Symmetry Breaking in Symmetric Tensor Decomposition
Optimization and Control
2023-12-29 v2 Machine Learning
Abstract
In this note, we consider the highly nonconvex optimization problem associated with computing the rank decomposition of symmetric tensors. We formulate the invariance properties of the loss function and show that critical points detected by standard gradient based methods are \emph{symmetry breaking} with respect to the target tensor. The phenomena, seen for different choices of target tensors and norms, make possible the use of recently developed analytic and algebraic tools for studying nonconvex optimization landscapes exhibiting symmetry breaking phenomena of similar nature.
Cite
@article{arxiv.2103.06234,
title = {Symmetry Breaking in Symmetric Tensor Decomposition},
author = {Yossi Arjevani and Joan Bruna and Michael Field and Joe Kileel and Matthew Trager and Francis Williams},
journal= {arXiv preprint arXiv:2103.06234},
year = {2023}
}