Self-Consistent Neural Control: Learning Trajectories for Implicit Equilibrium
Self-Consistent Neural Control: Learning Trajectories for Implicit Equilibrium
This paper introduces Self-Consistent Neural Control (SCNC), a framework designed to optimize trajectories in physical systems defined by implicit equilibrium. The authors address limitations of adjoint learning, which relies on frozen-tangent approximations that neglect higher-order sensitivity terms. SCNC derives a mathematical bound on gradient error and uses a practical finite-difference approximation to control sensitivity variations. Validated on deformable objects ranging from elastic rods to thin-walled tubes and Slinky-like structures, SCNC demonstrates faster convergence, reduced switching to undesirable equilibrium branches, and a doubling of the stable optimization rate compared to adjoint learning (83.3% vs. 41.7%), with average loss reductions exceeding 1.5 orders of magnitude on complex systems like thin-walled tubes.
The authors propose Self-Consistent Neural Control (SCNC), a method that explicitly controls sensitivity variations during trajectory optimization for systems with implicit equilibrium, achieving faster convergence and higher stability on deformable objects compared to adjoint learning and iCEM baselines.
Source: arXiv Robotics — research abstracts · Read original article ↗
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loss reduction factor
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reducing switching to undesirable equilibrium branches, doubling the stable optimization rate over adjoint learning 83.3% vs. 41.7% and reducing the average loss by more than 1.5 orders of magnitude on thin-walled tubes, where sensitivity variations are pronounced.
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reducing switching to undesirable equilibrium branches, doubling the stable optimization rate over adjoint learning 83.3% vs. 41.7% and reducing the average loss by more than 1.5 orders of magnitude on thin-walled tubes, where sensitivity variations are pronounced.
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e approximation. We validate the framework on deformable objects, which are representative of implicit equilibrium systems, ranging from simple quadratic energy models such as elastic rods to complex systems including thin-walled tubes, measuring tapes, and Slinky-like structures. Compared with the adjoint learning and the gradient-free iCEM baselines, SCNC achieves faster convergence and more stable optimization by
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arXiv:2611.03885v1 Announce Type: new Abstract: One big challenge in physical AI is interacting with systems whose states are defined by implicit equilibrium. Learning in these systems is difficult because their responses can be multistable, path-dependent, and sensitive over long horizons. Adjoint learning provides an efficient way to optimize trajectories without unrolling iterative equilibrium solvers, but its gra
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Self-Consistent Neural Control: Learning Trajectories for Implicit Equilibrium
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dient relies on the frozen-tangent approximation, which neglects higher-order sensitivity terms and can become inaccurate when the local equilibrium varies rapidly. In this work, we introduce Self-Consistent Neural Control (SCNC), optimizing trajectories along which sensitivity variations are explicitly controlled. We derive a mathematical bound on the resulting gradient error and develop a practical finite-differenc
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Source：arXiv Robotics — research abstracts · arxiv.org