Central Limit Theorems for Stochastic Gradient Descent Quantile Estimators

Researchers have proposed two new algorithms, one for functional gradient descent and another for data mixture discovery, both aiming to improve efficiency and accuracy in machine learning tasks.

A new functional gradient descent algorithm adapts the representation of functional gradients over the course of optimization, establishing convergence to a stationary point and to a global minimizer regardless of approximations^[1]. This method has been shown to consistently outperform FGD with fixed approximations and neural network baselines in efficiency and accuracy. Meanwhile, researchers have also introduced FASTMIX, a novel framework that automates data mixture discovery while training a single proxy model, jointly optimizing mixture coefficients and model parameters^[2]. FASTMIX improves efficiency and scalability over prior approaches and outperforms baselines while drastically reducing search cost. Both papers were submitted to arXiv in June 2026, with the functional gradient descent paper submitted on an unspecified date and the FASTMIX paper submitted on June 12, 2026.