Gradient-Flow Optimization as Dynamic Random-Effects Inference: Testing and Early Stopping with Applications to Deep Learning

arXiv:2605.27991v3 Announce Type: replace Abstract: Gradient-flow optimization is usually viewed as an algorithmic procedure for minimizing empirical loss, with training duration selected by validation or heuristic early stopping rules. We develop a statistical inference framework for gradient-flow training. We show that whenever fitted values evolve through a time-invariant positive semidefinite training operator, the output at each time is equivalent to the best linear unbiased predictor under a corresponding random-effects model. Training time then becomes a variance-component parameter gov