PermVLA: Factorization Order as a Regularizer for VLA Learning

Yanqiao Chen; Yuhan Rui; Dongsheng Hou; Zijie Nie; Yutong Wan; Qi Hao

cs.AIOct 3, 2026

PermVLA: Factorization Order as a Regularizer for VLA Learning

Authors: Yanqiao Chen, Yuhan Rui, Dongsheng Hou, Zijie Nie, Yutong Wan, Qi Hao

Organizations: Southern University of Science and Technology · Huazhong University of Science and Technology

Abstract

Vision-language-action (VLA) policies commonly learn action chunks through a fixed left-to-right (LTR) factorization, although the same expert trajectory distribution admits many valid chain-rule factorizations. We identify factorization order as an overlooked regularization choice and introduce causally anchored permutation (CAP), which samples action reveal orders with a tunable chronological prefix. Its auxiliary objective trains one shared policy to predict actions from different known subsets of the same expert chunk, while deployment retains deterministic LTR control. We call this conditional-set augmentation: it creates multiple conditional prediction problems from one expert chunk without adding demonstrations. This discourages reliance on the single chronological prefix used by ordinary teacher forcing. Controlled experiments show that CAP consistently outperforms standard LTR training on LIBERO and LIBERO-Plus, with the same advantage appearing in cross-dataset CALVIN evaluation. A diagnostic that measures the expected squared difference between a chunk's joint log likelihood under two reveal orders verifies that CAP training internalizes agreement across reveal orders. These findings position sampled subset-conditioned auxiliary objectives as a general recipe for constructing VLA regularizers, illustrated by an extension to diffusion action generators.

Figures & tables

Figure 1: Overview of PermVLA . Autoregressive VLA training conventionally factorizes each expert action chunk in chronological order, so every action slot is always predicted from the same teacher-forced prefix. PermVLA treats this reveal order as a training-only degree of freedom: the same physical actions are supervised under multiple valid conditioning subsets, while the expert target, action identities, and chronological autoregressive deployment remain unchanged.

Figure 2: PermVLA architecture. A pretrained VLM with a Perceiver-style resampler produces context tokens that condition a two-stream action decoder; the sampled reveal order enters only through the attention masks during training, while deployment always executes a chronological action prefix.

Representative published policies
Model	Robot pretraining	Action generator	Spatial	Object	Goal	Long	Mean
Diffusion Policy ( Chi et al., 2023 )	None	Diffusion	78.3	92.5	68.3	50.5	72.4
Octo ( Ghosh et al., 2024 )	Yes	Diffusion	78.9	85.7	84.6	51.1	75.1
OpenVLA ( Kim et al., 2025b )	Yes	Token autoregression	84.7	88.4	79.2	53.7	76.5
$\pi_{0}$ ( Black et al., 2025b )	Yes	Flow matching	96.8	98.8	95.8	85.2	94.2
SmolVLA-0.45B ( Shukor et al., 2025 )	None	Flow matching	90.0	96.0	92.0	71.0	87.3

Table 1: LIBERO success rate (%). Published rows retain their original protocols. Diffusion Policy and Octo values follow Kim et al. (2025b) ,

\pi_{0}

follows Driess et al. (2025) , and the remaining values follow their cited sources. Our rows use suite-specific policies trained for 30k updates and evaluated over 500 episodes per suite. Labels abbreviate configuration values; e.g., M1/H16/O1/E8 denotes

M=1,H=16,O=1,e=8

Controlled factor	Setting	Spatial	Object	Goal	Long	Mean
Objective	LTR-1pass	93.8	88.0	62.0	6.4	62.6
	LTR-2pass	95.2	65.4	64.8	23.4	62.2
	PermVLA reference	95.4	89.4	69.8	32.2	71.7
CAP orders $M$	4	93.6	87.4	66.0	42.0	72.3
Horizon $H$	8	88.6	97.0	90.2	34.2	77.5
History $O$	2	85.0	96.0	75.4	38.4	73.7

Table 2: Objective and temporal comparisons on LIBERO success rate (%). The reference is

M=1,H=16,O=1,e=8,K=1,\lambda=0.25

, 30k updates, seed zero, and 500 episodes per suite. Every non-objective row changes only the named value.

