Symmetry Breaking in Symmetric Tensor Decomposition

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.

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Cited by in corpus (3)

• Symmetry & critical points for a model shallow neural network
• Analytic Study of Families of Spurious Minima in Two-Layer ReLU Neural Networks: A Tale of Symmetry II
• Equivariant bifurcation, quadratic equivariants, and symmetry breaking for the standard representation of $S_n$