arXiv Machine Learning September 16, 2026 By Alex Borisevich

Certified Inference and Training for Deep Equilibrium Networks: A Continuation Framework with Polynomial Complexity Guarantees

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The paper introduces a certified continuation framework for computing and training deep equilibrium networks (DEQs). It uses compact input homotopy and a rounded Newton tracker for inference, and augments local-plus-low-rank recurrence with programmable dormant bilinear rank‑one channels for training. The approach guarantees polynomial‑time bit complexity, with certified bounds on inference and training error budgets.

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