# Asymptotic Behavior of Multi--Task Learning: Implicit Regularization and Double Descent Effects

arXiv: https://arxiv.org/abs/2603.05060 · HTML: https://mlsanity.com/paper/2603.05060/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 38 references that are in the map.
- First posted on arXiv 5 Mar 2026.

## Builds on (most cited first, 15 of 15)

- [Multi-Task Learning with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2009.09796/) (2020)
- [Two models of double descent for weak features](https://mlsanity.com/paper/1903.07571/) (2019)
- [To understand deep learning we need to understand kernel learning](https://mlsanity.com/paper/1802.01396/) (2018)
- [Harmless interpolation of noisy data in regression](https://mlsanity.com/paper/1903.09139/) (2019)
- [Overfitting or perfect fitting? Risk bounds for classification and regression rules that interpolate](https://mlsanity.com/paper/1806.05161/) (2018)
- [A Model of Double Descent for High-dimensional Binary Linear Classification](https://mlsanity.com/paper/1911.05822/) (2019)
- [A framework to characterize performance of LASSO algorithms](https://mlsanity.com/paper/1303.7291/) (2013)
- [The Impact of Regularization on High-dimensional Logistic Regression](https://mlsanity.com/paper/1906.03761/) (2019)
- [Phase Transitions in Transfer Learning for High-Dimensional Perceptrons](https://mlsanity.com/paper/2101.01918/) (2021)
- [Universality laws for randomized dimension reduction, with applications](https://mlsanity.com/paper/1511.09433/) (2015)
- [On the Inherent Regularization Effects of Noise Injection During Training](https://mlsanity.com/paper/2102.07379/) (2021)
- [Large Dimensional Analysis and Improvement of Multi Task Learning](https://mlsanity.com/paper/2009.01591/) (2020)
- [A Novel Gaussian Min-Max Theorem and its Applications](https://mlsanity.com/paper/2402.07356/) (2024)
- [A Precise Performance Analysis of Support Vector Regression](https://mlsanity.com/paper/2105.10373/) (2021)
- [Precise Performance Analysis of the Box-Elastic Net under Matrix Uncertainties](https://mlsanity.com/paper/1901.04469/) (2019)

## Abstract (arXiv)

Multi--task learning seeks to improve the generalization error by leveraging the common information shared by multiple related tasks. One challenge in multi--task learning is identifying formulations capable of uncovering the common information shared between different but related tasks. This paper provides a precise asymptotic analysis of a popular multi--task formulation associated with misspecified perceptron learning models. The main contribution of this paper is to precisely determine the reasons behind the benefits gained from combining multiple related tasks. Specifically, we show that combining multiple tasks is asymptotically equivalent to a traditional formulation with additional regularization terms that help improve the generalization performance. Another contribution is to empirically study the impact of combining tasks on the generalization error. In particular, we empirically show that the combination of multiple tasks postpones the double descent phenomenon and can mitigate it asymptotically.