Lost in Reconstruction: Aligning Action Representations with Language in Vision-Language-Action Models

Vision-Language-Action (VLA) models commonly adapt pretrained Vision-Language Models (VLMs) to robot control by mapping visual observations and language instructions to continuous actions. Existing approaches typically take an action-insufficiency view, assuming that pretrained VLM latents either lack directly usable action information or should be shielded from action-learning signals. Against this view, our \textit{Quotient Theory for VLA} shows that pretrained VLM latents are not action-insufficient but action-sufficient: they already contain the information needed for control, yet remain overcomplete by distinguishing prompt-level variations that induce the same optimal action behavior. To operationalize this theory, we propose QuoVLA, a quotient-space framework for VLA that compresses pretrained VLM latents into action-sufficient representations. Specifically, QuoVLA instantiates this principle with a quantization module and a dual-branch design with relative temporal-complexity regularization, preserving action-relevant information while removing prompt-level redundancy. Extensive experiments across multiple benchmarks demonstrate that QuoVLA achieves strong performance, with particularly notable improvements in generalization under visual, linguistic, and environmental distribution shifts. Our code will be made publicly available.

Discrete action tokenization provides a compact interface for autoregressive VLA policies, but accurately recovering continuous robot actions from discrete codes remains challenging. Existing tokenizers typically map each discrete code to a fixed continuous action prototype, ignoring the robot's current proprioceptive state. This limitation is particularly pronounced in manipulation, where the same action token may require different continuous controls under different joint configurations, object poses, and contact conditions. We therefore propose SA-VLA, a state-aware action tokenizer that conditions action decoding on robot state. We study two state-injection mechanisms for VQ-based action tokenization: cross-attention between state and action features, and a lightweight state adapter that predicts action-wise modulation factors for state-conditioned action modulation and reconstruction. The adapter formulation expands the effective support of a finite codebook by allowing each discrete token to represent a family of state-dependent continuous actions, while preserving the efficiency and compatibility of discrete action modeling. Integrated into an LLM-based VLA policy, SA-VLA supports both autoregressive and parallel action-token decoding with minimal changes to the model interface. On 12 RoboTwin manipulation tasks, SA-VLA improves the average success rate from 0.29 to 0.56 over the strongest tokenizer baseline. In zero-shot sim-to-real experiments on three real-world tasks, it further improves average success from 0.15 to 0.33 over the strongest tokenizer baseline. These results demonstrate that state-conditioned action decoding is a simple and effective mechanism for reducing the compression gap in discrete VLA policies.

We take a Gromov-Wasserstein perspective on Vision-Language-Action (VLA) learning, where the goal is to make the relational geometry of action representations compatible with the semantic geometry of VL embeddings. However, this alignment is non-trivial due to the mathematical heterogeneity between the domains: the semantic space of vision-language is topologically linear and isotropic, whereas the physical manifold of robotic action is non-Euclidean and anisotropic. Their disjoint metric structures render direct regression ill-posed. To resolve this incompatibility, we introduce LAST (Lie-algebraic Action Space Tokenizer), which reconstructs the action space to establish local metric compatibility with the VL modality via a two-stage transformation: (1) Global Topological Linearization: linearizing the action manifold via Lie-algebraic mapping, converting trajectories into a fixed-length, physically additive representation. (2) Local Metric Discretization: hierarchically discretizing the representation into schemas and whitened residuals, yielding approximately isotropic local charts that are statistically aligned with the semantic metric. By resolving the structural mismatch at both global and local levels, LAST enables VLA models with superior convergence and generalizability.