# Optimization Landscape of Tucker Decomposition

arXiv: https://arxiv.org/abs/2006.16297 · HTML: https://mlsanity.com/paper/2006.16297/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2020.

## Built on by (most cited first, 10 of 10)

- [Scaling and Scalability: Provable Nonconvex Low-Rank Tensor Estimation from Incomplete Measurements](https://mlsanity.com/paper/2104.14526/) (2021)
- [The loss landscape of deep linear neural networks: a second-order analysis](https://mlsanity.com/paper/2107.13289/) (2021)
- [Approximately Optimal Core Shapes for Tensor Decompositions](https://mlsanity.com/paper/2302.03886/) (2023)
- [Subquadratic Kronecker Regression with Applications to Tensor Decomposition](https://mlsanity.com/paper/2209.04876/) (2022)
- [Provably Accelerating Ill-Conditioned Low-rank Estimation via Scaled Gradient Descent, Even with Overparameterization](https://mlsanity.com/paper/2310.06159/) (2023)
- [TensorGRaD: Tensor Gradient Robust Decomposition for Memory-Efficient Neural Operator Training](https://mlsanity.com/paper/2501.02379/) (2025)
- [Fast Low-Rank Tensor Decomposition by Ridge Leverage Score Sampling](https://mlsanity.com/paper/2107.10654/) (2021)
- [A Complete Loss Landscape Analysis of Regularized Deep Matrix Factorization](https://mlsanity.com/paper/2506.20344/) (2025)
- [A Tight Lower Bound for the Approximation Guarantee of Higher-Order Singular Value Decomposition](https://mlsanity.com/paper/2508.06693/) (2025)
- [Benign Loss Landscapes Can Coexist with Worst-Case Hardness](https://mlsanity.com/paper/2609.13057/) (2026)

## Abstract (arXiv)

Tucker decomposition is a popular technique for many data analysis and machine learning applications. Finding a Tucker decomposition is a nonconvex optimization problem. As the scale of the problems increases, local search algorithms such as stochastic gradient descent have become popular in practice. In this paper, we characterize the optimization landscape of the Tucker decomposition problem. In particular, we show that if the tensor has an exact Tucker decomposition, for a standard nonconvex objective of Tucker decomposition, all local minima are also globally optimal. We also give a local search algorithm that can find an approximate local (and global) optimal solution in polynomial time.