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

Junle Li, Weixian Waylon Li, Fuxiang Wu, Fusheng Hao, Fengxiang He

arXiv:2609.16641v1cs.RO

TL;DR

VLAs lack a prescribed rotational-symmetry structure in the frozen vision-language backbone, so an equivariant action head alone cannot guarantee end-to-end equivariance. SAVLA pairs that backbone with typed equivariant flow matching and image canonicalization, improving LIBERO success over GR00T N1.5 and raising LIBERO-Goal performance under rotation.

  • Problem

    A frozen vision-language backbone has no prescribed rotational transformation law, so an equivariant action head alone cannot guarantee end-to-end equivariance.

    Source: A. Equivariant Action Head · p. 4

  • Method

    SAVLA combines a frozen vision-language backbone with a typed equivariant flow-matching action head and a learned canonicalizer that warps oblique images and rotates geometric conditions.

    Source: §I · p. 1, A. Equivariant Action Head · pp. 3–4, C. Canonicalization · p. 5

  • Results

    5.1 points: SAVLA raises average success across four LIBERO suites from 86.5% to 91.6% versus GR00T N1.5, while LIBERO-Goal mean under rotation rises from 41.5% to 90.4%.

    Source: A. LIBERO Experimental Results · p. 5, §VI · p. 8

  • Takeaways & Limitations

    On LIBERO, SAVLA's average advantage over GR00T N1.5 widens as the demonstration budget shrinks, and its rotation evaluation concerns gravity-axis scene rotations.

    Source: §VI · p. 8

    The canonicalizer estimates only gravity-axis rotation, and approximate canonicalization causes parallax and field-of-view errors that grow at large angles.

    Source: §VI · p. 8

Abstract

from arXiv · show

Vision-language-action (VLA) models have become the dominant paradigm for language-conditioned robot manipulation. However, although images and language instructions inherently encode geometric information, VLAs acquire their spatial competence purely from demonstrations. As a result, they are reliable only within the range of scene poses that the demonstrations cover. We propose SAVLA, an end-to-end symmetry-aware VLA model for robust and data-efficient policy learning. Our approach keeps the pretrained vision-language backbone entirely frozen while combining it with an equivariant flow-matching action head and a learned canonicalizer. The head decomposes its state, action, and conditioning inputs into invariant and equivariant channels, and preserves this typing throughout all of its layers. The canonicalizer transforms oblique-view images into a canonical frame and rotates the geometric conditions consistently. We evaluate our model on LIBERO. Compared with the GR00T N1.5 baseline, SAVLA improves the success rate averaged over all four LIBERO suites by 5.1 points and increases the mean success rate under rotation on LIBERO-Goal from 41.5% to 90.4%.

I. INTRODUCTION

SAVLA addresses rotational sensitivity in vision-language-action models by adding symmetry-aware action generation and canonicalization around a frozen backbone. The paper reports improved LIBERO success against GR00T N1.5, including under rotation.

I. INTRODUCTION

  • Standard VLAs lack an explicit rotational-symmetry prior and remain sensitive to changes in object layout, camera viewpoint, and robot initial state.Prior approaches add spatial encodings or use point clouds, but the former does not explicitly constrain rotational equivariance and the latter limits direct integration with RGB-based VLAs.Source: §I · p. 1
  • SAVLA combines a frozen, non-equivariant vision-language backbone with an equivariant flow-matching action head and canonicalizes oblique-view images while rotating geometric conditions consistently.Its interface treats backbone features as invariant and combines them with equivariant geometric conditions.Source: §I · p. 1
  • 5.1 points: SAVLA improves average success rate across four LIBERO suites over GR00T N1.5; LIBERO-Goal mean success under rotation rises from 41.5% to 90.4%.The introduction reports these results for the complete SAVLA model.Source: §I · p. 1

B. Diffusion and Flow-Matching Policies

C. Canonicalization

Canonicalization normalizes an oblique view for the frozen backbone, while rotating geometric conditions for the action head. The policy generates future action chunks through flow matching, with end-to-end equivariance scoped to gravity-axis rotations.

