# Hotelling Deflation on Large Symmetric Spiked Tensors

arXiv: https://arxiv.org/abs/2304.10248 · HTML: https://mlsanity.com/paper/2304.10248/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 16 references that are in the map.
- First posted on arXiv 20 Apr 2023.

## Builds on (most cited first, 5 of 5)

- [High-dimensional limit theorems for SGD: Effective dynamics and critical scaling](https://mlsanity.com/paper/2206.04030/) (2022)
- [A Random Matrix Perspective on Random Tensors](https://mlsanity.com/paper/2108.00774/) (2021)
- [When Random Tensors meet Random Matrices](https://mlsanity.com/paper/2112.12348/) (2021)
- [Optimizing Orthogonalized Tensor Deflation via Random Tensor Theory](https://mlsanity.com/paper/2302.05798/) (2023)
- [Best rank-k approximations for tensors: generalizing Eckart-Young](https://mlsanity.com/paper/1711.06443/) (2017)

## Built on by (most cited first, 1 of 1)

- [Statistical Limits in Random Tensors with Multiple Correlated Spikes](https://mlsanity.com/paper/2503.03356/) (2025)

## Abstract (arXiv)

This paper studies the deflation algorithm when applied to estimate a low-rank symmetric spike contained in a large tensor corrupted by additive Gaussian noise. Specifically, we provide a precise characterization of the large-dimensional performance of deflation in terms of the alignments of the vectors obtained by successive rank-1 approximation and of their estimated weights, assuming non-trivial (fixed) correlations among spike components. Our analysis allows an understanding of the deflation mechanism in the presence of noise and can be exploited for designing more efficient signal estimation methods.