Published contextual references
Method	Original	Camera	Robot	Language	Light	Background	Noise	Layout
OpenVLA	76.5	0.8	3.5	23.0	8.1	34.8	15.2	28.5
$\pi_{0}$ -FAST	85.5	65.1	21.6	61.0	73.2	73.2	74.4	68.8
WorldVLA	79.1	0.1	27.9	41.6	43.7	17.1	10.9	38.0
RIPT-VLA	97.5	55.2	31.2	77.6	88.4	91.6	73.5	74.2
Our controlled study

Table 3: Zero-shot LIBERO-Plus success rate (%). “Original” is the corresponding standard-LIBERO score; the remaining columns partition the 10,030 perturbation instances. Published rows are transcribed from Table 2 of Fei et al. (2026) under their published protocols. We retain representative token, regression, and fast-action baselines here. Our rows use standard-LIBERO training trajectories and frozen policies.

External protocol context
Method	Avg. length	Success@1	Success@2	Success@3	Success@4	Success@5
Diffusion Policy-CNN ( Reuss et al., 2025 )	1.350	63.5	35.3	19.4	10.7	6.4
OpenVLA ( Kim et al., 2025b ; Xiao et al., 2026 )	3.270	91.3	77.8	62.0	52.1	43.5
Matched Gaussian autoregressive controls
LTR-1pass	1.090	61.0	27.6	12.2	5.9	2.3
LTR-2pass	0.694	40.3	18.4	7.6	2.3	0.8

Table 4: CALVIN ABC

\rightarrow

D evaluation on 1,000 fixed five-instruction chains. Success@

k

is the percentage completing at least

k

consecutive instructions. External rows use independently published training and model-selection protocols and provide context; bold denotes the best result within each block.

Appendix figures & tables29 assets

Supplementary material from the paper’s appendix.

Appendix

Backbone	Adaptation	Spatial	Object	Goal	Long	Mean
Qwen3-VL-4B-Instruct	LoRA-32	95.4	89.4	69.8	32.2	71.7
PaliGemma 2–3B	LoRA-32	90.0	82.8	79.0	23.4	68.8

Appendix

Table 5: Backbone replacement under the fixed CAP

M=1,H=16,O=1,e=8

protocol. Entries are 500-episode LIBERO success rates (%).

Objective	$M$	$H$	$O$	$e$	$K$	Spatial	Object	Goal	Long	Mean
Main $O=1$ configurations
PermVLA	1	8	1	8	1	88.6	97.0	90.2	34.2	77.5
LTR-1pass	1	16	1	8	1	93.8	88.0	62.0	6.4	62.6
LTR-2pass	1	16	1	8	1	95.2	65.4	64.8	23.4	62.2
PermVLA ( $\lambda=.25$ )	1	16	1	8	1	95.4	89.4	69.8	32.2	71.7
PermVLA	4	16	1	8	1	93.6	87.4	66.0	42.0	72.3

Appendix

Table 6: Four-suite LIBERO configurations (%). Every row uses 30k updates and 500 evaluation episodes per suite. The

O=1

block supports the main controlled analysis; the

O=2

block reports the observation-history comparison and the earlier

M=4

variants.

