Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial-time Tensor Decompositions with Sum-of-Squares   We give new algorithms based on the sum-of-squares method for tensor
decomposition. Our results improve the best known running times from
quasi-polynomial to polynomial for several problems, including decomposing
random overcomplete 3-tensors and learning overcomplete dictionaries with
constant relative sparsity. We also give the first robust analysis for
decomposing overcomplete 4-tensors in the smoothed analysis model. A key
ingredient of our analysis is to establish small spectral gaps in moment
matrices derived from solutions to sum-of-squares relaxations. To enable this
analysis we augment sum-of-squares relaxations with spectral analogs of maximum
entropy constraints.

3
The categories of this paper are: physics
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas