Beyond Instruction Following: Learning Grounded Skill-Following with Skill Contracts

Jianghan Shen; Zhenjie Liu; Yue Li; Jie Huang; Siqi Luo; Yiming Cheng; Yizhi Yao; Kaijie Zhang

cs.AIOct 4, 2026

Beyond Instruction Following: Learning Grounded Skill-Following with Skill Contracts

Authors: Jianghan Shen, Zhenjie Liu, Yue Li, Jie Huang, Siqi Luo, Yiming Cheng, Yizhi Yao, Kaijie Zhang, +5 more

Organizations: Nanjing University · Shanghai Artificial Intelligence Laboratory · Peking University · Yiyue Technology · Tsinghua University · Northeastern University

Abstract

Instruction following typically enforces discrete, response-level requirements, whereas an expert-authored skill prescribes procedural requirements spanning multiple phases and environment interactions. Given such a skill, we train the executor to execute all required phases instead of focusing solely on the final answer. We therefore introduce Grounded Skill-Following, which requires an agent to execute a fixed, expert-authored skill across its required phases by grounding decisions in environment observations. To achieve verifiable procedural execution, we formulate each skill as a skill contract combining visible skill instructions with an explicit contract runtime. The runtime specifies required phases, admissible actions, permitted transitions, and accepted termination. This structure provides a dense, verifiable training signal throughout execution. We leverage this by introducing Verified Progress Credit, which assigns rewards upon the initial completion of contract milestones and aggregates them into the trajectory return to guide policy optimization. During rollout, the contract runtime continuously tracks state transitions to provide Contract-State Feedback, which indicates whether the latest action is accepted and guides the agent toward valid next actions. To measure procedural compliance, we introduce the Protocol Completion Rate (PCR), defined as reaching accepted termination through all required phases, and decouple it from the final Task Outcome. Jointly trained with our framework, Qwen3.5-4B achieves Protocol Completion Rates of 99.27% on Math and 99.96% on Search, while slightly outperforming original baselines in Task Outcome (82.95% and 46.61%, respectively). Controlled studies examine how skill instructions, training signals, and contract-state feedback affect both metrics, while withholding interventions evaluate behavioral dependence on observation content.

Figures & tables

Figure 1: Complementary views of skills. Grounded skill-following fixes an expert-authored skill and trains its executor, alongside local instruction compliance and skill-lifecycle optimization. The views overlap and are not a historical taxonomy.

Figure 2: Skill-contract training for grounded skill-following. The contract $\mathcal{C}_{j}$ pairs visible skill instructions $z_{j}$ with a contract runtime. The runtime checks each action, credits newly verified progress, and provides contract-state feedback after each nonterminal transition. The feedback describes the current phase without exposing internal bookkeeping.

Qwen2.5-3B
	Math					Search
Setting	MATH tr	GSM tr	Avg.	PCR	RF-PCR	NQ tr	TQA ho	Pop ho	HQA tr	2W ho	MuS ho	Bam ho	Avg.	PCR	RF-PCR
Direct	17.00	26.08	21.54	n/a	n/a	2.27	6.31	3.11	2.84	5.16	0.12	1.60	3.06	n/a	n/a
Prompt	0.16	0.00	0.08	0.16	0.00	0.08	0.14	0.14	0.09	0.25	0.00	0.00	0.10	0.20	0.00
Recipe	45.16	81.20	63.18	n/a	n/a	45.26	61.73	44.00	32.14	29.21	6.37	10.40	32.73	n/a	n/a
Ours-S	48.62	80.59	64.61	97.29	94.54	46.34	60.53	45.67	30.34	29.87	6.91	16.00	33.67	99.82	98.54

Table 1: Task Outcome, PCR, and RF-PCR on Math and Search (%). RF-PCR excludes samples that receive rejected-action feedback. Direct evaluates frozen checkpoints without the contract runtime, while Prompt preloads the skill and uses the runtime. Recipe pairs task-specific adaptations, Ours-S trains each domain separately, Ours-J trains them jointly, and n/a denotes an absent protocol metric. Bold marks the highest value in each metric column within each model block, including ties. Averages are unweighted, while tr and ho mark training and held-out datasets.

Figure 3: Qwen2.5-3B learning dynamics under the same contract runtime with feedback disabled. Each point averages a fixed monitor of 250 examples per dataset: (a) MATH and GSM8K, (b) Natural Questions and MuSiQue. Verified progress credit yields nonzero PCR and Task Outcome in both domains, while Outcome-only remains at zero.

