Approximate Real Symmetric Tensor Rank
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Abstract (arXiv)
We investigate the effect of an varepsilon-room of perturbation tolerance on symmetric tensor decomposition. To be more precise, suppose a real symmetric d-tensor f, a norm ||.|| on the space of symmetric d-tensors, and varepsilon >0 are given. What is the smallest symmetric tensor rank in the varepsilon-neighborhood of f? In other words, what is the symmetric tensor rank of f after a clever varepsilon-perturbation? We prove two theorems and develop three corresponding algorithms that give constructive upper bounds for this question. With expository goals in mind; we present probabilistic and convex geometric ideas behind our results, reproduce some known results, and point out open problems.
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References · 14
- 2016Tensor Decomposition for Signal Processing and Machine Learningcited by 223
- 2021Tensor Methods in Computer Vision and Deep Learningcited by 52
- 2019Revisiting the Approximate Carath'eodory Problem via the Frank-Wolfe Algorithmcited by 11
- 2019Robust and Resource Efficient Identification of Two Hidden Layer Neural Networkscited by 10
- 2021Landscape analysis of an improved power method for tensor decompositioncited by 7
- 2019The sum-of-squares hierarchy on the sphere, and applications in quantum information theorycited by 3
- 2013On the Nuclear Norm and the Singular Value Decomposition of Tensorscited by 2
- 2016Symmetric Tensor Nuclear Normscited by 2
- 2014Approximating Nash Equilibria and Dense Subgraphs via an Approximate Version of Carath'eodory's Theoremcited by 1
- 2016Approximating Nonnegative Polynomials via Spectral Sparsificationcited by 1
- 2018Waring Rank, Parameterized and Exact Algorithmscited by 1
- 2020Approximate tensor decompositions: disappearance of many separationscited by 1
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