EquiVLA: A General Framework for Rotationally Equivariant Vision-Language-Action Models

Abstract: 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 $72\%$.

• The paper introduces EquiVLA, an SO(2)-equivariant framework that enforces geometric structure across visual, language, and action modalities.
• It achieves significant gains with up to 27.3× reduction in equivariance error and enhanced performance on simulation (LIBERO, CALVIN) and real-robot tasks.
• The modular design combines EQUIPERCEPTOR and EQUIACTOR, preserving pretrained VLM weights while ensuring robust rotational generalization in action generation.

EquiVLA: A General Framework for Rotationally Equivariant Vision-Language-Action Models

Motivation and Problem Statement

Vision-Language-Action (VLA) models have advanced robot manipulation by leveraging multimodal representation learning and action generation conditioned on visual input and natural-language instructions. Nonetheless, standard VLA architectures lack explicit geometric inductive biases, resulting in data inefficiency when generalizing to novel object or workspace orientations. This deficiency arises from the failure to encode the inherent SO(2) symmetry in planar manipulation; task knowledge learned at one orientation should transfer seamlessly across all others, yet conventional VLAs treat each orientation as an independent input, requiring redundant learning. Data augmentation partially addresses this, but offers no architectural guarantee of equivariance and cannot fully resolve sample inefficiency.

Summary of Contributions

EquiVLA introduces an end-to-end SO(2)-equivariant VLA framework, applicable to any architecture coupling a frozen vision-language backbone (VLM) with a flow-matching diffusion transformer (DiT) action head. The key modules—EQUIPERCEPTOR and EQUIACTOR—forge an equivariance pipeline from visual perception through to action generation, systematically injecting geometric structure into the VLA data flow. Importantly, EquiVLA achieves this without retraining or modifying the pretrained VLM weights, making it compatible with existing large-scale multimodal foundation models.

• EQUIPERCEPTOR: Extends Frame Averaging (FA) to spatially indexed ViT patch token sequences, leveraging token-level group orbit averaging coupled with spatial realignment and regular representation transforms. This yields approximately SO(2)-equivariant visual features while preserving spatial information essential for manipulation tasks. Invariant and equivariant streams are projected separately and fused via a learned invariant gating mechanism, ensuring preservation of equivariance into downstream components.
• EQUIACTOR: Implements the first SO(2)-equivariant diffusion transformer action head for robot policy learning. All projections, attention mechanisms, encoders, and decoders are replaced by steerable layers operating in regular feature space, enforcing exact equivariance in action generation. Temporal position embeddings are handled via invariant representations and projected equivariantly, maintaining temporal consistency under scene rotation.
• EquiVLA Modular Design: By combining EQUIPERCEPTOR and EQUIACTOR, EquiVLA establishes an approximate SO(2)-equivariance chain from raw camera observations to predicted action streams, achieving systematic rotational generalization without compromising large-scale visual-linguistic priors.

Theoretical Foundation and Architecture

The framework builds on group representation theory, exploiting the cyclic subgroup $C_u \subset SO(2)$ for discrete planar rotations. Token-level Frame Averaging is extended to preserve spatial alignments; permutations are computed via patched centers and regular representation of $C_u$. Approximation error stemming from spatial discretization—especially for rotations not aligned with grid axes—is theoretically characterized and shown to be bounded. The equivariant adapter fuses invariant and equivariant feature streams via invariant gating, proved to preserve group equivariance under linear transformation. EQUIACTOR’s action representation leverages SO(2)-equivariant decomposition for end-effector pose, with separate channels for gripper state.

EquiVLA’s flow-matching objective is shown to be strictly SO(2)-invariant, and ODE integration preserves equivariance at inference. A formal analysis quantifies the functional defect due to finite grid spatial sampling, offering closed-form bounds on equivariance violation and connecting these to sample complexity reduction.

Empirical Results and Analysis

Simulation Benchmarks

• LIBERO: EquiVLA achieves 92.6% success rate on LIBERO under relative end-effector control, outperforming the GR00T N1.5 baseline (78.1%) and prior non-equivariant VLAs. Absolute control results show similar improvements (+13.5 percentage points relative to baseline). Ablation studies reveal EQUIACTOR alone captures the bulk of the advantage, with EQUIPERCEPTOR contributing further gains.
• CALVIN: On the ABCD→D zero-shot generalization task, EquiVLA achieves an average task chain length of 4.03, considerably surpassing the non-equivariant baseline and approaching state-of-the-art multi-frame methods, despite using only single-frame input. Notably, long-horizon tasks benefit disproportionately, confirming equivariance mitigates error accumulation.

Real Robot Experiments

Evaluated on Mobile ALOHA across five tabletop manipulation tasks, EquiVLA achieves 72% average success, outperforming GR00T N1.5 (54%). For tasks requiring orientation-invariant grasping (e.g., Letter Aligning, House Building), success rates improve by 30-35 percentage points. Tasks lacking rotational symmetry (Shorts Folding) show comparable performance, indicating no performance penalty in the absence of symmetry.

Equivariance Error and Sample Complexity

Quantitative measurement of equivariance error ($E_{eq}$) confirms the theoretical analysis: the non-equivariant baseline exhibits substantial violation, while EQUIACTOR reduces error by $9.3\times$, and full EquiVLA achieves $27.3\times$ reduction. The sample efficiency analysis demonstrates that equivariant structure achieves up to $8\times$ reduction in empirical Rademacher complexity for the group $C_8$, directly translating to lower demonstration requirements for achieving a given generalization error.

Controlled Orientation-Shift Evaluation

EquiVLA exhibits stable performance across unseen object rotation angles (within practical limits), maintaining high success rates for moderate rotations, while the baseline rapidly deteriorates outside the canonical orientation.

Practical and Theoretical Implications

EquiVLA provides a general-purpose modular approach for imposing geometric structure on large-scale VLA models without retraining visual-linguistic backbones. This demonstrates that geometric inductive biases can be composed onto existing pretrained architectures, extending their generalization capabilities and reducing demonstration requirements—a critical advantage for scalable robot policy learning.

The architectural principles extend beyond planar equivariance, suggesting immediate applicability to 3D rotational (SO(3)) or rigid-body (SE(3)) symmetries for more complex manipulation domains. The theoretical bounds on equivariance defect and sample complexity quantify the fundamental efficiency benefits obtainable via symmetry-informed architecture design.

Limitations and Future Directions

EquiVLA targets SO(2) symmetry, limiting its scope to planar manipulation with top-down visual input. Tasks involving spatially complex or out-of-plane rotations will require extension to higher groups (SO(3), SE(3)), demanding additional architectural innovations and careful management of increased representational complexity. Current inference latency is increased due to multiple forward passes in token-level Frame Averaging; stochastic approximation strategies or adaptation of equivariant backbone architectures may mitigate this. EQUIACTOR is trained from scratch due to incompatibility with pretrained DiT weights; knowledge distillation or equivariant fine-tuning remains an open research direction.

Conclusion

EquiVLA demonstrates that combining geometric equivariance and large-scale VLA pretraining yields complementary benefits in robot manipulation: systematic rotational generalization, higher sample efficiency, and improved performance on both simulation and real-robot tasks. The modular approach enables scalable adoption of symmetry-informed architecture principles in vision-language-action pipelines, furthering the design of data-efficient and capable robotic systems. Extensions to more general symmetries and efficient inference schemes constitute compelling avenues for future research in AI-driven robotics (2606.19784).