	A: Recovery coefficient				B: Feedback removal
Domain	$\rho$	Task Outcome	PCR	RF-PCR	Task Outcome			PCR
Domain	$\rho$	Task Outcome	PCR	RF-PCR	On	Off	Change	On	Off
Math	0.90	62.12	94.46	93.78	64.61	58.25	$-6.36$	97.29	86.93
Math	1.00	64.61	96.23	0.00	64.61	58.25	$-6.36$	97.29	86.93
Search	0.90	28.81	98.90	98.18	30.11	13.15	$-16.96$	98.90	43.05
Search	1.00	29.51	99.53	88.33	30.11	13.15	$-16.96$	98.90	43.05

Table 2: Training- and inference-time recovery interventions. Panel A compares independently trained Qwen2.5-3B joint conditions with

\rho=0.90

and

\rho=1.00

. Panel B removes feedback at inference from frozen Qwen2.5-3B single-task checkpoints. Both panels report unweighted averages over MATH and GSM8K for Math and 2WikiMultiHopQA and HotpotQA for Search. Values are percentages, and changes are percentage points.

Figure 4: Qwen2.5-3B interventions on (a) contract-state feedback and verified progress credit during training, (b) visible skill instructions at inference, and (c) observation content at inference. Values are percentages or percentage-point changes.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Phase	Accepted action	Next phase
NEED_SKILL	Expected skill call	NEED_PLAN
NEED_PLAN	Substantive planning thought	NEED_ACTION
NEED_ACTION	Admissible environment action	NEED_EVIDENCE_THINK
NEED_EVIDENCE_THINK	Substantive evidence reasoning	CAN_CONTINUE_OR_ANSWER after a valid observation, otherwise NEED_ACTION
CAN_CONTINUE_OR_ANSWER	Repeated environment action, first optional Search evidence-organization action with <summary> , or final answer	NEED_EVIDENCE_THINK , CAN_CONTINUE_OR_ANSWER , or DONE , respectively. A repeated evidence-organization action is rejected
DONE	None	Terminal

Appendix

Table 3: Phase set

\mathcal{Q}_{j}

shared by Math and Search. A rejected action preserves the current phase and returns one admissible next action. Table 6 defines substantive thought.

Order	Operation	Update
1	Initialize	Set initial contract state $S_{0}^{j}=(\texttt{NEED\_SKILL},\varnothing,0)$ . Initialize context $x_{0}^{j}$ with system scaffold and task prompt (Appendix B.1 ).
2	Generate	Sample action $a_{t}\sim\pi_{\theta}(\cdot\mid x_{t}^{j})$ .
3	Transition	Execute state transition via Equation 4 . Set $o_{t+1}=\bot$ when no observation is generated. Action rejection preserves $q_{t}^{j}$ and $\mathcal{M}_{t}^{j}$ , setting $h_{t+1}=1$ when feedback is enabled. Action acceptance records new milestones scaled by $\rho^{h_{t}}$ , then resets $h_{t+1}=0$ .
4	Record	Record newly verified milestones $\Delta\mathcal{M}_{i,t}^{j}$ and update context via Equation 5 , omitting $\bot$ and prepending skill instructions $z_{j}$ upon first accepted skill call.
5	Repeat	Repeat Order 2–4 until accepted termination or budget exhaustion. Exhaustion does not constitute Protocol Completion.
6	Score	Compute final trajectory return $R_{i}$ using Equation 7 .

Appendix

Table 4: Runtime execution order for one skill-contract trajectory.

Milestone	Scope	Weight	Contract location	First-completion condition
Skill	Both	0.10	NEED_SKILL	The expected <skill_call> is accepted.
Plan	Both	0.10	NEED_PLAN	A substantive <think> is accepted.
Action	Both	0.20	NEED_ACTION	The first admissible <code> , <search> , or <research> passes its task adapter.
Observation	Both	0.20	NEED_ACTION $\rightarrow$ NEED_EVIDENCE_THINK	Math execution produces nonempty output, or Search returns at least one nonempty document.
Evidence reasoning	O-Math	0.20	NEED_EVIDENCE_THINK	A substantive <think> is accepted.
Evidence reasoning	O-Search	0.10	NEED_EVIDENCE_THINK	A substantive <think> is accepted.

Appendix

Table 5: Milestone set

\mathcal{M}_{j}

and first-completion weights used for verified progress credit. Each contract location maps the credit event to the shared phase or transition in Table 3 . The task reward is a separate binary term. Table 6 defines substantive thought. For Search, evidence organization through <summary> is optional for accepted termination. Its verified progress credit encourages this optional action, so permitted trajectories need not receive equal progress credit.

