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Generalization and properties of the neural response

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dc.contributor.advisor Tomaso Poggio and Lorenzo Rosasco. en_US
dc.contributor.author Wibisono, Andre Yohannes en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. en_US
dc.date.accessioned 2011-03-07T14:38:26Z
dc.date.available 2011-03-07T14:38:26Z
dc.date.copyright 2010 en_US
dc.date.issued 2010 en_US
dc.identifier.uri http://hdl.handle.net/1721.1/61517
dc.description Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010. en_US
dc.description This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. en_US
dc.description Cataloged from student-submitted PDF version of thesis. en_US
dc.description Includes bibliographical references (p. 79-83). en_US
dc.description.abstract Hierarchical learning algorithms have enjoyed tremendous growth in recent years, with many new algorithms being proposed and applied to a wide range of applications. However, despite the apparent success of hierarchical algorithms in practice, the theory of hierarchical architectures remains at an early stage. In this thesis we study the theoretical properties of hierarchical algorithms from a mathematical perspective. Our work is based on the framework of hierarchical architectures introduced by Smale et al. in the paper "Mathematics of the Neural Response", Foundations of Computational Mathematics, 2010. We propose a generalized definition of the neural response and derived kernel that allows us to integrate some of the existing hierarchical algorithms in practice into our framework. We then use this generalized definition to analyze the theoretical properties of hierarchical architectures. Our analysis focuses on three particular aspects of the hierarchy. First, we show that a wide class of architectures suffers from range compression; essentially, the derived kernel becomes increasingly saturated at each layer. Second, we show that the complexity of a linear architecture is constrained by the complexity of the first layer, and in some cases the architecture collapses into a single-layer linear computation. Finally, we characterize the discrimination and invariance properties of the derived kernel in the case when the input data are one-dimensional strings. We believe that these theoretical results will provide a useful foundation for guiding future developments within the theory of hierarchical algorithms. en_US
dc.description.statementofresponsibility by Andre Yohannes Wibisono. en_US
dc.format.extent 83 p. en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.rights.uri http://dspace.mit.edu/handle/1721.1/7582 en_US
dc.subject Electrical Engineering and Computer Science. en_US
dc.title Generalization and properties of the neural response en_US
dc.type Thesis en_US
dc.description.degree M.Eng. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. en_US
dc.identifier.oclc 703286375 en_US


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