NDLI: Learning with incomplete information in the committee machine

Content Provider	Springer Nature Link
Author	Bergmann, Urs M. Kühn, Reimer Stamatescu, Ion Olimpiu
Copyright Year	2009
Abstract	We study the problem of learning with incomplete information in a student–teacher setup for the committee machine. The learning algorithm combines unsupervised Hebbian learning of a series of associations with a delayed reinforcement step, in which the set of previously learnt associations is partly and indiscriminately unlearnt, to an extent that depends on the success rate of the student on these previously learnt associations. The relevant learning parameter λ represents the strength of Hebbian learning. A coarse-grained analysis of the system yields a set of differential equations for overlaps of student and teacher weight vectors, whose solutions provide a complete description of the learning behavior. It reveals complicated dynamics showing that perfect generalization can be obtained if the learning parameter exceeds a threshold λ c , and if the initial value of the overlap between student and teacher weights is non-zero. In case of convergence, the generalization error exhibits a power law decay as a function of the number of examples used in training, with an exponent that depends on the parameter λ. An investigation of the system flow in a subspace with broken permutation symmetry between hidden units reveals a bifurcation point λ* above which perfect generalization does not depend on initial conditions. Finally, we demonstrate that cases of a complexity mismatch between student and teacher are optimally resolved in the sense that an over-complex student can emulate a less complex teacher rule, while an under-complex student reaches a state which realizes the minimal generalization error compatible with the complexity mismatch.
Starting Page	401
Ending Page	410
Page Count	10
File Format	PDF
ISSN	03401200
Journal	Biological Cybernetics
Volume Number	101
Issue Number	5
e-ISSN	14320770
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-11-04
Publisher Place	Berlin/Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Reinforcement learning Online learning Committee machine Credit assignment Coarsegrained analysis Statistical Physics, Dynamical Systems and Complexity Neurobiology Computer Application in Life Sciences Neurosciences Bioinformatics
Content Type	Text
Resource Type	Article
Subject	Computer Science Biotechnology

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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