# Long SKILL Compliance as Logical Reasoning: Closure-Grounded Detection with Scaling-Guided On-Policy Distillation

arXiv: https://arxiv.org/abs/2608.08146 · HTML: https://mlsanity.com/paper/2608.08146/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 28 of its 39 references that are in the map.
- First posted on arXiv 8 Aug 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 28 of 28)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [From Local to Global: A Graph RAG Approach to Query-Focused Summarization](https://mlsanity.com/paper/2404.16130/) (2024)
- [τ-bench: A Benchmark for Tool-Agent-User Interaction in Real-World Domains](https://mlsanity.com/paper/2406.12045/) (2024)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [τ2-Bench: Evaluating Conversational Agents in a Dual-Control Environment](https://mlsanity.com/paper/2506.07982/) (2025)
- [LongLLMLingua: Accelerating and Enhancing LLMs in Long Context Scenarios via Prompt Compression](https://mlsanity.com/paper/2310.06839/) (2023)
- [LLMLingua-2: Data Distillation for Efficient and Faithful Task-Agnostic Prompt Compression](https://mlsanity.com/paper/2403.12968/) (2024)
- [LightRAG: Simple and Fast Retrieval-Augmented Generation](https://mlsanity.com/paper/2410.05779/) (2024)
- [SkillsBench: Benchmarking How Well Agent Skills Work Across Diverse Tasks](https://mlsanity.com/paper/2602.12670/) (2026)
- [Generalizing Verifiable Instruction Following](https://mlsanity.com/paper/2507.02833/) (2025)
- [MiniLLM: On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2306.08543/) (2023)
- [Context Length Alone Hurts LLM Performance Despite Perfect Retrieval](https://mlsanity.com/paper/2510.05381/) (2025)
- [Multi-IF: Benchmarking LLMs on Multi-Turn and Multilingual Instructions Following](https://mlsanity.com/paper/2410.15553/) (2024)
- [SWE-Skills-Bench: Do Agent Skills Actually Help in Real-World Software Engineering?](https://mlsanity.com/paper/2603.15401/) (2026)
- [Inference Scaling for Long-Context Retrieval Augmented Generation](https://mlsanity.com/paper/2410.04343/) (2024)
- [SkillLearnBench: Benchmarking Continual Learning Methods for Agent Skill Generation on Real-World Tasks](https://mlsanity.com/paper/2604.20087/) (2026)
- [KGGen: Extracting Knowledge Graphs from Plain Text with Language Models](https://mlsanity.com/paper/2502.09956/) (2025)
- [AGENTIF: Benchmarking Instruction Following of Large Language Models in Agentic Scenarios](https://mlsanity.com/paper/2505.16944/) (2025)
- [Skill Retrieval Augmentation for Agentic AI](https://mlsanity.com/paper/2604.24594/) (2026)
- [LIFBench: Evaluating the Instruction Following Performance and Stability of Large Language Models in Long-Context Scenarios](https://mlsanity.com/paper/2411.07037/) (2024)
- [Beyond IVR: Benchmarking Customer Support LLM Agents for Business-Adherence](https://mlsanity.com/paper/2601.00596/) (2026)
- [SkillTester: Benchmarking Utility and Security of Agent Skills](https://mlsanity.com/paper/2603.28815/) (2026)
- [CompliBench: Benchmarking LLM Judges for Compliance Violation Detection in Dialogue Systems](https://mlsanity.com/paper/2604.12312/) (2026)
- [Predicting Task Performance with Context-aware Scaling Laws](https://mlsanity.com/paper/2510.14919/) (2025)
- [SkillAudit: From Fixed-Suite Benchmarking to Skill-Centered Assessment](https://mlsanity.com/paper/2606.22613/) (2026)

## Abstract (arXiv)

The increasing complexity of enterprise business scenarios has promoted the widespread adoption of long SKILL documents in agent systems, posing new challenges for compliance detection: large models incur substantial inference costs, while small models may fail to maintain detection accuracy. To address this gap, we propose SkillCDG, a graph-based framework for long SKILL compliance detection. SkillCDG represents complex business policies as a two-layer constraint dependency graph, where the upper layer indexes SKILL descriptions for scenario routing and the lower layer captures dependencies among atomic constraints within each SKILL. During inference, two-level retrieval followed by dependency closure supports compliance judgment and source traceability. We comprehensively evaluate the framework on three enterprise datasets and two controlled public benchmark variants. Experimental results demonstrate that SkillCDG outperforms baseline methods by up to 12.8 percentage points in detection F1 score, while reducing token consumption by a maximum 64.3%. Moreover, we further investigate the inherent relationships among policy-graph complexity, model scale, and detection performance. Comparative experiments conducted on four checkpoints from a single model family validate a concise and effective scaling trend: end-to-end detection correctness exhibits a complexity-differentiated scaling pattern, and the complexity metric derived from the constraint dependency graph can effectively quantify instance difficulty and the performance improvement potential of models. Leveraging this insightful scaling trend, we conduct adaptive training sample selection and adopt on-policy distillation to efficiently enhance the compliance detection capability of small-scale models.