# Lagrange: An Open-Vocabulary, Energy-Based Sparse Framework for Generalized End-to-End Driving

arXiv: https://arxiv.org/abs/2606.20274 · HTML: https://mlsanity.com/paper/2606.20274/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning VLA and VLM driving policies, one of 9 directions in End-to-end autonomous driving.
- Builds on 6 of its 10 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Placed in

- End-to-end autonomous driving / [Reasoning VLA and VLM driving policies](https://mlsanity.com/driving/reasoning-vla-and-vlm-driving-policies/)

## Builds on (most cited first, 6 of 6)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [Planning-oriented Autonomous Driving](https://mlsanity.com/paper/2212.10156/) (2022)
- [DriveVLM: The Convergence of Autonomous Driving and Large Vision-Language Models](https://mlsanity.com/paper/2402.12289/) (2024)
- [CODA: A Real-World Road Corner Case Dataset for Object Detection in Autonomous Driving](https://mlsanity.com/paper/2203.07724/) (2022)

## Abstract (arXiv)

Scaling end-to-end autonomous driving to complex, open-world environments requires perceptual models that generalize to anomalous scenarios and planners that produce kinematically valid trajectories. Existing paradigms face a distinct dichotomy between representational efficiency and generalization capacity. Dense models (e.g., occupancy networks), while geometrically robust, incur critical computational bottlenecks and struggle with high-level semantic reasoning. Conversely, sparse, query-based planners are efficient but reliant on closed-set definitions, rendering them vulnerable to out-of-distribution (OOD) events. Although recent Vision-Language-Action (VLA) models offer open-vocabulary reasoning, their autoregressive, discrete token generation fundamentally conflicts with the continuous, high-frequency control requirements of vehicle dynamics. To address this, we propose Lagrange, an open-vocabulary, computationally sparse driving framework based on Masked Latent Fields (MLF). Rather than relying on dense volumetric reconstructions or closed-set query mechanisms, Lagrange exploits Vision-Language Models (VLMs) to encode class-agnostic object proposals into continuous semantic visual tokens. We introduce an intent-driven masked cross-attention module that temporally filters irrelevant entities, decoding the attended tokens into an implicit continuous energy field defined over spatial coordinates. By framing decision-making as a Lagrangian action minimization problem spanning this energy field, we enforce strict compliance with vehicle kinematics while executing collision avoidance. Extensive offline evaluations on both standard (nuScenes) and long-tail (CODA) benchmarks demonstrate that Lagrange establishes a promising framework for robust, interpretable, and kinematically feasible open-world autonomy.