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Tensor Reconstruction Beyond Constant Rank
[article]

2022
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arXiv
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pre-print

We give reconstruction algorithms for subclasses of depth-3 arithmetic circuits. In particular, we obtain the first efficient algorithm for finding tensor rank, and an optimal tensor decomposition as a sum of rank-one tensors, when given black-box access to a tensor of super-constant rank. We obtain the following results: 1. A deterministic algorithm that reconstructs polynomials computed by Σ^[k]⋀^[d]Σ circuits in time 𝗉𝗈𝗅𝗒(n,d,c) ·𝗉𝗈𝗅𝗒(k)^k^k^10 2. A randomized algorithm that reconstructs

arXiv:2209.04177v1
fatcat:7hyqmmah7rf6rnxhw5uj3zj3hy