One-factor comparisons
Controlled change	Held fixed	Spatial	Object	Goal	Long	Mean
Objective: LTR-1pass $\rightarrow$ CAP	M1/H16/O1/E8	+1.6	+1.4	+7.8	+25.8	+9.2
Objective: LTR-2pass $\rightarrow$ CAP	M1/H16/O1/E8	+0.2	+24.0	+5.0	+8.8	+9.5
Objective: LTR-1pass $\rightarrow$ CAP	M1/H16/O1/E16	+1.0	+20.4	+13.8	+23.4	+14.7
$H:16\rightarrow 8$	CAP/M1/O1/E8	-6.8	+7.6	+20.4	+2.0	+5.8
$O:1\rightarrow 2$	CAP/M1/H16/E8	-10.4	+6.6	+5.6	+6.2	+2.0

Appendix

Table 7: Signed change in LIBERO success rate (percentage points) for four-suite comparisons. Each transition is treatment minus parent. The one-factor panel changes only the parameter named in the first column; the coupled panel is descriptive. Positive values denote improvement and negative values denote regression. The Mean column averages the unrounded suite changes.

Task	CAP ref	Change from CAP reference (percentage points)
		LTR-1	LTR-2	H8	O2	CAP/E16	LTR/E16	K0	K8	$\lambda=.50$
Between plate/ramekin	100	0	-2	0	0	-2	-2	0	0	-2
Next to ramekin	100	-14	-28	-18	-2	-2	-8	-2	-16	-38
Table center	100	0	0	-2	0	-4	0	0	-2	0
On cookie box	96	+2	+2	-16	+4	+4	-2	0	+2	-2
Top cabinet drawer	80	-2	+10	-4	+2	-18	-16	+8	-16	+10

Appendix

Table 8: Task-resolved LIBERO-Spatial comparison (%). Every task places the black bowl on the plate; the first column identifies its initial location.

Task	CAP ref	Change from CAP reference (percentage points)
		LTR-1	LTR-2	H8	O2	CAP/E16	LTR/E16	K0	K8	$\lambda=.50$
Alphabet soup	82	+16	-34	+18	+4	-24	-6	0	+12	-16
Cream cheese	92	0	-18	+8	+4	+4	+8	-42	-20	+2
Salad dressing	100	-2	-12	0	0	0	-74	-2	-22	0
BBQ sauce	52	+14	-26	+44	+34	-10	-42	-34	+18	-20
Ketchup	82	0	-14	+18	+16	-18	-74	-30	-42	+14

Appendix

Table 9: Task-resolved LIBERO-Object comparison (%). Every task places the named object in the basket.

Task	CAP ref	Change from CAP reference (percentage points)
		LTR-1	LTR-2	H8	O2	CAP/E16	LTR/E16	K0	K8	$\lambda=.50$
Open middle drawer	62	-44	-34	+26	-4	+24	-12	-16	-18	+20
Bowl $\to$ stove	98	+2	+2	+2	+2	0	+2	+2	-6	-4
Wine $\to$ cabinet	98	-8	-40	+2	-10	-4	-16	-8	0	-8
Open top drawer + bowl	2	+72	+62	+70	+46	+36	+50	+50	+30	+44
Bowl $\to$ cabinet	82	+14	+12	+18	+10	+12	+16	+14	0	+6

Appendix

Table 10: Task-resolved LIBERO-Goal comparison (%). The first column gives a compact form of each language-conditioned goal.

Task	CAP ref	Change from CAP reference (percentage points)
		LTR-1	LTR-2	H8	O2	CAP/E16	LTR/E16	K0	K8	$\lambda=.50$
Soup + sauce $\to$ basket	32	-32	-16	-30	-30	+6	-30	-12	-14	+16
Cream cheese + butter $\to$ basket	30	-30	+2	+18	+6	+2	-24	+56	+8	+38
Stove on + moka pot	84	-82	-44	-66	-2	-18	-64	-70	+8	-16
Bowl $\to$ drawer + close	60	-60	-26	+8	-18	-12	-56	-26	+16	-26
Two mugs $\to$ plates	40	-40	-14	+14	-8	-8	-40	+10	0	+6

Appendix

Table 11: Task-resolved LIBERO-Long comparison (%). The first column summarizes each multi-stage instruction.

