$\ddot{I}{€}_0$-EqM: Equilibrium Matching for Closed-Loop Vision-Language-Action Control

Abstract

Currently, Vision-Language-Action (VLA) models have become the most adopted paradigm for robotic manipulation for its great potential for task generalization. While most generative flow-matching action decoders for VLA control are often deployed with fixed sampling horizons, limiting state-dependent compute and temporal reuse across control cycles. We present $\ddot{I}{€}_0$-EqM, which replaces the flow-matching expert in $\ddot{I}{€}_0$ with an Equilibrium Matching (EqM) decoder while leaving the upstream VLA stack unchanged. Under a matched 300-step budget, $\ddot{I}{€}_0$-EqM improves RoboTwin average success from 40.4% to 50.2% across 19 tasks and remains competitive on LIBERO, with its clearest gain on LIBERO-10 (87.0%). Two threshold scans reveal a task-dependent non-monotonic relation between residual and success, which we term the stationarity--executability gap. The results suggest that inference depth in iterative VLA control is part of policy design and introduce an energy-based VLA perspective that may inform future work on composable action generation across tasks and embodiments.

Preprint. 5 pages, 3 figures