Understanding Expert Structures on Minimax Parameter Estimation in Contaminated Mixture of Experts
This work addresses convergence challenges in prompt learning for fine-tuning pre-trained models, offering theoretical insights but is incremental in nature.
The paper tackles the prompt vanishing issue and parameter interaction slowdown in prompt learning by introducing a distinguishability condition and analyzing expert structures, providing convergence rates and minimax lower bounds for parameter estimation.
We conduct the convergence analysis of parameter estimation in the contaminated mixture of experts. This model is motivated from the prompt learning problem where ones utilize prompts, which can be formulated as experts, to fine-tune a large-scale pre-trained model for learning downstream tasks. There are two fundamental challenges emerging from the analysis: (i) the proportion in the mixture of the pre-trained model and the prompt may converge to zero during the training, leading to the prompt vanishing issue; (ii) the algebraic interaction among parameters of the pre-trained model and the prompt can occur via some partial differential equations and decelerate the prompt learning. In response, we introduce a distinguishability condition to control the previous parameter interaction. Additionally, we also investigate various types of expert structure to understand their effects on the convergence behavior of parameter estimation. In each scenario, we provide comprehensive convergence rates of parameter estimation along with the corresponding minimax lower bounds. Finally, we run several numerical experiments to empirically justify our theoretical findings.