SCOPE: Selective Certification of Program Edits for Embodied Heuristic Learning

Junyang Shu; Bingqing Wei; Jishuo Li; Zheqi He; Yongtao Wang

cs.ROOct 16, 2026

SCOPE: Selective Certification of Program Edits for Embodied Heuristic Learning

Authors: Junyang Shu, Bingqing Wei, Jishuo Li, Zheqi He, Yongtao Wang

Organizations: Wangxuan Institute of Computer Technology, Peking University, China · Beijing Academy of Artificial Intelligence · VGI Labs

Abstract

Embodied heuristic learning must balance strategic adaptation with the preservation of previously successful behavior. Local repairs may leave structural failures unresolved, whereas broader revisions can introduce regressions that are costly to detect through repeated environment interaction. We introduce SCOPE (Selective Certification Of Program Edits), which uses failed and successful executions as complementary evidence for program revision. Frontier-guided program search annotates a shared diagnostic graph with execution evidence to distinguish supported progress from unresolved checks. Selective behavioral certification uses stateful API replay to restore recorded responses and mutations, checking whether edits preserve selected historical successes. Diagnosis and certification feedback, supplemented by sparse environment diagnostics, guide consecutive repairs across configurations. SCOPE outperforms the strongest baseline in both simulation and real-world tasks. On LIBERO-PRO and Robosuite, it achieves mean success rates of 80.66% and 84.48%, with respective gains of 6.51 and 3.48 percentage points. Our code is available at https://github.com/VDIGPKU/SCOPE.

Figures & tables

Figure 1: Overview of SCOPE. Execution evidence annotates a shared diagnostic graph to guide local repair, stage redesign, or strategy regeneration. Success updates the accepted program and historical success bank. When the accepted source changes, selected historical tapes are replayed by a local executor. Full matches certify the recorded instances under the replay assumptions. Sparse environment diagnostics on uncertified configurations supply failure evidence for subsequent repair. The accepted program is frozen after search.

Figure 2: Stateful full-trace replay. (a) A local executor compares each API request and pre-call state with the tape, reproduces the recorded response and mutations while preserving shared references, and resumes the program. Omitting a mutation changes the next request in this illustrative example. (b) Matching every event, making no extra external calls, and terminating normally certifies success on the recorded instance $\xi_{w}$ under the replay assumptions. A changed argument stops replay at the first divergence, leaving the instance uncertified.

Method	Object		Goal		Spatial		Overall
Method	Pos	Task	Pos	Task	Pos	Task	Pos	Task	All
OpenVLA	$0.00$	$0.00$	$0.00$	$0.00$	$0.00$	$0.00$	$0.00$	$0.00$	$0.00$
$\pi_{0}$	$0.00$	$0.00$	$0.00$	$0.00$	$0.00$	$0.00$	$0.00$	$0.00$	$0.00$
SUREFlow	$0.00$	$0.00$	$0.00$	$0.00$	$0.00$	$0.00$	$0.00$	$0.00$	$0.00$
MolmoAct	$6.00$	$0.00$	$0.00$	$0.00$	$0.00$	$0.00$	$2.00$	$0.00$	$1.00$
X-VLA	$2.00$	$8.00$	$1.00$	$9.00$	$0.00$	$0.00$	$1.00$	$5.67$	$3.33$

Table 1: LIBERO-PRO results. Success rates (%) under position swaps (Pos) and task changes (Task). Overall averages over suites, and All averages over both settings.

Method	Cube lift	Cube stack	Cube restack	Spill wipe	Two arm handover	Two arm lift	Nut assembly	Mean
CaP-Agent0	$97.00$	$98.00$	$89.00$	$\mathbf{100.00}$	$20.00$	$74.00$	$0.00$	$68.29$
RHO †	$98.00$	$98.00$	$54.00$	$\mathbf{100.00}$	$86.00$	$53.00$	$1.00$	$70.00$
ASPIRE Opus 4.6	$97.00$	$\mathbf{99.00}$	$\mathbf{100.00}$	$99.00$	$\mathbf{92.00}$	$71.00$	$9.00$	$81.00$
ASPIRE GLM-5.3-Flash	$98.33$ $\pm\,1.53$	$97.33$ $\pm\,1.53$	$97.67$ $\pm\,1.53$	$98.33$ $\pm\,1.15$	$88.67$ $\pm\,5.13$	$70.33$ $\pm\,6.81$	$10.67$ $\pm\,4.73$	$80.19$ $\pm\,2.14$
SCOPE GLM-5.3-Flash	$\mathbf{100.00}$ $\pm\,0.00$	$\mathbf{99.00}$ $\pm\,1.00$	$\mathbf{100.00}$ $\pm\,0.00$	$\mathbf{100.00}$ $\pm\,0.00$	$91.67$ $\pm\,3.21$	$\mathbf{86.00}$ $\pm\,3.61$	$\mathbf{14.67}$ $\pm\,4.93$	$\mathbf{84.48}$ $\pm\,1.67$

Table 2: Robosuite results. Success rates (%) on seven manipulation tasks. Mean averages over tasks.