C. Canonicalization

  • Canonicalization maps the input into a predicted canonical pose before the backbone and maps the output back; SAVLA uses the estimated scene rotation to rotate geometric conditions as well.Canonicalization errors propagate to predictions, while full architectural equivariance is impractical for a multi-billion-parameter pretrained backbone.Source: C. Canonicalization · p. 2

III. PRELIMINARIES

  • The policy observes third-person and wrist images, proprioceptive state, and language, then predicts a chunk of future actions with horizon T_p.Flow matching interpolates between a noise sample and the ground-truth action chunk, learns the connecting velocity, and integrates that field from noise to produce the predicted chunk.Source: §III · p. 2
  • Equivariance means that transforming inputs by a group action transforms outputs correspondingly, while invariance leaves outputs unchanged; this model's end-to-end guarantee concerns gravity-axis rotations.The action head is exactly SO(3)-equivariant, but the canonicalizer operates on the SO(2) subgroup of gravity-axis rotations.Source: §III · p. 2

IV. METHOD

SAVLA keeps the pretrained vision-language backbone frozen and builds rotational structure into the action head through typed invariant and equivariant channels. A learned canonicalizer supplies a canonical image and consistently rotated geometric conditions.

IV. METHOD

  • SAVLA treats frozen-backbone tokens as invariant conditions and fixed geometric reference points as equivariant conditions, then uses symmetry-preserving operations throughout the flow-matching velocity network.A learned canonicalizer maps the oblique third-person image into a canonical view and rotates the geometric conditions consistently.Source: §IV · p. 2, Figure 1 · p. 3

A. Equivariant Action Head

  • Each velocity-network token separates invariant scalar features from vectors that co-rotate with the input, preserving these transformation types through the network layers.The state and action embeddings form the velocity-network input tokens, which pass through repeated normalization and modulation, attention, and feed-forward blocks.Source: A. Equivariant Action Head · p. 3
  • The typed state encodes centered end-effector position, orientation columns, gravity direction, and gripper positions; actions include world-frame position increments and incremental rotation.The state representation has signature 4ρ1⊕2ρ0.Source: A. Equivariant Action Head · p. 3
  • Equivariant attention uses invariant weights to aggregate scalar and vector values, preserving invariant scalar outputs and equivariant vector outputs.The attention weights remain unchanged under rotation because the query-key inner products are preserved.Source: A. Equivariant Action Head · p. 4
  • The vector-track FFN applies GELU only to the component parallel to an equivariant direction and leaves the perpendicular component unchanged.This activation choice preserves equivariance, unlike applying GELU directly to vector features.Source: A. Equivariant Action Head · p. 4
  • An equivariant action head alone cannot guarantee end-to-end equivariance because the frozen vision-language backbone has no prescribed rotational transformation law.The typed conditioning interface and learned canonicalizer extend the head-level guarantee to approximate end-to-end rotational equivariance.Source: A. Equivariant Action Head · p. 4

B. Symmetry-aware Conditions

Because frozen VLM tokens do not obey a known rotation transformation law, SAVLA supplies the action head with separate invariant and equivariant conditioning tracks. Canonicalized images support approximately invariant features, while rotated reference points provide geometric conditions.

B. Symmetry-aware Conditions

  • The typed interface gives the action head invariant and equivariant conditions because frozen VLM output tokens lack an imposed transformation law.Its construction assumes a canonical third-person image and a scene-rotation estimate.Source: B. Symmetry-aware Conditions · p. 4
  • Canonicalized third-person images, wrist images, and language instructions yield VLM features treated as approximately invariant to scene rotations.Source: B. Symmetry-aware Conditions · p. 4
  • Rotating fixed reference points by the estimated scene angle pairs third-person visual tokens with equivariant locations; wrist and language tokens receive zero vectors.Source: B. Symmetry-aware Conditions · p. 4

C. Canonicalization

SAVLA canonicalizes oblique-view images with a homography so the frozen backbone receives a canonical view, while geometric reference points co-rotate. A learned rotation estimate drives both transformations.

