Sensorimotor Alignment: A Platonic Proxy for Embodied Policy Success

Yunfei Xie; Howard H. Qian; Shiyi Lan; Kaiyu Hang; Chen Wei

cs.CVOct 22, 2026

Sensorimotor Alignment: A Platonic Proxy for Embodied Policy Success

Authors: Yunfei Xie, Howard H. Qian, Shiyi Lan, Kaiyu Hang, Chen Wei

Organizations: Rice University · NVIDIA

Abstract

Robotic foundation models are typically evaluated through costly closed-loop rollouts, which motivates cheap offline proxies for model capability. The Platonic Representation Hypothesis (PRH) suggests that as representations improve, different modalities such as vision and language converge toward a shared statistical model of reality. We ask whether motion trajectories form another such modality: as embodied models become more capable, should their sensory representations converge toward the structure of physical motion? To examine this, we propose Sensorimotor Alignment ( $S^2$ ), a training-free offline metric that measures how well a model's sensory representation aligns with the geometry of physical motion. We find that $S^2$ correlates positively with downstream robot task success across embodied model families, making it a low-cost offline proxy for prioritizing models before closed-loop evaluation. $S^2$ can also identify promising vision-language model (VLM) backbones even before costly fine-tuning into vision-language-action models (VLAs). Beyond this correlation, $S^2$ offers representation-level explanations for phenomena observed in VLAs and world action models (WAMs). With $S^2$ , we extend PRH to embodied models and make sensorimotor alignment empirically measurable, offering insight into why an embodied model succeeds beyond its closed-loop success rate.

Figures & tables

Figure 1: Left: We test the Platonic Representation Hypothesis (PRH) in robotics, using image–text features as the sensory representation and end-effector trajectories as the motor representation: a more capable embodied model should have sensory representations that align more closely with this motor representation. To validate this, we define Sensorimotor Alignment ( $\mathrm{S}^{2}$ ). Right: We measure $\mathrm{S}^{2}$ across 12 vision-language-action models (VLAs) and find that $\mathrm{S}^{2}$ correlates positively with SimplerEnv task success rate (Pearson $r=+0.717$ ), providing empirical support for this PRH-inspired view of embodiment.

Figure 2: Measuring Sensorimotor Alignment ( $\mathrm{S}^{2}$ ) by nearest-neighbor overlap. For the query episode (left), sensory neighbors (bottom right) have similar vision-text features, and motor neighbors (top right) have similar trajectories. Green checks mark shared neighbors; red crosses mark neighbors found only in the sensory set. A larger overlap means that episodes with similar sensory representations also follow similar motor trajectories.

Figure 3: Sensorimotor Alignment (

\mathrm{S}^{2}

) correlates with task success across model families and in simulated and real-world evaluations. Each panel plots offline

\mathrm{S}^{2}

(

x

-axis) against downstream task success rate (

y

-axis) for (a) fine-tuned vision-language-action models (VLAs), (b) raw vision-language models (VLMs), (c) world action models (WAMs), and (d) real-robot policies. For raw VLMs, task success is measured after VLA fine-tuning. These correlations (Pearson’s

r

; unadjusted one-tailed

p

-values) support

\mathrm{S}^{2}

as an offline proxy across model families.

Figure 4: Sensorimotor Alignment (

\mathrm{S}^{2}

) correlates with VLA success rate where VQA scores do not. Across 8 raw vision-language models (VLMs) [ 57 ] ,

\mathrm{S}^{2}

(left) correlates strongly with SimplerEnv task success after fine-tuning into vision-language-action models (VLAs), whereas visual question answering (VQA) scores (right) show virtually no correlation.

Figure 5: Sensorimotor Alignment (

\mathrm{S}^{2}

) correlates with WAM success rate more closely than video-quality metrics. For 3 world action models (WAMs) evaluated on RoboTwin, video-quality metrics (SSIM, PSNR, FID) show no significant correlations with task success. In contrast, only

\mathrm{S}^{2}

correctly recovers the success-rate ordering. Only 3 of the 6 WAMs are compared because the others do not generate future video during closed-loop task evaluation.

