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How I learned to stop worrying and love StopGrads: Stationarity, Convergence, and a case study on Flow Map Learning

arXiv · AI, language, vision and robotics · article · Sep 14, 2026 · UTC

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 the

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