C. Canonicalization

  • The same estimated rotation warps the third-person image toward a canonical view and transforms geometric reference points to co-rotate with the scene.Source: C. Canonicalization · p. 4
  • Oblique-view scene rotation is not an in-plane image rotation, so rotating an image about its center can misalign the scene.SAVLA instead warps the image using a homography induced by the dominant tabletop plane.Source: C. Canonicalization · p. 5
  • The homography uses camera intrinsics, relative camera motion, and tabletop-plane parameters computed from simulator camera specifications and table geometry.Under the stated inverse-sampling convention, warping the rotated observation maps its content back to the canonical view.Source: C. Canonicalization · p. 5
  • A three-layer CNN with global average pooling scores eight candidate scene rotations to estimate the canonicalizing angle.Source: C. Canonicalization · p. 5
  • The rotation scorer is trained self-supervised on demonstrations by creating synthetic rotated frames from original demonstration frames.The predicted angle for the synthetic frame is compared with the prediction for its original frame.Source: C. Canonicalization · p. 5
  • At inference, a gain calibrated using 12 simulator frames at known angles scales the rotation estimate used for both image warping and reference-point rotation.The calibration frames are disjoint from the evaluation set.Source: C. Canonicalization · p. 5
  • Canonicalization makes third-person images approximately rotation-invariant, while rotated reference points provide equivariant conditions for the action head.Together these components yield approximate end-to-end rotational equivariance.Source: C. Canonicalization · p. 5

V. EXPERIMENTS

The experiments evaluate standard LIBERO performance, rotation robustness, and data efficiency, with real-world tasks also included in the evaluation plan. The primary comparison uses a budget-matched GR00T N1.5 baseline.

V. EXPERIMENTS

  • The evaluation plan covers standard manipulation performance, unseen scene rotations, reduced demonstration budgets, and three real-world tasks.All four LIBERO suites are the primary benchmark.Source: §V · p. 5
  • SAVLA and GR00T N1.5 use the same frozen backbone, demonstrations, and checkpoint-selection procedure, with both action heads trained from scratch.The baseline head is adjusted to match parameter count: 100.8M trainable parameters for GR00T N1.5 versus 103.3M for SAVLA.Source: §V · p. 5
  • For each suite, checkpoints at 20K, 40K, and 80K steps are screened with the same 200-episode preliminary evaluation; the canonicalizer is trained separately for 3,000 steps.Source: §V · p. 5

A. LIBERO Experimental Results

On all four LIBERO suites, SAVLA outperforms the GR00T N1.5 baseline, raising average success from 86.5% to 91.6%.

A. LIBERO Experimental Results

  • 5.1 points: SAVLA raises average success across all four LIBERO suites from 86.5% to 91.6% over GR00T N1.5.Each model is evaluated on 500 episodes per suite, with results averaged over three random seeds.Source: A. LIBERO Experimental Results · p. 5, Table I · p. 5

ARE TAKEN FROM THE ORIGINAL PAPERS OR SUBSEQUENT PUBLISHED

SAVLA improves average success over GR00T N1.5 on the four LIBERO suites; the supplied material also identifies longer task horizons as a challenge and names a rotation-augmentation results table.

B. Rotation Generalization

SAVLA improves rotation robustness on LIBERO, with gains varying across suites and augmentation variants. The rotation-augmentation comparison reports higher success rates for SAVLA without additional rotated demonstration trajectories.