Figure 8: Fine-tuned VLAs rely mainly on visual rather than language representations. We correlate Sensorimotor Alignment (

\mathrm{S}^{2}

) from vision, text, and joint vision-text features (left to right) with SimplerEnv task success rate. Top: For fine-tuned vision-language-action models (VLAs), vision and joint features correlate similarly strongly, while text features correlate weakly. Bottom: For raw vision-language models (VLMs), joint-feature

\mathrm{S}^{2}

correlates with task success after VLA fine-tuning, while neither modality alone reaches significance.

Figure 9: Freezing the vision encoder reduces both Sensorimotor Alignment (

\mathrm{S}^{2}

) and task success rate. For Qwen2.5-VL-3B vision-language-action models fine-tuned on BridgeDataV2, we compare end-to-end training with a frozen vision encoder. Freezing lowers

\mathrm{S}^{2}

from joint vision-text features (top) and SimplerEnv success rate (bottom), linking lower success to weaker alignment. Trajectory horizon

h=7

Panel of Figure 10 — Figure 10: Sensorimotor Alignment ( $\mathrm{S}^{2}$ ) is already high at early denoising steps and peaks at mid-depth blocks. For 3 world action models (WAMs), (a) $\mathrm{S}^{2}$ remains nearly flat across denoising, suggesting early-step features already align with robot trajectories; (b) schedule-averaged $\mathrm{S}^{2}$ peaks at Block 14, showing peak alignment at mid-depth.

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Removed group	Pearson’s $r$	One-tailed $p$
StarVLA	$+0.526$	$0.113$
CogACT	$+0.785$	$0.006$
GR00T	$+0.745$	$0.007$
Pi0	$+0.783$	$0.002$
SpatialVLA	$+0.687$	$0.010$

Appendix

Table 1: Leave-one-out over architecture groups for 12 fine-tuned vision-language-action models. Each row removes one group and recomputes the correlation between Sensorimotor Alignment (

\mathrm{S}^{2}

) and SimplerEnv-WidowX task success rate. The remaining model counts

n

are 7, 9, 10, 11, and 11 in row order.

Figure 11: Sensorimotor Alignment (

\mathrm{S}^{2}

) of frozen vision encoders correlates with downstream policy success rate. Points represent the 14 frozen backbones of Hu et al. [19] , scored by

\mathrm{S}^{2}

on DROID without policy training. The vertical axis shows the interquartile mean (IQM) of task success rates over 21 tasks, using low-data behavior cloning (left) or reinforcement learning with visual reward functions (right).

Model	SR (%)	$h\!=\!1$	$h\!=\!3$	$h\!=\!7$	$h\!=\!15$	$h\!=\!25$	$h\!=\!40$	$h\!=\!75$	$h\!=\!110$	$h\!=\!150$	$h\!=\!220$
Qwen2.5-GR00T-Bridge	71.4	0.034	0.034	0.036	0.040	0.043	0.051	0.065	0.076	0.086	0.097
Qwen3-GR00T-RT-1-Bridge	65.3	0.028	0.027	0.029	0.032	0.036	0.044	0.057	0.071	0.083	0.096
Qwen2.5-GR00T-RT-1-Bridge	63.6	0.034	0.034	0.035	0.040	0.042	0.048	0.062	0.071	0.080	0.090
CogACT-Large	58.3	0.031	0.031	0.033	0.037	0.040	0.048	0.062	0.075	0.086	0.097
GR00T-N1.6-Bridge	57.1	0.023	0.024	0.026	0.029	0.031	0.038	0.051	0.064	0.076	0.091
CogACT-Base	51.3	0.031	0.031	0.032	0.037	0.040	0.049	0.062	0.074	0.086	0.098

