Symmetry Breaking in Symmetric Tensor Decomposition

2021/03/10 by Yossi Arjevani, Arjevani, Yossi, Joan Bruna +9 · 1 citation
Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2103.06234

openalex publication_date 2021/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

Citations

• The Loss Surfaces of Multilayer Networks
• Tensor Decompositions and Applications
• Subspace power method for symmetric tensor decomposition
• Analytic Characterization of the Hessian in Shallow ReLU Models: A Tale of Symmetry

Cited by

• Ubiquitous Symmetry at Critical Points Across Diverse Optimization Landscapes

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