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This research provides theoretical grounding for stopgrad techniques, establishing closed-form characterizations of stationary points and proving convergence guarantees for flow map objectives used in diffusion samplers and reinforcement learning. By unifying these disparate objectives under a single regression principle, the study offers a rigorous framework that reduces training memory requirements while ensuring the learned models accurately represent true underlying distributions.
How I learned to stop worrying and love StopGrads: Stationarity, Convergence, and a case study on Flow Map Learning
arXiv:2609.16222v1 Announce Type: new Abstract: Stopgrads are widely used in training machine learning models, but stopgrads can alter the gradient, stationary points and convergence guarantees of the original objective, which can make stopgrad training theoretically ungrounded. We introduce a stopgrad regression principle, which identifies a general template for stopgrad objectives with a closed-form characterization of stationary points and their uniqueness, unifying stopgrad objectives for flow maps, reinforcement learning, and diffusion samplers. We provide theoretical grounding for optimizing stopgrad flow map objectives by showing their unique stationary point is the true flow map, and showing positive convergence results for Eulerian and Lagrangian objectives, including MeanFlow and improved MeanFlow. Remarkably, we show that under functional semi-gradient flow, the learned flow map has a closed-form expression composing the initial flow map and the true flow map. We additionally use our stopgrad regression principle to propose modified stopgrad placements for flow map objectives which reduce training memory by 2x.
Abstract:Stopgrads are widely used in training machine learning models, but stopgrads can alter the gradient, stationary points and convergence guarantees of the original objective, which can make stopgrad training theoretically ungrounded. We introduce a stopgrad regression principle, which identifies a general template for stopgrad objectives with a closed-form characterization of stationary points and their uniqueness, unifying stopgrad objectives for flow maps, reinforcement learning, and diffusion samplers. We provide theoretical grounding for optimizing stopgrad flow map objectives by showing their unique stationary point is the true flow map, and showing positive convergence results for Eulerian and Lagrangian objectives, including MeanFlow and improved MeanFlow. Remarkably, we show that under functional semi-gradient flow, the learned flow map has a closed-form expression composing the initial flow map and the true flow map. We additionally use our stopgrad regression principle to propose modified stopgrad placements for flow map objectives which reduce training memory by 2x.
Machine Learning (cs.LG)
arXiv:2609.16222 [cs.LG]
(or arXiv:2609.16222v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.16222 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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