SAVLA: Symmetry-Aware Vision-Language-Action Models for Robotic Manipulation

Vision-Language-Action (VLA) models have emerged as a powerful paradigm for generalist robot manipulation, yet they lack geometric inductive biases: policies trained at specific orientations require substantially more data to generalize across rotational configurations. We present \textsc{EquiVLA}, the first general framework for end-to-end $\mathrm{SO}(2)$-equivariant VLA models, applicable to any architecture coupling a frozen vision-language backbone with a flow-matching Diffusion Transformer action head. \textsc{EquiVLA} introduces \textsc{EquiPerceptor}, which produces approximately $\mathrm{SO}(2)$-equivariant visual representations from frozen ViT features; and \textsc{EquiActor}, an exactly $\mathrm{SO}(2)$-equivariant flow-matching Diffusion Transformer action head. Together, they establish an approximate $\mathrm{SO}(2)$ equivariance chain from camera observations to predicted action sequences. Instantiated on GR00T~N1.5 and evaluated across four LIBERO suites, CALVIN ABCD$\to$D, and five real-robot tasks on Mobile ALOHA, \textsc{EquiVLA} achieves $92.6\%$ average success on LIBERO (vs. $78.1\%$ baseline), an average sequence length of $4.03$ on CALVIN (vs. $3.45$), and improves real-robot success from $54\%$ to $72\%$.

Vision-Language-Action (VLA) models achieve strong benchmark performance but still struggle in real-world deployment with unseen objects, background shifts, and different robot embodiments. We argue that this stems from the lack of a unified geometry-aware manipulation representation, leaving existing VLAs vulnerable to low-level trajectory supervision, misaligned 3D features, and embodiment differences. To address this, we propose GEAR-VLA, a VLA framework for learning unified geometry-aware action representations for generalizable robotic manipulation. GEAR-VLA adopts coarse-to-fine action learning, where multi-source embodied pretraining equips the VLM with embodied reasoning and discrete action understanding before latent action tokens connect action semantics to a gradient-decoupled DiT continuous action expert. It further performs semantic-aligned 3D integration by aligning a trainable 3D spatial backbone with the VLA representation while freezing the original VLM-aligned visual pathway. To share this representation across robots, GEAR-VLA uses embodiment canonicalization, where embodiment-aware states and embodiment-invariant actions confine robot differences to the low-level interface. Extensive simulation and real-world experiments demonstrate strong generalization: GEAR-VLA achieves state-of-the-art performance on LIBERO, zero-shot LIBERO-Plus, and RoboTwin 2.0, reaches 85.9% success on AgileX and 81.0% on the pretraining-unseen LDT-01 embodiment, and obtains 90.1% success on a 6,360-trial universal grasping benchmark with 212 unseen objects. Code and models will be released at https://github.com/babynabeauty/GEAR-VLA.

Vision-language-action (VLA) models have made rapid progress in generalist robot manipulation by harnessing semantic knowledge from pretrained vision-language backbones, but their visual tokens remain grounded in 2D image coordinates rather than the calibrated geometry of the robot's cameras -- a mismatch especially pronounced in multi-camera setups, where views are coupled by known intrinsics and extrinsics yet processed as independent images. We propose G$^3$VLA, a camera-aware geometric module that injects calibrated structure into the visual-token stream of a pretrained VLA without altering its action space or imitation objective, combining intrinsic-conditioned ray embeddings, projective positional encoding (PRoPE), and bidirectional cross-view fusion. Geometric supervision is provided either from ground-truth point maps when available, or from confidence-gated $π^3$X teacher predictions, requiring no depth sensors or manual annotations. Instantiated on $π_0$, G$^3$VLA yields consistent gains across the LIBERO suites, RoboCasa24, RoboTwin2.0, and real-robot settings, with the largest improvements on spatially and object-sensitive tasks. We further validate on $π_{0.5}$ and GR00T 1.5, with results suggesting that geometric transfer is most effective when geometry-aware tokens have direct access to the action generation pathway. Our project page is at https://sites.google.com/view/g3vla