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A theory paper introducing Decoupled Descent (DD), a training method that uses approximate message passing Onsager corrections to enforce asymptotic equality between training and test error during gradient descent, potentially enabling better stopping and hyperparameter tuning.
This paper develops a precise theoretical characterization of the empirical risk landscape for multi-index models in high dimensions, proposing an incremental approximate message passing (IAMP) algorithm that achieves near-optimal performance among polynomial-time methods, using concepts from statistical physics such as replica symmetry breaking.