Meta-Ctrl: Guaranteed Plan Generation by Decoupling Syntactic and Semantic Constraints

Gwen Yidou-Weng; Edward Sun; Tianyi Ma; Metin Alp Dogan; Benjie Wang; Allen Peng; Guy Van den Broeck; Yuchen Cui

cs.ROAug 23, 2026

Meta-Ctrl: Guaranteed Plan Generation by Decoupling Syntactic and Semantic Constraints

Authors: Gwen Yidou-Weng, Edward Sun, Tianyi Ma, Metin Alp Dogan, Benjie Wang, Allen Peng, Guy Van den Broeck, Yuchen Cui

Organizations: University of California, Los Angeles · Michigan State University

Abstract

LLMs generate fluent plans for robots but routinely violate the syntactic and se8mantic constraints they must satisfy to execute, and existing remedies trade formal guarantees against plan quality: soft methods (affordance scoring, grounded decoding) give no guarantee, while symbolic planners (LLM+P) discard the LM's commonsense. We propose Meta-Ctrl, a constrained-decoding framework that guarantees the encoded constraints while preserving the base LM's plan quality. Meta-Ctrl introduces meta-tokens---a compact vocabulary of grounded actions---enforcing syntax at the token level and semantics (preconditions, goals, ordering) at the action level, an exact factorization that cuts the memory of constrained decoding from over 107TB to under 2GB. With it, a small open-weight LM becomes competitive where it otherwise sits at the bottom of the leaderboard: on WAH-NL under the LoTa-Bench protocol it reaches the highest reported subgoal success rate, exceeding GPT-4's, with consistent gains across the Embodied Agent Interface. We further demonstrate it on a real tabletop robot, where every generated plan satisfies its preconditions and goals by construction. Project website: https://metactrlg.github.io

Figures & tables

Figure 1: Meta-Ctrl enforces preconditions that the base LM violates. Task: put dishes in dishwasher; PUTIN requires holding an object and an open container. The base LM (top) attempts PUTIN while the dishwasher is closed. Meta-Ctrl (bottom) enforces the action-level precondition, inserting OPEN (dishwasher).

Panel of Figure 2 — Figure 2: Level 2: action-level semantics. The parser $\tau$ projects each action block of tokens (e.g. {"GRAB":"plate"} ) to one meta-token ( Grab (plate)). A DFA $\mathcal{D}_{\beta}$ over meta-tokens enforces preconditions and goal progress (e.g. Put requires the container open). Operating on a small action vocabulary, rather than raw tokens, is what makes the factored computation below tractable.

External references (different LM / executor)
Method	Base LM	SR	SSR	Exec
SayCan	—	0.010	0.021	—
ProgPrompt	—	0.030	0.187	—
LoTa-Bench	GPT-4	—	0.342	—
LoTa-Bench	LLaMA-1 65B	—	0.433	—
STEP †	(larger)	0.400	0.620	—

Table 2: WAH-NL (single-agent,

n=100

) under the LoTa-Bench protocol. External references use different LMs and executors; we report them as ballpark context, not strict baselines. Empty entries are not reported. Same-LM rows (Llama 3.1 8B) are direct comparisons. † STEP is closed-loop; ours is open-loop.

	Action Sequencing				Subgoal Decomposition
	Task SR		Exec SR		Task SR		Exec SR
Model	VH	BEH	VH	BEH	VH	BEH	VH	BEH
Representative baselines
GPT-4o	71.5	47.0	81.3	53.0	87.6	49.0	91.1	55.0
Claude-3.5 Sonnet	76.1	60.0	81.3	69.0	89.1	39.0	92.0	44.0
o1-preview	65.2	81.0	72.5	91.0	89.4	60.0	93.2	62.0

Table 3: Embodied Agent Interface results on VirtualHome (V;

n{=}342

AS,

338

SD) and BEHAVIOR (B;

n{=}100

AS,

100

SD). Task SR and Execution SR (%). Leaderboard baselines from [ 9 ] ; Each base LM is grouped with its full Meta-Ctrl (

\gamma{+}\beta

) result. Bold : best per column; underline : second-best. ‡ The gpt-oss rows use a keyword-based BEHAVIOR affordance prior; the Llama rows use the taxonomy-derived specification of Appendix G . Our VirtualHome cells are means over six evaluator seeds (Appendix K ).

Base LM	unconstrained	+ Meta-Ctrl	changed lines
Llama 3 8B Instruct	21.3 / 23.6	90.7 / 97.7	—
Qwen3-8B	50.8 / 58.4	90.7 / 97.7	${\sim}40$
Gemma-3-12B-it	47.5 / 50.5	89.4 / 96.1	${\sim}35$

Table 4: Porting Meta-Ctrl to newer base LMs, VH AS (

n{=}342

), task / execution SR (%). Each port rebuilds

\gamma

over the new tokenizer automatically and uses a uniform token-level HMM over the new vocabulary; the meta level is unchanged (uniform meta-surrogate rows for all three bases). No training of any kind. VH-AS means over six evaluator seeds.

with our meta-level automata:
Method (Llama 3 8B)	VH AS	VH SD	BEH AS	BEH SD
LLM only (unconstrained)	21.3 / 23.6	48.8 / 58.0	10 / 16	22 / 29
LLM + syntax-only GCD ( $\gamma$ mask)	1.4 / 97.3	0.0 / 96.0	12 / 20	19 / 31
Classical planner, full domain	47.2 / 84.6	n/a	13 / 37	n/a
Search, no LLM	83.8 / 93.1	72.5 / 79.0	31 / 77	52 / 64
LLM + masking (reachability only)	81.7 / 87.5	88.7 / 92.6	33 / 85	38 / 51