Appendix

Table 2: Sensorimotor Alignment (

\mathrm{S}^{2}

) from joint vision-text features at the language-model output versus SimplerEnv-WidowX task success rate (SR) across trajectory horizons

h

. We score 12 fine-tuned vision-language-action models on DROID (

N=6{,}000

episodes,

k=10

neighbors). Bottom rows report Spearman’s

\rho

and Pearson’s

r

with their one-tailed

p

-values. Bold marks the horizon of peak Pearson

r

(

h=7

Setting	$r$	$p$
Number of neighbors $k$
$k\!=\!2$	$+0.679$	$0.0076$
$k\!=\!5$	$+0.667$	$0.0089$
$k\!=\!10^{\ast}$	$+0.717$	$0.0043$
$k\!=\!15$	$+0.665$	$0.0091$
$k\!=\!20$	$+0.644$	$0.0119$

Appendix

Table 5: Sensitivity of the Sensorimotor Alignment (

\mathrm{S}^{2}

)–success-rate correlation to implementation choices. Pearson’s

r

and one-tailed

p

compare

\mathrm{S}^{2}

with SimplerEnv-WidowX task success rate across 12 fine-tuned vision-language-action models. Each block varies one choice; ∗ marks the default.

	$\mathrm{S}^{2}$ (mean over 12 VLAs)			$\mathrm{S}^{2}$ –SR Pearson $r$
Horizon $h$	w/ DTW	w/o DTW	rel. change	w/ DTW	w/o DTW	rel. change
$1$	$0.0268$	$0.0268$	$+0.0\%$	$+0.692$	$+0.692$	$+0.0\%$
$3$	$0.0268$	$0.0269$	$-0.6\%$	$+0.699$	$+0.700$	$-0.1\%$
$7$	$0.0280$	$0.0277$	$+1.2\%$	$+0.717$	$+0.713$	$+0.6\%$
$15$	$0.0314$	$0.0302$	$+4.1\%$	$+0.696$	$+0.710$	$-2.0\%$
$25$	$0.0342$	$0.0317$	$+7.7\%$	$+0.689$	$+0.711$	$-3.2\%$

Appendix

Table 6: Comparing Sensorimotor Alignment (

\mathrm{S}^{2}

) with and without Dynamic Time Warping (DTW). DTW raises absolute

\mathrm{S}^{2}

more at longer trajectory horizons

h

, while its Pearson correlation

r

with SimplerEnv-WidowX task success rate (SR) stays stable. Each relative change is

100(v_{\mathrm{DTW}}/v_{\mathrm{no\,DTW}}-1)\%

for the quantity

v

in that block.

Figure 12: Sensorimotor Alignment (

\mathrm{S}^{2}

) is sensitive to a mismatch in arm configuration. For 3 world action models (WAMs) evaluated on bimanual RoboTwin, the matched bimanual ALOHA reference (left) recovers the success-rate ordering, while the single-arm DROID reference (right) weakens the correlation.

\mathrm{S}^{2}

thus reflects whether reference data matches the target arm configuration.

Feature position	Pearson’s $r$	One-tailed $p$
ViT-out	$+0.567$	$0.0274$
LLM-in vision-text	$+0.580$	$0.0239$
LLM-out vision-only	$+0.701$	$0.0056$
LLM-out vision-text ∗	$+0.717$	$0.0043$
LLM-in text-only	$-0.325$	$0.8486$
LLM-out text-only	$+0.245$	$0.2215$

Appendix

Table 7: Correlation between Sensorimotor Alignment (

\mathrm{S}^{2}

) and task success by feature position. Pearson’s

r

and one-tailed

p

compare

\mathrm{S}^{2}

with SimplerEnv-WidowX task success rate across 12 fine-tuned vision-language-action models on DROID (

N=6{,}000

episodes, trajectory horizon

h=7

). ViT-out, LLM-in, and LLM-out denote the vision-encoder output, language-model input, and language-model output; ∗ marks the default feature.

