Smoothed analysis of discrete tensor decomposition and assemblies of neurons
Name
NeurIPS-2018-smoothed-analysis-of-discrete-tensor-decomposition-and-assemblies-of-neurons-Paper.pdf
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Published version
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437.86 KB
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Adobe PDF
Checksum (MD5)
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Author(s)
Anari, N
Daskalakis, C
Maass, W
Papadimitriou, CH
Saberi, A
Vempala, S
Date Issued
January 1, 2018
Journal
Advances in Neural Information Processing Systems
Citation
Anari, N, Daskalakis, C, Maass, W, Papadimitriou, CH, Saberi, A et al. 2018. "Smoothed analysis of discrete tensor decomposition and assemblies of neurons." Advances in Neural Information Processing Systems, 2018-December.
Version
Final published version
Abstract
© 2018 Curran Associates Inc.All rights reserved. We analyze linear independence of rank one tensors produced by tensor powers of randomly perturbed vectors. This enables efficient decomposition of sums of high-order tensors. Our analysis builds upon Bhaskara et al. [3] but allows for a wider range of perturbation models, including discrete ones. We give an application to recovering assemblies of neurons. Assemblies are large sets of neurons representing specific memories or concepts. The size of the intersection of two assemblies has been shown in experiments to represent the extent to which these memories co-occur or these concepts are related; the phenomenon is called association of assemblies. This suggests that an animal's memory is a complex web of associations, and poses the problem of recovering this representation from cognitive data. Motivated by this problem, we study the following more general question: Can we reconstruct the Venn diagram of a family of sets, given the sizes of their `-wise intersections? We show that as long as the family of sets is randomly perturbed, it is enough for the number of measurements to be polynomially larger than the number of nonempty regions of the Venn diagram to fully reconstruct the diagram.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://papers.nips.cc/paper/2018/hash/5cc3749a6e56ef6d656735dff9176074-Abstract.html
