aiqbench analysis
This paper provides a rigorous mathematical framework for auxiliary learning, deriving closed-form expressions that quantify how task correlations and label noise influence generalization error in neural networks. By modeling the dynamics of stochastic gradient descent through differential equations, the study reveals the specific mechanisms by which auxiliary tasks balance optimization forces with gradient noise to improve performance. These theoretical insights offer a deeper understanding of multi-task optimization beyond empirical observation, directly advancing machine learning theory.
An Analytical Theory of Auxiliary Learning
arXiv:2609.29774v1 Announce Type: new Abstract: Auxiliary learning is an optimization paradigm in which a neural network's performance on a target task is improved by jointly training it on additional tasks. However, the mechanisms behind this improvement remain poorly understood. We study this problem using a teacher-student framework and derive a closed system of differential equations describing the dynamics of online stochastic gradient descent in the large-input limit. For linear networks, we obtain a closed-form expression for the generalization error to leading order in the learning rate, quantifying how task correlations and label noise determine the benefit of auxiliary learning. For non-linear activation functions, we develop a fluctuation-dissipation analytical theory that establishes a general relation linking the main and auxiliary errors to the corresponding single-task error. Numerical experiments support the theoretical predictions and show how auxiliary tasks improve generalization by balancing the forcing dynamics towards the optimal solution with gradient noise.
Abstract:Auxiliary learning is an optimization paradigm in which a neural network's performance on a target task is improved by jointly training it on additional tasks. However, the mechanisms behind this improvement remain poorly understood. We study this problem using a teacher-student framework and derive a closed system of differential equations describing the dynamics of online stochastic gradient descent in the large-input limit. For linear networks, we obtain a closed-form expression for the generalization error to leading order in the learning rate, quantifying how task correlations and label noise determine the benefit of auxiliary learning. For non-linear activation functions, we develop a fluctuation-dissipation analytical theory that establishes a general relation linking the main and auxiliary errors to the corresponding single-task error. Numerical experiments support the theoretical predictions and show how auxiliary tasks improve generalization by balancing the forcing dynamics towards the optimal solution with gradient noise.
Machine Learning (cs.LG)
arXiv:2609.29774 [cs.LG]
(or arXiv:2609.29774v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.29774 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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