Objective	Training configuration	$e$	Long
PermVLA	M1/H8/O1	4	30.4
PermVLA	M1/H8/O1	8	34.2
PermVLA	M1/H16/O1	8	32.2
PermVLA	M1/H16/O1	16	31.6
PermVLA	M4/H16/O2	4	35.2
PermVLA	M4/H16/O2	8	37.2

Appendix

Table 12: Execution-length ablation on LIBERO Long (%). Within each adjacent configuration block, training and model selection are fixed; only the number of open-loop executed actions

e

changes.

CAP gradient route	Goal
VLM, resampler, and action decoder	77.0
Action decoder only	74.0

Appendix

Table 13: CAP gradient-routing diagnostic on LIBERO Goal (%). Both rows use

M=4,H=16,O=2,e=8

. Decoder-only routing detaches VLM and resampler context for the CAP loss while preserving LTR gradients through all modules.

Suite	Original	Camera	Robot	Language	Light	Background	Noise	Layout	Plus mean
Spatial	88.6	25.5	50.6	84.6	92.8	78.3	32.8	76.9	61.9
Object	97.0	16.4	34.9	97.7	78.8	71.0	19.4	55.3	50.2
Goal	90.2	42.6	39.9	28.0	74.2	44.1	33.2	49.6	43.2
Long	34.2	8.8	13.5	19.1	6.6	12.5	3.8	13.1	10.9
All	77.5	23.3	34.3	56.2	63.9	50.0	21.2	50.6	41.3

Appendix

Table 14: Suite-resolved zero-shot LIBERO-Plus success rate (%) for the

H=8,O=1,M=1

PermVLA policy. “Original” is the corresponding standard-LIBERO score. The All row averages Original over suites and aggregates each perturbation family over its official instances.

Suite	Original	Camera	Robot	Language	Light	Background	Noise	Layout	Plus mean
Spatial	95.4	33.2	57.7	87.2	97.3	91.5	35.9	91.4	69.3
Object	89.4	23.2	26.9	93.2	73.4	70.6	27.0	56.1	50.1
Goal	69.8	42.2	27.6	36.1	52.3	29.2	41.4	33.9	37.1
Long	32.2	9.1	16.3	38.1	18.6	17.6	4.2	12.8	16.2
All	71.7	26.7	31.4	62.7	61.2	50.6	26.0	50.0	42.9

Appendix

Table 15: Suite-resolved zero-shot LIBERO-Plus success rate (%) for the matched

H=16,O=1,M=1

PermVLA policies deployed with

e=8

. Every cell contains a released task-map suite–factor block. The final row aggregates each factor over all four suites, and Plus mean aggregates the full 10,030-instance perturbation partition.

Suite	Original	Camera	Robot	Language	Light	Background	Noise	Layout	Plus mean
Spatial	93.8	33.8	49.4	75.6	89.0	89.9	37.9	81.8	63.9
Object	88.0	19.2	33.7	70.1	78.5	69.4	22.5	62.3	48.0
Goal	62.0	36.0	32.8	21.5	52.7	26.0	24.8	35.1	32.1
Long	6.4	1.2	4.1	4.4	3.3	4.5	0.7	3.8	3.0
All	62.6	22.2	29.5	42.2	56.8	45.5	20.3	47.7	36.4

Appendix

Table 16: Suite-resolved zero-shot LIBERO-Plus success rate (%) for the

H=16,O=1

LTR-1pass policies deployed with

e=8

. Every cell contains a released task-map suite–factor block. The final row aggregates each factor over its four suite blocks, and Plus mean aggregates the full 10,030-instance perturbation partition.