Table 5: What each component contributes, task / execution SR (%) on Llama 3 8B. Rows 3–6 share the same constraint construction (meta-tokens,

\gamma

and

\beta

compiled from the prompt and the public object taxonomy) and the same guarantee; they differ only in the guidance signal. Search, no LLM is breadth-first search over the meta-level automaton with the LM removed. Masking keeps only the support of the lookahead term, a reachability yes/no. Uniform and trained instantiate the lookahead measure itself. Classical planner is Fast Downward given the benchmark’s own PDDL domain, i.e. a complete transition model, strictly more information than our automata encode; SD asks for goal states rather than actions, so planners do not apply.

Figure 3: Real robot setup with xArm 7 and deployed tabletop manipulation tasks. Top-row tasks require only pick-and-place; bottom-row tasks require specialized motion primitives (e.g. open door).

	Meta-Ctrl (ours)			Baseline (Llama 3 8B)
Task	Planning	Perception	Execution	Planning	Perception	Execution
Put donut in canister	20/20	17/20	16/20	2/20	18/20	1/20
Pick up green block (under blocker)	20/20	19/20	18/20	1/20	19/20	1/20
Stack dishes by size	20/20	20/20	17/20	0/20	19/20	0/20

Table 6: Real robot evaluations on an XArm7,

20

repetitions per task. Meta-Ctrl columns are a cascade: plan success holds by construction; perception and execution are conditional on preceding stages. Baseline perception is scored per-module, independent of plan validity; its execution is end-to-end and bounded by planning failures. Baseline downstream columns are thus not directly comparable to Meta-Ctrl’s.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

	Vocab	Token-level HMM	Meta-token HMM
VH-AS	132 actions / $128$ K tokens	${\sim}16.4$ M	${\sim}33$ K
VH-SD	123 predicates / $128$ K	${\sim}16.4$ M	${\sim}32$ K
BEH-AS	132 actions / $128$ K	${\sim}16.4$ M	${\sim}33$ K
BEH-SD	123 predicates / $128$ K	${\sim}16.4$ M	${\sim}32$ K
WAH-NL	7 actions + 128 ids / $128$ K	${\sim}16.4$ M	${\sim}34$ K

Appendix

Table 7: HMM parameter counts. Token-level HMM size is dominated by the emission matrix

H\times|V|

; meta-token HMM is dominated by the

H\times H

transition matrix at this scale.

H{=}128

throughout; token-level

|V|

shown for the Llama-3 tokenizer (gpt-oss uses

|V|{\approx}201

\Rightarrow

{\sim}25.7

M).

Task	Prompt id	DFA-only ( $\gamma$ mask)	Meta-Ctrl ( $\gamma{+}\beta$ )
Turn on light	scene_1_125_2	NEXT_TO(character.65, light.411)	PLUGGED_IN(light.411), ON(light.411)

Appendix

Table 9: Representative outputs from DFA-only (

\gamma

hard mask) and Meta-Ctrl (

\gamma{+}\beta

) on VirtualHome Subgoal Decomposition. DFA-only emits a single locally-true predicate and stops; Meta-Ctrl produces the predicates required to reach the goal.

Module	Error class	Raw Llama 3 8B	Meta-Ctrl
			Total	Benchmark-side	LM-fault
BEH AS	Parsing	0.0%	0.0%	0.0%	0.0%
	Hallucination	15.0%	0.0%	0.0%	0.0%
	Parameter	9.0%	0.0%	0.0%	0.0%
	Sum format/hallucination	24.0%	0.0%	0.0%	0.0%
VH AS	Parsing	14.4%	1.3%	1.3% a	0.0%

Appendix

Table 10: Format and hallucination error rates for raw Llama 3 8B and Meta-Ctrl. Parsing : output fails the evaluator’s parser. Hallucination : output references objects or predicates not present in the evaluator’s per-task vocabulary. Parameter : argument arity, type, or formatting mismatch. The Meta-Ctrl benchmark-side column counts plans rejected by the evaluator even though they comply with the prompt’s stated grammar and vocabulary (footnotes identify each case). The LM-fault column is the residual after removing benchmark-side rejections, and is zero across every module and error class.

Recent frontier models
	Action Sequencing				Subgoal Decomposition
	VH		BEH		VH		BEH
Model	T	E	T	E	T	E	T	E	Avg
Claude Opus 4.8	87.9	86.2	74.0	81.0	90.8	93.8	61.0	65.0	78.4
Claude Opus 4.7	77.7	76.1	73.0	82.0	91.1	93.8	64.0	71.0	76.5
Claude Opus 4.6	74.4	74.8	78.0	87.0	92.9	95.6	78.0	82.0	80.8

Appendix

Table 11: Extended Embodied Agent Interface results on recent models, evaluated by us under the official EAI protocol. Task SR (T) and Execution SR (E) on VirtualHome (VH;

n=342

AS,

338

SD) and BEHAVIOR (BEH;

n=100

AS,

100

SD). Meta-Ctrl rows from Table 3 included for reference. Bold : best per column; underline : second-best.

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Large language model-based robot planning turns natural-language goals and sensory observations into grounded, executable actions for robots.

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