Measuring the Stability Assumption Behind Action Chunking

Aryan Goyal

cs.AIOct 1, 2026

Measuring the Stability Assumption Behind Action Chunking

Authors: Aryan Goyal

Organizations: Independent Researcher

Abstract

Action chunking improves the performance of policies learned by behavioural cloning, and several mechanisms have been proposed to explain why, including temporal consistency, horizon reduction, representation learning, and reduced error compounding. We instead study what happens to an action error once it enters the system. At each state, we inject a small action error and measure how fast it grows or shrinks under two execution regimes: open-loop, where the rest of the chunk is replayed without replanning, and closed-loop, where the policy replans after the perturbation. The fitted rate labels each state as contracting, expanding, or unresolved. Across twelve manipulation tasks from three benchmark suites, we find that confidently stable states are rare, while error amplification is common among states whose propagation rate can be resolved. We further find that the measured propagation rate depends strongly on the fitting horizon: amplification is typically front-loaded, so short windows can overestimate longer-horizon propagation. Finally, we train predictors on these labels and find that a state's open-loop regime can be recovered from camera frames and proprioception alone, while its closed-loop propagation is only partially recoverable because it also depends on how the policy acts after the perturbation. These results suggest that error-compounding arguments alone do not provide a complete account of action chunking: neither passive open-loop dynamics nor policy replanning consistently contracts an injected error, and replanning rarely turns open-loop amplification into confident contraction. This suggests that closed-loop reactivity should be trained explicitly, using perturbation- and tree-coverage-oriented training to expose policies to deviations they must recover from, rather than expected to emerge reliably from standard imitation learning.

Figures & tables

Figure 1: Per-state measurement of open-loop and closed-loop error propagation. At a state $s_{t}$ , a small action perturbation $\delta$ produces $\tilde{a}_{t}=a_{t}+\delta$ . We measure the resulting deviation from a nominal rollout under two regimes: (a) open-loop, where the remainder of the recorded action chunk is replayed without replanning, and (b) closed-loop, where the deployed policy replans at each subsequent step. Nominal and perturbed closed-loop branches share the same policy randomness. For each regime, we fit the log state deviation to obtain a propagation rate $\lambda_{\mathrm{ol}}$ or $\lambda_{\mathrm{cl}}$ , which is classified as stable, deadband, or unstable using the amplification and uncertainty gates.

Stamp type	State from	Actions used	$K$
demonstration	demonstration file	demonstrator actions, as recorded	24
rollout	policy rollout	policy actions, as recorded	24
policy chunk	policy rollout, at a replan boundary	chunk emitted by the policy	8 or 24
closed loop	policy rollout, at a replan boundary	policy replans at every step	24

Table 1: The four stamp types used in the analysis.

K

denotes the fitting window. For policy-chunk stamps,

K

is capped by the emitted chunk length, which is 8 actions for the diffusion policies and up to 24 on RoboCasa.

	CL stable	CL deadband	CL unstable
OL stable	both modes are non-amplifying; little propagation-based reason to shorten	no clear propagation-based preference	replanning introduces amplification; continued execution may avoid it
OL deadband	replanning provides evidence of contraction; shorter horizons may help	neither regime is resolved	replanning shows amplification; shortening should be weighed against other considerations
OL unstable	replanning contracts an otherwise growing error; shortening has direct propagation-based motivation	shortening removes the measured open-loop amplification but gives no evidence of contraction	both regimes amplify the error; shortening alone does not resolve the measured propagation problem

Table 2: Interpretation of the joint open- and closed-loop stability labels. The entries describe what the measured error-propagation behaviour implies for the execution-horizon decision. They are not prescriptions for chunk length: stability is one factor in that decision and does not determine task performance, action quality, or the globally preferred horizon.

Panel of Figure 2 — Figure 2: Distributions of the measured propagation rate $\lambda_{\mathrm{mean}}$ , pooled within each benchmark family. Columns correspond to robomimic, MimicGen, and RoboCasa; rows correspond to demonstration, rollout, policy-chunk, and closed-loop stamps. Stable, deadband, and unstable regions are shown by the bar segments. Vertical lines show the reference Gate-1 thresholds $\pm\ln(m)/16$ for $m\in\{1.5,2.0,3.0\}$ ; these are shown as a common visual reference and do not replace the window-specific threshold used for labeling. The demonstration, rollout, and closed-loop rates are fitted over $K=24$ , whereas the policy-chunk rate is capped by the emitted chunk length.

Dataset	Stamps	$\sigma_{u}$	$K$	$n$	median	p5–p95	$\lambda_{\mathrm{se}}$	G1 pass	G2 keep
robomimic — per-task diffusion policies
lift	demos	0.165	24	2,485	.015	$-$ .012–.184	.0076	543	96.7%
lift	rollouts	0.165	24	2,585	.019	$-$ .020–.127	.0084	690	97.0%
lift	policy	0.165	8	3,056	.090	.021–.458	.0216	2,620	83.8%
can	demos	0.225	24	9,254	.009	$-$ .032–.115	.0059	1,844	90.2%
can	rollouts	0.225	24	8,360	.019	$-$ .022–.116	.0078	2,511	95.5%

Table 3:

\lambda_{\mathrm{mean}}

on the open-loop axis, per dataset and stamp type.

\sigma_{u}

is the probe scale, the policy’s measured action RMSE;

K

is the fitting window, bounded on policy stamps by the emitted chunk.