B. Rotation Generalization

  • On LIBERO-Goal rotations, SAVLA reaches 90.4% versus 41.5% for GR00T N1.5; gains are smaller on Long.The scene is rotated about the gravity axis in 5° steps from −30° to +30°; both methods train only on the original dataset.Source: B. Rotation Generalization · p. 6
  • The warped augmentation variant samples rotations from −30° to +30°, while the re-rendered variant uses camera views at the 13 evaluation angles.Both variants transform images, proprioceptive state, and actions, and use the same training recipe and budget as the unaugmented baseline.Source: B. Rotation Generalization · p. 6
  • Table III reports real-robot success rates by task over 20 episodes per task.Source: Table III · p. 6
  • SAVLA reaches 90.4% and 64.5%, exceeding re-rendered augmentation’s 74.5% over −30° to 30° and 59.2% at extrapolation angles without extra rotated trajectories.Source: B. Rotation Generalization · p. 6

C. Ablation Study

The LIBERO-Goal ablation compares SAVLA’s components, while data-efficiency results show a widening advantage as demonstrations decrease. Rotation robustness also varies across the four LIBERO suites.

C. Ablation Study

  • On LIBERO-Goal rotations, full SAVLA reaches 90.4%, versus 63.5% for canonicalized GR00T N1.5 and 46.0% for SAVLA without canonicalization.The ablation evaluates variants over 200 episodes with three random seeds.Source: C. Ablation Study · p. 6, Figure 3 · p. 7
  • Replacing the estimated rotation with the ground-truth angle raises the mean from 90.4 to 90.9; using the true canonical view raises it to 97.3 and yields 96.8 when |θ| ≥25°.The authors suggest the remaining headroom lies primarily in front-end image geometry rather than scene-rotation estimation.Source: C. Ablation Study · p. 6

D. Data Efficiency

  • For the reduced-data comparison, models and canonicalizer are retrained on identical per-task subsets at 10% and 25% of demonstrations; the full-data result comes from Table I.Evaluation uses 200 episodes with three random seeds.Source: D. Data Efficiency · p. 6
  • Across the 13-angle rotation sweep, SAVLA’s mean success rates are 81.8% on Spatial, 53.9% on Object, 90.4% on Goal, and 25.4% on Long.The comparison is against GR00T N1.5 on the same scene-rotation sweep.Source: Figure 2 · p. 7
  • The four-suite average-success gap grows from 5.1 points with full data to 5.8 points at 25% data and 8.8 points at 10% data.Table V is titled as reporting average success across the four suites.Source: D. Data Efficiency · p. 7, Table V · p. 7

E. Real Robot Experiment

The real-robot study compares SAVLA with GR00T N1.5 on three manipulation tasks and under rotation; the conclusion also reports LIBERO results and identifies limits in rotation coverage and canonicalization.

E. Real Robot Experiment

  • The real-robot evaluation uses the SO-101 across three tasks, with 50 demonstrations per task and 20 evaluation episodes per task.Both models are trained multitask for 40K steps on 150 demonstrations total.Source: E. Real Robot Experiment · p. 7
  • SAVLA outperforms GR00T N1.5 on all three real-world tasks, increasing mean success rate from 61.7% to 71.7%, consistent with simulation findings and indicating improved real-world manipulation performance.Source: E. Real Robot Experiment · p. 7
  • 47.9% to 57.1% mean success rate across seven angles: SAVLA shows stronger real-world rotation robustness on pick-and-place.The tested rotations were ±10°, ±20°, and ±30°; Table VI reports success rates under rotation.Source: E. Real Robot Experiment · p. 7, Table VI · p. 8

VI. CONCLUSION

  • SAVLA combines a frozen pretrained vision-language backbone with an equivariant action head, typed invariant and equivariant conditions, and a canonicalization head.The canonicalization head brings the oblique view into a canonical frame.Source: §VI · p. 8
  • 5.1 points: SAVLA outperforms GR00T N1.5 on average across the four LIBERO suites; under scene rotations on LIBERO-Goal, mean success rises from 41.5% to 90.4%.The gap widens as the demonstration budget shrinks.Source: §VI · p. 8
  • The canonicalization head estimates only gravity-axis rotation, and the rotation experiments cover only such rotations; approximate canonicalization causes larger-angle performance drops as parallax and field-of-view errors grow.The action head itself is equivariant to the full SO(3) rotation group.Source: §VI · p. 8

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