# New Tight Relaxations of Rank Minimization for Multi-Task Learning

arXiv: https://arxiv.org/abs/2112.04734 · HTML: https://mlsanity.com/paper/2112.04734/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 29 references that are in the map.
- First posted on arXiv 9 Dec 2021.

## Builds on (most cited first, 2 of 2)

- [Multi-Task Attention-Based Semi-Supervised Learning for Medical Image Segmentation](https://mlsanity.com/paper/1907.12303/) (2019)
- [Multi-task learning for natural language processing in the 2020s: where are we going?](https://mlsanity.com/paper/2007.16008/) (2020)

## Abstract (arXiv)

Multi-task learning has been observed by many researchers, which supposes that different tasks can share a low-rank common yet latent subspace. It means learning multiple tasks jointly is better than learning them independently. In this paper, we propose two novel multi-task learning formulations based on two regularization terms, which can learn the optimal shared latent subspace by minimizing the exactly k minimal singular values. The proposed regularization terms are the more tight approximations of rank minimization than trace norm. But it's an NP-hard problem to solve the exact rank minimization problem. Therefore, we design a novel re-weighted based iterative strategy to solve our models, which can tactically handle the exact rank minimization problem by setting a large penalizing parameter. Experimental results on benchmark datasets demonstrate that our methods can correctly recover the low-rank structure shared across tasks, and outperform related multi-task learning methods.