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cs.DS2026
Explicit tensors beyond the linear flattening barrier
Benjamin Lovitz
We construct explicit n x n x n tensors of border rank at least 3n-o(n), improving the previous record of (2 + )n due to (Landsberg and Michalek 2025). We also prove t…
cs.DS2025
A linear-time algorithm for Chow decompositions
Alexander Taveira Blomenhofer, Benjamin Lovitz
We propose a linear-time algorithm to compute low-rank Chow decompositions. Our algorithm can decompose concise symmetric 3-tensors in n variables of Chow rank n/3. The algorithm i…
cs.DS2022★ 6 cited
Computing linear sections of varieties: quantum entanglement, tensor decompositions and beyond
Nathaniel Johnston, Benjamin Lovitz, Aravindan Vijayaraghavan
We study the problem of finding elements in the intersection of an arbitrary conic variety in with a given linear subspace (where can be the real or com…