Feature	Vision encoder	Raw VLM	Finetuned VLA	Relative change
	(mean, $n\!=\!3$ )	(mean, $n\!=\!8$ )	(mean, $n\!=\!12$ )
ViT-out	$0.0246$	$0.0247$	$0.0278$	$+12.7\%$
LLM-in vision-only	–	$0.0244$	$0.0275$	$+12.7\%$
LLM-in vision-text	–	$0.0233$	$0.0275$	$+18.1\%$
LLM-out vision-only	–	$0.0212$	$0.0275$	$+29.9\%$
LLM-out text-only	–	$0.0140$	$0.0202$	$+45.0\%$

Appendix

Table 8: Mean Sensorimotor Alignment (

\mathrm{S}^{2}

) by feature position on DROID (

N=6{,}000

episodes, trajectory horizon

h=7

). ViT-out, LLM-in, and LLM-out denote the vision-encoder output, language-model input, and language-model output; standalone vision encoders have only ViT-out features. The last column is

100(\overline{\mathrm{S}^{2}}_{\mathrm{VLA}}/\overline{\mathrm{S}^{2}}_{\mathrm{VLM}}-1)\%

, where each bar denotes the model-group mean.

Model	ViT-out	LLM-in vision-only	LLM-in text-only	LLM-in vision-text	LLM-out vision-only	LLM-out text-only	LLM-out vision-text
Pretrained vision encoders, no LLM attached ( $n\!=\!3$ )
CLIP-ViT-L/14 [ 37 ]	$0.0240$	–	–	–	–	–	–
SigLIP-SO400M [ 56 ]	$0.0247$	–	–	–	–	–	–
SigLIP-2 Large [ 46 ]	$0.0250$	–	–	–	–	–	–
Raw VLMs from VLM4VLA ( $n\!=\!8$ )
KosMos-2	$0.0257$	$0.0238$	$0.0093$	$0.0239$	$0.0214$	$0.0151$	$0.0216$

Appendix

Table 9: Per-model Sensorimotor Alignment (

\mathrm{S}^{2}

) by feature position on DROID (

N=6{,}000

episodes, trajectory horizon

h=7

). ViT-out, LLM-in, and LLM-out denote the vision-encoder output, language-model input, and language-model output. Vision-only, text-only, and vision-text select image tokens, instruction tokens, or both from the same model input. Group means are in Table 8 .

Horizon $h$	Unfrozen $\mathrm{S}^{2}$	Frozen $\mathrm{S}^{2}$	Relative change
$1$	$0.0231$	$0.0143$	$-38.1\%$
$3$	$0.0232$	$0.0141$	$-39.0\%$
$7$	$0.0245$	$0.0144$	$-41.1\%$
$15$	$0.0268$	$0.0158$	$-41.2\%$
$25$	$0.0295$	$0.0166$	$-43.8\%$
$40$	$0.0352$	$0.0191$	$-45.7\%$

Appendix

Table 10: Sensorimotor Alignment (

\mathrm{S}^{2}

) with a frozen and an unfrozen vision encoder across trajectory horizons

h

. Qwen2.5-VL-3B vision-language-action models trained with the same recipe, evaluated using joint vision-text features at the language-model output on DROID (

N=6{,}000

episodes). Relative change is

100(\mathrm{S}^{2}_{\mathrm{frozen}}/\mathrm{S}^{2}_{\mathrm{unfrozen}}-1)\%

Feature	0 %	25 %	50 %	75 %	100 %
	earliest				latest
Motus random baseline $=0.012\pm 0.002$
Block 0	0.044	0.203	0.307	0.321	0.324
Block 7	0.342	0.388	0.399	0.390	0.378
Block 14	0.479	0.492	0.482	0.479	0.471
Block 21	0.454	0.448	0.447	0.436	0.424

Appendix

Table 11: Layer-wise Sensorimotor Alignment (

\mathrm{S}^{2}

) along the denoising schedule for 3 world action models (WAMs). Columns label 5 selected positions in each model’s native schedule, not matched noise levels. Motus and LingBot-VA use 500 episodes over 50 RoboTwin tasks; Vidar uses 480 episodes over 48 tasks. Rows give 6 video-backbone positions and the text embedding. Block 14 (bold) has the highest

\mathrm{S}^{2}

at 13 of the 15 model and schedule positions. The random baseline is the mean

\pm

standard deviation (divisor 10) over 10 draws of independent standard-normal features with the same shape.

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