Suite	Original	Camera	Robot	Language	Light	Background	Noise	Layout	Plus mean
Spatial	95.2	29.3	51.4	83.6	92.1	85.3	34.2	83.1	64.3
Object	65.4	20.5	19.6	66.4	27.3	56.0	32.5	36.7	35.7
Goal	64.8	38.2	26.9	29.3	44.4	30.6	27.2	34.6	32.7
Long	23.4	5.5	8.7	23.0	5.5	13.8	3.6	8.0	9.6
All	62.2	23.1	25.9	50.0	42.8	45.1	23.5	42.0	35.2

Appendix

Table 17: Suite-resolved zero-shot LIBERO-Plus success rate (%) for the

H=16,O=1

LTR-2pass policies deployed with

e=8

. Every entry is computed from a released task-map suite–factor block. The All row pools the four suites within each perturbation family; its Plus mean aggregates the full 10,030-instance perturbation partition.

Suite	Samples seen	LTR NLL	CAP NLL	L1	First L1	End L1	Grip	Samples/s
Spatial	479,940	-12.455	-10.880	0.0451	0.1505	0.0421	98.28	6.33
Object	479,874	-13.832	-12.914	0.0386	0.1568	0.0333	98.09	6.47
Goal	479,900	-14.759	-13.837	0.0321	0.1272	0.0253	98.95	6.60
Long	479,960	-14.462	-13.635	0.0359	0.1581	0.0282	98.20	6.47

Appendix

Table 18: Final training-window diagnostics at step 30k for the

H=16,O=2,M=4

policies. “CAP NLL” is the sampled anchored-permutation NLL. L1, First L1, and End L1 are mean absolute action errors over all, first, and final chunk slots; Grip is gripper-state accuracy (%).

Training objective	LTR NLL	CAP NLL	L1	First L1	End L1	Grip	Mean log-std	Min-std	Success
LTR-1pass	-14.223	n/a	0.0354	0.1607	0.0280	98.24	-3.383	24.22	6.4
LTR-2pass	-14.522	n/a	0.0355	0.1617	0.0286	98.13	-3.383	23.92	23.4
CAP	-14.392	-13.681	0.0361	0.1646	0.0282	98.32	-3.379	23.87	32.2

Appendix

Table 19: Matched final training diagnostics and closed-loop Long success. All three objectives use

H=16,O=1,M=1

, seed zero, 30k updates, and deterministic LTR deployment with

e=8

. L1, First L1, and End L1 are mean absolute action errors over all, first, and final chunk slots. “Min-std” is the fraction of Gaussian log-scale outputs at the configured lower bound; Grip and Success are percentages.

Symbol	Meaning	Reference	Values represented in the study
$M$	sampled CAP orders per context and update	1	1, 4
$H$	action steps predicted per policy query	16	8, 16
$O$	temporal observations supplied per camera view	1	1, 2
$V$	simultaneous RGB camera views per observation	2	2 (primary + wrist; fixed)
$e$	leading predicted actions executed before replanning	8	4, 8, 16
$K$	fixed chronological prefix length in CAP orders	1	0, 1, 8 (0 = unrestricted orders)

Appendix

Table 20: Meaning and experimental role of the principal PermVLA parameters. The final column lists settings represented by measured results.

Category	Parameter	Value
Data	Benchmark / suites	LIBERO Spatial, Object, Goal, Long; 10 tasks each
	Demonstrations after no-op filtering	432 / 454 / 428 / 379
	Input source	no-op-filtered Reinforcement Learning Datasets (RLDS) format; evaluation uses fixed benchmark episodes
	Temporal stride / shuffle buffer	1 / 10,000
Context	Backbone	Qwen3-VL-4B-Instruct
	Adaptation	LoRA rank 32, alpha 16, dropout 0

Appendix

Table 21: Consolidated parameters for the controlled Gaussian PermVLA study. Sweep rows in Table 2 replace one named value and keep every other entry fixed.

Panel of Figure 3 — Figure 3: PermDiffusion architecture. During training, a sampled anchored order and cut divide the expert chunk into clean revealed slots $S$ and noisy prediction slots $U$ . Physical positions, per-slot noise levels, and revealed-mask embeddings identify every input to the shared denoiser. Standard diffusion is the special case in which all slots are noisy. Deployment begins from Gaussian noise and applies ordinary synchronous DDIM updates to the full physical-time chunk; the sampled subset construction is used only for training.