Task	Capability	ASPIRE	SCOPE
Cube into basket	Base–arm coordination	9/20 (45.0%)	15/20 (75.0%)
Two arm lift	Bimanual coordination	10/20 (50.0%)	14/20 (70.0%)
Cube restack	Fine manipulation	5/20 (25.0%)	11/20 (55.0%)
Overall	—	24/60 (40.0%)	40/60 (66.7%)

Table 3: Real-world generalization. Successes/trials (success rate) for frozen programs on 20 held-out physical configurations per task. Overall pools 60 trials per method. Bold marks the higher success rate.

Figure 3: Real-world repair of a cube-in-basket task. (a) Gripper occlusion prompts backward motion for localization. (b) The target is visible but out of reach, prompting forward motion. (c) Renewed occlusion motivates caching the target position before approaching. (d) The revised program completes the task. Each panel pairs a key frame with the corresponding repair or outcome.

Method / variant	Goal–Task	Spatial–Pos
ASPIRE (baseline)	$48.80\,\pm\,11.68$	$54.47\,\pm\,3.45$
Full SCOPE	$61.87\,\pm\,5.41$	$65.40\,\pm\,3.82$
w/o certification feedback	$57.60\,\pm\,7.33$	$59.33\,\pm\,4.16$
w/o failure-frontier guidance	$55.07\,\pm\,9.10$	$59.93\,\pm\,3.72$
w/o explicit revision-level planning	$58.87\,\pm\,7.11$	$62.13\,\pm\,3.88$

Table 4: Component ablations on LIBERO-PRO. Success rates (%) on all 10 tasks in each setting with GLM-5.3-Flash, reported as mean

\pm

sample standard deviation over three runs.

Figure 4: Certification rates and feedback costs of SCOPE. Each point is a task macro-average for one setting with GLM-5.3-Flash, covering 60 LIBERO-PRO task–setting pairs and seven Robosuite tasks. (a) Certification rate versus replay time relative to the corresponding original environment execution. (b) Certification-pipeline and diagnostic environment-execution times, each relative to total development learning time. Labels give

(x,y)

in percent. Circles and triangles denote LIBERO-PRO Pos and Task settings, while stars denote Robosuite. The certification pipeline includes replay, retrieval, verification, and self-matching. Diagnostic time covers environment execution only.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Setting	Certification rate	Replay time / original execution time	Certification time / total learning time	Diagnostic trial time / total learning time
Object–Pos	60.6	4.93	0.54	0.87
Object–Task	55.3	5.53	0.83	1.41
Goal–Pos	49.0	6.12	0.75	1.28
Goal–Task	38.9	6.59	1.36	2.67
Spatial–Pos	42.1	6.25	1.04	2.04
Spatial–Task	41.9	5.94	0.98	2.12

Appendix

Table 5: Certification rates and costs of SCOPE. Task macro-averages (%) with GLM-5.3-Flash over 60 LIBERO-PRO task-setting pairs and seven Robosuite tasks.

Figure 5: Real-world task executions. Representative frames progress from left to right for Cube into basket (top), Two arm lift (middle), and Cube restack (bottom). The tasks evaluate mobile manipulation with base–arm coordination, bimanual coordination, and fine manipulation, respectively.

LIBERO-Object
Task	ASPIRE Opus 4.6	ASPIRE GLM-5.3-Flash	SCOPE GLM-5.3-Flash
Alphabet soup	$\mathbf{100.00}$	$98.67\,\pm\,1.15$	$\mathbf{100.00}\,\pm\,0.00$
BBQ sauce	$\mathbf{100.00}$	$99.33\,\pm\,1.15$	$\mathbf{100.00}\,\pm\,0.00$
Butter	$\mathbf{100.00}$	$98.67\,\pm\,2.31$	$99.33\,\pm\,1.15$
Chocolate pudding	$\mathbf{100.00}$	$98.67\,\pm\,2.31$	$\mathbf{100.00}\,\pm\,0.00$
Cream cheese	$\mathbf{100.00}$	$98.00\,\pm\,2.00$	$\mathbf{100.00}\,\pm\,0.00$

Appendix

Table 6: Success rates (%) for individual LIBERO tasks under the Pos setting.

LIBERO-Object
Task	ASPIRE Opus 4.6	ASPIRE GLM-5.3-Flash	SCOPE GLM-5.3-Flash
Alphabet soup	$\mathbf{100.00}$	$98.00\,\pm\,2.00$	$\mathbf{100.00}\,\pm\,0.00$
BBQ sauce	$\mathbf{100.00}$	$99.33\,\pm\,1.15$	$\mathbf{100.00}\,\pm\,0.00$
Butter	$98.00$	$98.67\,\pm\,2.31$	$\mathbf{100.00}\,\pm\,0.00$
Chocolate pudding	$\mathbf{100.00}$	$98.67\,\pm\,1.15$	$99.33\,\pm\,1.15$
Cream cheese	$72.00$	$84.00\,\pm\,5.29$	$\mathbf{91.33}\,\pm\,4.16$

Appendix

Table 7: Success rates (%) for individual LIBERO tasks under the Task setting.

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