Paper Info
Title
Smoothed Analysis of Discrete Tensor Decomposition and Assemblies of Neurons.
Abstract
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 l-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.
Year
Venue
Keywords
2018
ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 31 (NIPS 2018)
smoothed analysis,linear independence,general question,venn diagram,family of sets,tensor decomposition
DocType
Volume
ISSN
Conference
31
1049-5258
Citations 
PageRank 
References 
0
0.34
3
Authors
6
Name
Order
Citations
PageRank
Nima Anari17914.83
Constantinos Daskalakis2117985.25
Wolfgang Maass33717391.51
Christos H. Papadimitriou4166713192.54
Amin Saberi52824224.27
Santosh Vempala63546523.21