Logic-VLA: A Temporal Logic Conditioned Vision-Language-Action Model
Organizations: Thomas Lord Department of Computer Science, University of Southern California
Abstract
Vision-language-action (VLA) models can follow natural-language (NL) task instructions, but such instructions may not precisely specify safety-critical or spatiotemporal requirements on the resulting behavior. We introduce Logic-VLA, a formal-requirement-aware VLA that conditions on Signal Temporal Logic (STL) specifications supplied at inference time. Logic-VLA uses a syntax-graph-based STL encoder pre-trained to capture temporal logic semantics. Policy adaptation proceeds in two stages: STL-conditioned supervised fine-tuning on satisfying demonstrations is followed by trajectory-level preference optimization over matched satisfying-violating rollout pairs using a flow-matching surrogate for Identity Preference Optimization. This formulation improves formal requirement satisfaction while preserving the nominal NL task. We evaluate Logic-VLA in closed-loop quadcopter navigation simulation across randomized photorealistic environments and test generalization to STL formulas unseen during training. Across the evaluation benchmarks, Logic-VLA improves STL satisfaction rate over an STL-blind base policy by 24.8 to 40.7 percentage points (pp) while reducing nominal NL task success by at most 1.8 pp, showing that a single VLA can adapt its behavior to varying formal requirements without requiring a separate policy for each specification.
Figures & tables
| Seen | Unseen Parameter | Unseen Structure | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Method | STL Sat. | Mean | NL Task | STL Sat. | Mean | NL Task | STL Sat. | Mean | NL Task | |||
| Base | 41.3 | -9.11 | 90.5 | 50.0 | -5.80 | 93.9 | 56.8 | -6.98 | 89.3 | |||
| STL-SFT | 61.7 | -5.09 | 87.2 | 59.5 | -5.05 | 91.2 | 64.5 | -4.64 | 85.2 | |||
| Smooth Robust Semantics ( ) | 76.2 | -5.72 | 68.5 | 71.1 | -4.94 | 75.9 | 77.5 | -4.92 | 68.6 | |||
| Smooth Robust Semantics ( ) | 78.8 | -5.79 | 45.0 | 72.1 | -7.31 | 47.4 | 81.8 | -3.82 | 42.0 | |||
| Logic-VLA | 82.0 | -1.62 | 89.0 | 74.8 | -3.79 | 92.2 | 82.0 | -2.46 | 87.5 | |||
Vision-Language-Action Models
Vision-language-action models turn visual observations and natural-language instructions into actions for robots and other embodied agents.
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