Outcome-Conditioned End-Effector Geometry Across Vision-Language-Action Policies

Xingyu Lin; Zhuang Li; Zhongrun Wu; Shouquan Zhou; Dehui Du

cs.ROSep 18, 2026

Outcome-Conditioned End-Effector Geometry Across Vision-Language-Action Policies

Authors: Xingyu Lin, Zhuang Li, Zhongrun Wu, Shouquan Zhou, Dehui Du

Organizations: School of Software Engineering, East China Normal University, Shanghai, China · School of Computer Science and Technology, East China Normal University, Shanghai, China · School of Maritime Economics and Management, Dalian Maritime University, Dalian, China

Abstract

Vision-language-action (VLA) policies solve the same manipulation task through different action interfaces, but task success alone does not establish whether their physical executions agree. We study cross-policy end-effector geometry in 15,000 closed-loop LIBERO rollouts from four policies. The primary clean-condition analysis forms 3,600 configuration-matched, and therefore dependent, policy pairs. Both-success pairs have a median normalized dynamic time warping distance of 0.0120 m versus 0.0380 m when exactly one policy succeeds. This ordering holds in every task, every policy pair, and nine sampling and band-limited representations; however, the ratio varies severalfold across representations, so we report the direction rather than a fixed multiple. Both-failure pairs are more separated again but rest on thin, uneven support, so we report them as exploratory. Within successful executions, partner replacements separate more across tasks than across initial states. A matched baseline still reveals measurable, heterogeneous residual policy differences, so a low cross-policy distance does not imply interchangeability. Successful executions sit about as far from same-task demonstrations as those demonstrations sit from each other, compatible with task-associated geometry without separating training-data overlap from task constraints. A common 72-action window preserves the ordering but reduces its magnitude; endpoint and duration adjustment likewise leaves a positive mixed-outcome coefficient relative to both-success pairs, though its magnitude is specification-dependent. Under composite visual stress, policy rankings and pair composition change together.

Figures & tables

Fig. 1: Primary comparison design. (a) Recorded end-effector paths from a selected clean configuration with two successes and two failures. (b) The six unordered cross-policy pairs; blank cells omit self- and duplicate pairings, and distances describe this example, not population medians. (c) A successful

\pi_{0.5}

anchor is retained while its UniVLA partner changes state or task, holding policy pair, template, level, and successful outcomes fixed. Views are orthographic projections; DTW uses the original 3D coordinates.

Policy	Inputs	Pixel grid	Cadence
OpenVLA	E	$224^{2}$	1
OFT	E,W,P	$256^{2}$	8
UniVLA	E	$224^{2}$	1
$\pi_{0.5}$	E,W,P	$256^{2}$	5

TABLE I: Interfaces used by the collector. E/W denote external/wrist views and P denotes proprioception. The pixel grid is where visual corruption is applied. Cadence is executed actions per policy query.

Level	Brightness	$\sigma$	Shift	Masks
L0	1	$0$	0	none
L1	[0.8,1.2]	$10$	$\pm 8$ horiz.	none
L2	[0.6,1.4]	$20$	$\pm 16$ both	$1\times 40^{2}$
L3	[0.45,1.6]	$35$	$\pm 24$ both	$2\times 60^{2}$
L4	[0.3,1.9]	$55$	$\pm 32$ both	$3\times 80^{2}$

TABLE II: Final operators per visual level. Brightness is uniform on the interval. Noise is in 8-bit pixel units; shift is in pixels. Mask notation gives count and side length.

Fig. 2: Clean L0 distances. (a) Configuration-matched pairs by outcome. (b) Successful partner controls. Marks are defined in the figure key; both panels use a logarithmic scale and describe observed distributions, not confidence bounds.

Fig. 3: Subgroup ordering at L0. Each row gives the SS and SF median on one logarithmic axis for ten tasks, six policy pairs and three templates from the same 3,600 pairs; SS lies left of SF in every row. FF is shown for reference (hollow:

n<10

; dash: absent) and holds no fixed rank against SF. Counts are SS

\cdot

\cdot

FF; rows are subgroups, not independent samples.

Anchor / partner	$n$	Within	Cross	$\widetilde{\delta}$
OFT / OpenVLA	$323$	$0.0117$	$0.0169$	$0.0051$
OFT / $\pi_{0.5}$	$401$	$0.0124$	$0.0176$	$0.0059$
OFT / UniVLA	$391$	$0.0121$	$0.0162$	$0.0043$
OpenVLA / $\pi_{0.5}$	$456$	$0.0142$	$0.0147$	$0.0007$
OpenVLA / UniVLA	$440$	$0.0144$	$0.0146$	$0.0003$
$\pi_{0.5}$ / UniVLA	$573$	$0.0141$	$0.0146$	$0.0006$

TABLE III: Successful state-variation controls. Within and cross denote the two distances in Eq. 3 ;

\widetilde{\delta}

is the median of paired differences, not a difference of medians. Distances are in meters. The first listed policy is the anchor.

