# On Unbiased Low-Rank Approximation with Minimum Distortion

arXiv: https://arxiv.org/abs/2505.09647 · HTML: https://mlsanity.com/paper/2505.09647/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 10 references that are in the map.
- First posted on arXiv 12 May 2025.

## Builds on (most cited first, 7 of 7)

- [PowerSGD: Practical Low-Rank Gradient Compression for Distributed Optimization](https://mlsanity.com/paper/1905.13727/) (2019)
- [ATOMO: Communication-efficient Learning via Atomic Sparsification](https://mlsanity.com/paper/1806.04090/) (2018)
- [Unbiased Online Recurrent Optimization](https://mlsanity.com/paper/1702.05043/) (2017)
- [Optimal Kronecker-Sum Approximation of Real Time Recurrent Learning](https://mlsanity.com/paper/1902.03993/) (2019)
- [Training recurrent networks online without backtracking](https://mlsanity.com/paper/1507.07680/) (2015)
- [Efficient Unbiased Sparsification](https://mlsanity.com/paper/2402.14925/) (2024)
- [An unbiased approach to low rank recovery](https://mlsanity.com/paper/1909.13363/) (2019)

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

- [Unbiased Approximate Vector-Jacobian Products for Efficient Backpropagation](https://mlsanity.com/paper/2602.14701/) (2026)

## Abstract (arXiv)

We describe an algorithm for sampling a low-rank random matrix Q that best approximates a fixed target matrix P∈mathbbCn× m in the following sense: Q is unbiased, i.e., mathbbE[Q] = P; mathsfrank(Q)≤ r; and Q minimizes the expected Frobenius norm error mathbbE|P-Q|F2. Our algorithm mirrors the solution to the efficient unbiased sparsification problem for vectors, except applied to the singular components of the matrix P. Optimality is proven by showing that our algorithm matches the error from an existing lower bound.