\lambda_{\mathrm{se}}

is the median per-stamp standard error over the eight branches. G1 pass counts stamps clearing Gate 1 at

m{=}2.0

and G2 keep the fraction of those also clearing the

t

-test. IQR and the remaining quantiles are in Table 7 . Policies: per-task diffusion policies on robomimic and MimicGen, GR00T N1.5 on RoboCasa. † proxy

\sigma_{u}

; no policy was trained for these tasks, so they have no rollout or policy stamps.

robomimic
		$K{=}24$			$K{=}8$ (matched)
Dataset	Stamps	S	D	U	S	D	U
lift	demos	0.0	78.9	21.1	0.0	30.3	69.7
lift	rollouts	1.4	74.1	24.5	1.7	34.8	63.5
lift	policy	–	–	–	0.2	28.1	71.7
can	demos	2.9	82.0	15.1	1.4	38.0	60.6

Table 4: Open-loop label shares (%) at

m{=}2.0

t{=}2.365

, at the stored window and refit at

K{=}8

on the same stamps. S, D, U = stable, deadband, unstable. Policy stamps on robomimic and MimicGen are emitted as 8-action chunks and have no

K{=}24

entry.

Panel of Figure 3 — Figure 3: Open-loop $\times$ closed-loop label matrices pooled by platform for $m=1.5,2.0,3.0$ . Cells show the percentage of stamps in each joint label pair (S = stable, D = deadband, U = unstable). Blue outlines mark [OL unstable, CL stable] cells; green outlines mark [OL unstable, CL deadband] cells.

		Open-loop			Closed-loop
Dataset	Input	MAE 0	MAE	$\rho$	MAE 0	MAE	$\rho$
lift	P	.0792	.0535	.757	.0322	.0178	.819
	A1	.0792	.0400	.795	.0322	.0164	.841
can	P	.0981	.0635	.706	.0395	.0323	.520
	A1	.0981	.0568	.762	.0395	.0305	.553
square	P	.0877	.0790	.510	.0370	.0364	.332

Table 5: Prediction of open- and closed-loop propagation rates at the same policy-replan stamps. Both heads use the same trunk and inputs; only the target differs.

\mathrm{MAE}_{0}

is the constant-median baseline, and

\rho

is Spearman correlation with the measured rate. Bold denotes improvement over the constant-median baseline.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 4 — Figure 4: Task-level breakdown of stability labels across the four stamp types. For each task, the three adjacent bars correspond to Gate-1 thresholds $m=1.5$ , $2.0$ , and $3.0$ ; each bar is partitioned into stable, deadband, and unstable stamps.

robomimic
		$m{=}1.5$			$m{=}2.0$ (primary)			$m{=}3.0$
Dataset	Stamps	S	D	U	S	D	U	S	D	U
lift	demos	0.2	70.0	29.8	0.0	78.9	21.1	0.0	84.1	15.9
lift	rollouts	2.4	60.8	36.8	1.4	74.1	24.5	0.5	83.4	16.1
lift	policy	0.2	24.0	75.9	0.2	28.1	71.7	0.2	37.9	61.9
can	demos	4.7	71.4	23.9	2.9	82.0	15.1	1.1	89.2	9.7

Appendix

Table 6: Open-loop label shares in percent at

t{=}2.365

, across all three amplification settings. S = stable, D = deadband, U = unstable; rows sum to 100. Each row is evaluated at its stored fitting window:

K{=}24

for demonstration and rollout stamps, and the emitted chunk length for policy stamps.

Dataset	Stamps	$K$	median	IQR	p5	p95	$\lambda_{\mathrm{se}}$	$e^{16\lambda}_{\mathrm{med}}$
robomimic
lift	demos	24	.015	.005–.035	$-$ .012	.184	.0076	1.26
lift	rollouts	24	.019	.005–.044	$-$ .020	.127	.0084	1.36
lift	policy	8	.090	.059–.139	.021	.458	.0216	4.23
can	demos	24	.009	$-$ .003–.028	$-$ .032	.115	.0059	1.15
can	rollouts	24	.019	.002–.048	$-$ .022	.116	.0078	1.36

Appendix

Table 7: Full

\lambda_{\mathrm{mean}}

quantiles on the open-loop axis. The table extends the main-text rate summaries with the interquartile and

5

–

95

percentile ranges.

e^{16\lambda}_{\mathrm{med}}

converts the median rate to error amplification over 16 steps. For rows measured at

K{=}8

, this extrapolates beyond the measured window and should therefore be read only as a derived quantity, not as an observed 16-step trajectory.

Panel of Figure 5 — Figure 5: $\lambda_{\mathrm{mean}}$ on the open-loop axis at $K{=}8$ , $16$ , and $24$ for the OpenCabinet demonstration stamps ( $n{=}33{,}238$ ), refit from the same stored per-branch log-distance matrices with no new simulation. The three curves therefore describe identical stamps and differ only in the length of the fitting interval. Verticals mark $\pm 0.0433$ , the primary Gate-1 threshold at $m{=}2.0$ .

Dataset	var	base MAE	MAE	$\rho$	AUROC	neg (per seed)
demonstration stamps
lift	P	.0351	.0272	.704	–	0; 0; 0
lift	A1	.0351	.0216	.718	–	0; 0; 0
can	P	.0281	.0284	.392	.722	50; 49; 46
can	A1	.0281	.0280	.426	.797	50; 49; 46
square	P	.0343	.0309	.526	.712	40; 45; 45

Appendix

Table 8: Open-loop prediction results, means over three seeds. base MAE is a constant-median predictor on the same validation split.

\rho

is the Spearman correlation between predicted and measured

\lambda

, and AUROC is computed over the confident subset. neg gives the number of negative examples behind each seed’s AUROC.

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