# Large Dimensional Analysis and Improvement of Multi Task Learning

arXiv: https://arxiv.org/abs/2009.01591 · HTML: https://mlsanity.com/paper/2009.01591/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2020.

## Built on by (most cited first, 9 of 9)

- [Analysing Multi-Task Regression via Random Matrix Theory with Application to Time Series Forecasting](https://mlsanity.com/paper/2406.10327/) (2024)
- [Two-way kernel matrix puncturing: towards resource-efficient PCA and spectral clustering](https://mlsanity.com/paper/2102.12293/) (2021)
- [PCA-based Multi Task Learning: a Random Matrix Approach](https://mlsanity.com/paper/2111.00924/) (2021)
- [Stereotype Detection in LLMs: A Multiclass, Explainable, and Benchmark-Driven Approach](https://mlsanity.com/paper/2404.01768/) (2024)
- [High-Dimensional Analysis of Bootstrap Ensemble Classifiers](https://mlsanity.com/paper/2505.14587/) (2025)
- [LLMs as In-Context Meta-Learners for Model and Hyperparameter Selection](https://mlsanity.com/paper/2510.26510/) (2025)
- [A Large Dimensional Analysis of Multi-task Semi-Supervised Learning](https://mlsanity.com/paper/2402.13646/) (2024)
- [Asymptotic Behavior of Multi--Task Learning: Implicit Regularization and Double Descent Effects](https://mlsanity.com/paper/2603.05060/) (2026)
- [α-TCAV: A Unified Framework for Testing with Concept Activation Vectors](https://mlsanity.com/paper/2605.15688/) (2026)

## Abstract (arXiv)

Multi Task Learning (MTL) efficiently leverages useful information contained in multiple related tasks to help improve the generalization performance of all tasks. This article conducts a large dimensional analysis of a simple but, as we shall see, extremely powerful when carefully tuned, Least Square Support Vector Machine (LSSVM) version of MTL, in the regime where the dimension p of the data and their number n grow large at the same rate. Under mild assumptions on the input data, the theoretical analysis of the MTL-LSSVM algorithm first reveals the "sufficient statistics" exploited by the algorithm and their interaction at work. These results demonstrate, as a striking consequence, that the standard approach to MTL-LSSVM is largely suboptimal, can lead to severe effects of negative transfer but that these impairments are easily corrected. These corrections are turned into an improved MTL-LSSVM algorithm which can only benefit from additional data, and the theoretical performance of which is also analyzed. As evidenced and theoretically sustained in numerous recent works, these large dimensional results are robust to broad ranges of data distributions, which our present experiments corroborate. Specifically, the article reports a systematically close behavior between theoretical and empirical performances on popular datasets, which is strongly suggestive of the applicability of the proposed carefully tuned MTL-LSSVM method to real data. This fine-tuning is fully based on the theoretical analysis and does not in particular require any cross validation procedure. Besides, the reported performances on real datasets almost systematically outperform much more elaborate and less intuitive state-of-the-art multi-task and transfer learning methods.