Treatment	Temporal config.	Suite	Success
PermDiffusion	H8/O1/E8	Spatial	87.6
PermDiffusion	H8/O1/E8	Object	89.8
PermDiffusion	H8/O1/E8	Goal	84.2
PermDiffusion	H8/O1/E8	Long	36.8
PermDiffusion	H16/O2/E8	Goal	82.2

Appendix

Table 22: PermDiffusion results on LIBERO. The

H=8,O=1,e=8

rows form the suite matrix, while the

H=16,O=2,e=8

Goal row is a standalone reference. Each entry is a 500-episode success rate (%).

Panel of Figure 4 — Figure 4: Loss construction in PermVLA . Standard LTR training follows one physical-time factorization and sums teacher-forced per-slot likelihoods against the expert chunk. CAP samples factorization orders over the same physical action variables, illustrated here with $K=1$ ; each order defines revealed subsets and a corresponding likelihood. Their Monte Carlo average is a training-only regularizer of the shared policy. The drawn losses are unnormalized within-chunk sums; Equations 3 – 4 define the normalized objectives. Action indices denote fixed physical slots in both panels, and deployment retains deterministic physical-time LTR control.

Figure 5: Illustration of CAP’s theoretical interpretation. In the upper path, a reveal order

z

defines a normalized joint density

q_{\theta}^{z}(\mathcal{A}\mid\mathcal{C})

; substituting this density into the mixed CAP risk

\mathcal{R}_{\mathrm{mix}}

(Equation 16 ) and minimizing it preserves the expert population target. In the lower path, a demonstrated action chunk creates a family of conditional prediction problems; these problems jointly constrain a finite-capacity model, so features that remain predictive across conditional sets receive repeated support, thereby forming CAP’s regularization mechanism.

Suite	Training objective	$\widetilde{\mathcal{S}}_{H}$ [IQR]	$\widetilde{\Delta}_{\mathrm{arb}}$	LTR NLL / slot
Long	LTR-1pass	384.85 [114.00, 1,473.49]	59.11	-15.16
	LTR-2pass	407.21 [110.73, 1,570.34]	59.98	-15.18
	CAP	0.108 [0.055, 0.215]	0.97	-15.16
Goal	LTR-1pass	787.74 [177.30, 7,161.38]	80.36	-15.34
	LTR-2pass	1,049.71 [216.04, 9,728.23]	84.91	-15.42
	CAP	0.113 [0.062, 0.223]	1.09	-15.28

Appendix

Table 23: Factorization sensitivity of matched

M=1,H=16,O=1

models. Tildes denote medians over 640 expert chunks per suite; brackets give the interquartile range of

\mathcal{S}_{H}

. Each chunk is scored under the same 16 uniformly sampled, causally anchored orders with

K=1

\widetilde{\Delta}_{\mathrm{arb}}

is arbitrary-order minus LTR NLL per action slot. Lower sensitivity and gap indicate greater agreement across factorization orders.

Suite	Training setting	$\lambda$	$M$	$K$	$\widetilde{\mathcal{S}}_{H}$	$\widetilde{\Delta}_{\mathrm{arb}}$ / Success
Long	LTR-1pass	0	–	–	384.850	59.11 / 6.4
	CAP reference	0.25	1	1	0.108	0.97 / 32.2
	CAP weight	0.50	1	1	0.079	0.66 / 40.6
	CAP orders	0.25	4	1	0.103	0.93 / 42.0
	Anchor	0.25	1	8	182.307	29.09 / 36.0
Goal	LTR-1pass	0	–	–	787.740	80.36 / 62.0

Appendix

Table 24: Factorization-sensitivity interventions on Goal and Long.

\widetilde{\mathcal{S}}_{H}

and

\widetilde{\Delta}_{\mathrm{arb}}

are medians under the same 16

\Pi_{1}

evaluation orders; success is the corresponding 500-episode LIBERO result (%). LTR is the

\lambda=0

endpoint.

