inference performance in densely connected single-layer feed-forward networks is developed for situations where a given data set is composed of correlated patterns. The framework is based on the assumption that the left and right singular value bases of the given pattern matrix are generated independently and uniformly from Haar measures. This assumption makes it possible...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1989
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/22/16/007