Metric	SS	SF	FF	State	Task
Original	$0.0120$	$0.0380$	$0.0439$	$0.0157$	$0.0817$
No startup	$0.0132$	$0.0401$	$0.0458$	$0.0163$	$0.0885$
Arc-length	$0.0117$	$0.0301$	$0.0478$	$0.0146$	$0.0794$
+ Centering	$0.0094$	$0.0305$	$0.0375$	$0.0109$	$0.0556$

TABLE IV: Clean metric sensitivity: median normalized DTW (m). SS/SF/FF counts are 2,588/923/89. State/task columns replace the successful partner within/across tasks, using the same 2,588 triples.

Outcome	$n$	Full	Trimmed	Prefix
SS	$2496$	$0.0120$	$0.0132$	$0.0140$
SF	$918$	$0.0380$	$0.0402$	$0.0240$
FF	$89$	$0.0439$	$0.0458$	$0.0340$

TABLE V: Observation-window comparison on the same active cohort. Entries are median DTW (m). Full retains initialization; trimmed removes it; prefix uses the first 72 control records. Both episodes are active beyond the cutoff.

Policy / suite	L0	L1	L2	L3	L4
OpenVLA / Spatial	$0.762$	$0.837$	$0.683$	$0.068$	$0.000$
OFT / Spatial	$0.673$	$0.650$	$0.522$	$0.320$	$0.013$
UniVLA / Spatial	$0.962$	$0.957$	$0.697$	$0.110$	$0.000$
$\pi_{0.5}$ / Spatial	$0.992$	$0.983$	$0.978$	$0.567$	$0.007$
$\pi_{0.5}$ / Object	$0.977$	$0.987$	$0.968$	$0.637$	$0.003$

TABLE VI: Empirical success rates, 600 rollouts per policy and level. Object is evaluated only for

\pi_{0.5}

	SS		SF		FF
Level	$d$	$n$	$d$	$n$	$d$	$n$
L0	$0.0120$	$2588$	$0.0380$	$923$	$0.0439$	$89$
L1	$0.0122$	$2652$	$0.0372$	$864$	$0.0443$	$84$
L2	$0.0133$	$1928$	$0.0354$	$1328$	$0.0301$	$344$
L3	$0.0206$	$223$	$0.0382$	$1471$	$0.0446$	$1906$
L4	–	$0$	$0.0580$	$36$	$0.0678$	$3564$

TABLE VII: Normalized DTW medians (m) and counts. Each level contains 3,600 configuration-matched pairs.

Vision-Language-Action Models

Vision-language-action models turn visual observations and natural-language instructions into actions for robots and other embodied agents.

See all 1,194 papers

A Phenomenology of Neural Geometry in Vision-Language-Action Models
Oct 14, 2026Mozes Jacobs, Aiden Swann, Mathilde Papillon +16Neural Representation Geometry Vision-Language-Action Models
Goodfire · Harvard University · Stanford University +1
Cross-View Action Consistency for Camera-Robust Vision-Language-Action Policies
Aug 7, 2026Bingqi Huang, Bingchuan Wei, Xuan Wang +2Multi-View Consistency Vision-Based Robot Control
Tsinghua University · Informatics Institute, University of Amsterdam & Faculty of Science, Vrije Universiteit Amsterdam
RePO-VLA: Recovery-Driven Policy Optimization for Vision-Language-Action Models
May 10, 2026Weijia Liufu, Xiaoyu Guo, Ruiyi Chen +16VLM Robustness Robot Failure Recovery
Sun Yat-sen University · South China University of Technology · Peng Cheng Laboratory +3

Oct 14, 2026J/K move · Enter open · S save

A Phenomenology of Neural Geometry in Vision-Language-Action Models

Mozes Jacobs, Aiden Swann, Mathilde Papillon, Siddharth Boppana+15

Goodfire · Harvard University · Stanford University+1

Neural Representation Geometry Vision-Language-Action Models

Open paper AskPDF arXiv

Robotic manipulation is inherently geometric, but what shape does the world take inside the policy that performs it? Prior work on vision-language-action (VLA) policies establishes that task-relevant variables are linearly readable from activations, yet readability certifies only that a variable is present and says nothing about the shape its values trace, which may be curved and multi-dimensional. Using controlled sweeps, natural rollouts, linear probes, and activation interventions, we build a taxonomy of seven task-relevant concepts in VLA models. We find that realized geometry is predominantly multi-dimensional and is shaped by the constraints under which the policy acts. Physical joint limits, for example, leave wrist orientation an open arc rather than a circle, and distance to the target, a single scalar, is realized in two orthogonal subspaces, a coarse ruler for the approach and a fine ruler for the grasp. The same geometries reappear in two further VLA models on real-world robot data, indicating that they are neither model-specific nor artifacts of simulation. We demonstrate how the findings are actionable by steering along the geometry a concept realizes. Overall, this work lays out an initial phenomenology of realized geometry in VLA policies and demonstrates that a concept's shape carries as much importance as its readability.

Abstract

Vision-Language-Action Models

Explore similar work

A Phenomenology of Neural Geometry in Vision-Language-Action Models

Cross-View Action Consistency for Camera-Robust Vision-Language-Action Policies

RePO-VLA: Recovery-Driven Policy Optimization for Vision-Language-Action Models