Phase	O-Math	O-Search
NEED_SKILL	Accept the expected code-interpreter-protocol skill call.	Accept the expected qa-search-protocol skill call.
NEED_PLAN	Accept a substantive <think> that plans the calculation.	Accept a substantive <think> that plans retrieval.
NEED_ACTION	Accept executable Python that prints a result in <code>...</code> . The restricted interpreter returns <interpreter> . The observation is valid when execution succeeds and printed output is nonempty. The accepted action enters NEED_EVIDENCE_THINK .	Accept the first admissible query in <search> and later nonrepeated admissible queries in <research> . The frozen retriever returns <information> . The observation is valid when at least one retrieved document is nonempty. The accepted action enters NEED_EVIDENCE_THINK .
NEED_EVIDENCE_ THINK	Accept a substantive <think> that interprets the interpreter result. A valid observation opens continuation or answering. An invalid one returns to NEED_ACTION .	Accept a substantive <think> that assesses the retrieved evidence. A valid observation opens continuation or answering. An invalid one returns to NEED_ACTION .
CAN_CONTINUE_ OR_ANSWER	Repeat <code>...</code> and re-enter evidence reasoning, or accept a nonempty boxed answer and enter DONE .	Repeat retrieval with <research> and re-enter evidence reasoning. Optionally accept one substantive <summary> as evidence organization, with no retriever call, no observation, and no phase change. Alternatively, accept a nonempty <answer> and enter DONE .
DONE	Terminal. Score the accepted answer by normalized numerical match.	Terminal. Score the accepted answer by dataset-normalized exact match.

Appendix

Table 6: Task-specific instantiation of

\operatorname{Step}_{j}

by phase. Table 3 defines the shared transitions, and Table 5 locates verified progress credit. For <think> , “substantive” requires at least 12 characters after whitespace normalization, including at least 6 alphanumeric characters. These are form-based checks and do not assess reasoning quality.

Condition	GPU	TP	Rounds	P/R	S/P	U/R	Batch
O-Math / Math interventions	4	2	200	72	5	5	72
O-Search / Search interventions	4	2	200	512	5	10	256
O-Joint	4	2	400	72	5	5	72
Recovery-coefficient comparison	4	2	400	72	5	5	72

Appendix

Table 7: Online training configurations. P/R is prompts per rollout, S/P is samples per prompt, and U/R is optimizer updates per rollout. Model-scale runs reuse the corresponding task profile, and the Feedback + Credit conditions in RQ2 reuse the main single-task runs.

Domain	Condition	Feedback	Credit	Outcome	PCR
Search	B00 Outcome-only	0	0	0.00	0.00
Search	B10 Feedback-only	1	0	0.00	0.00
Search	B01 Credit-only	0	1	29.28	98.69
Search	B11 Feedback + Credit	1	1	30.11	98.90
Math	B00 Outcome-only	0	0	0.00	0.00
Math	B10 Feedback-only	1	0	0.00	0.00

Appendix

Table 8: Training-time feedback-credit factorial on Qwen2.5-3B. Each condition is trained independently from the same base checkpoint within its domain. The task reward and contract runtime are fixed, while Feedback toggles contract-state feedback and Credit toggles verified progress credit. Outcome-only uses the contract runtime, in which rejected actions do not receive a penalty or terminate the trajectory, but only a final answer accepted after all required phases can receive the task reward. Task Outcome and PCR are unweighted averages over MATH and GSM8K for Math and 2WikiMultiHopQA and HotpotQA for Search.

Domain	Visible skill	MATH	GSM	2Wiki	Hotpot	Avg.	PCR	Hint Rate
Math	Original	48.62	80.59	–	–	64.61	97.29	5.59
Math	Removed	42.76	74.68	–	–	58.72	91.34	11.70
Math	Paraphrased	43.92	75.59	–	–	59.75	94.36	7.27
Math	Wrong Search	1.48	2.35	–	–	1.92	4.71	99.69
Search	Original	–	–	29.87	30.34	30.11	98.90	0.99
Search	Removed	–	–	22.57	18.51	20.54	63.81	14.86

Appendix

Table 9: Inference-time visible skill instruction interventions on frozen Qwen2.5-3B single-task checkpoints. Only the visible skill instructions

z_{j}

change. Paraphrased rewrites wording, plan descriptions, and transition language while preserving action tags, action order, environment-owned observations, repeated-action permission, and the termination format. Appendix E.2.1 gives the exact Math and Search bodies. Outcome is pass@1 for Math and exact match for Search.

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