Suite	Training family	Evaluate $\Pi_{1}$	Evaluate $\Pi_{8}$
Long	$\Pi_{1}$	0.108	0.055
	$\Pi_{8}$	182.307	0.038
Goal	$\Pi_{1}$	0.113	0.061
	$\Pi_{8}$	236.312	0.051

Appendix

Table 25: Anchor-family cross-evaluation. Entries are medians

\widetilde{\mathcal{S}}_{H}

over the same chunks. Training with

K=1

covers the broad

\Pi_{1}

family;

K=8

covers the narrower

\Pi_{8}

family.

Figure 6: Matched robot rollouts under a table-appearance shift. Columns align physical action steps across policies, including the initial state and the full time limit. The final-frame border records the instantaneous official goal predicate. Both LTR-1pass and CAP satisfy that predicate at the limit, despite visibly different pot poses and gripper interactions.

Policy	First success	Goal at limit	Goal losses	Tilt at limit	Gripper contact
LTR-1pass	240	True	4	$90.0^{\circ}$	Absent
LTR-2pass	–	False	0	$58.4^{\circ}$	Absent
CAP	265	True	0	$29.8^{\circ}$	Present

Appendix

Table 26: Measurements for the full-horizon case in Figure 6 . Goal losses count transitions from true to false after first success. Tilt is the angle between the pot’s body vertical axis and the world vertical; contact denotes any pot–gripper contact at the limit.

Figure 7: State diagnostics throughout the same rollouts. The top and bottom panels vertically offset each policy’s binary trace for readability. Success and gripper contact are evaluated from the simulator at each step; pot tilt is measured from its body orientation. Sustained predicate satisfaction can coexist with a tilted pot or continued gripper contact.

Figure 8: Bowl placement and drawer closure in original LIBERO. CAP satisfies both subgoals from action 386 through the time limit. At the limit, LTR-1pass satisfies bowl containment alone, while LTR-2pass satisfies neither containment nor closure. Each row shows actual policy execution through all 520 actions.

Figure 9: Two-object basket placement in original LIBERO. CAP and LTR-2pass first satisfy the joint placement predicate at actions 230 and 338, respectively, and retain it through action 520. LTR-1pass places the alphabet soup in the basket but leaves the cream cheese box outside. Common action-step columns expose progress through both placements.

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Chen Zhao, Zhuoran Wang, Haoyang Li, Shifeng Bao+5

School of Information, Renmin University of China · Key Laboratory of Data Engineering and Knowledge Engineering, Beijing, China · Beijing University of Posts and Telecommunications+1

Vision-Language-Action Models VLA Model Training

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Test-time sampling can improve Vision-Language-Action (VLA) policies, but only if the model can efficiently select a good action from multiple candidates. Prior work often relies on separately trained external verifiers, adding extra models and inference overhead. We propose Token Probability Bucketing (TokenPB), a self-verification approach that discretizes continuous action chunks into bucket tokens and co-trains a single VLA checkpoint with a joint objective: a flow-matching loss for action generation and an auxiliary bucket loss

\mathcal{L}_{\text{bucket}}

that teaches the VLM backbone to model observation-conditioned distributions over bucket-token sequences. At inference, TokenPB samples

M

candidates, scores each via teacher-forced evaluation under the learned distribution, and selects the best---enabling efficient batched scoring with observation-prefix KV-cache reuse. We provide theory connecting the training objective to a monotonic ranking property and bounds on expected selection regret that separate candidate-set effects from calibration. Across multiple backbones and benchmarks, TokenPB yields consistent success-rate improvements over single-sample inference from the same checkpoint (+2.7 in simulation, +17.1 in real-world, +16.4 under out-of-distribution shifts), and further improves over external-verifier baselines under the same sampling budget. The code is publicly available at https://github.com/RUCKBReasoning/TokenPB.

Abstract

Vision-Language-Action Models

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