SkillGraph: Graph Foundation Priors for LLM Agent Tool Sequence Recommendation

As LLM agents act across personal applications, web browsers, and other interfaces, their reusable skill libraries can scale to thousands of skills. This scale introduces two challenges. First, loading the full library saturates the context window, driving up token costs, hallucination, and latency. Second, semantic retrieval surfaces topically relevant skills but can miss upstream and downstream prerequisite skills, creating a prerequisite gap that leaves the retrieved bundle insufficient for execution. We present Graph-of-Skills (GoS), an inference-time structural retrieval layer for large skill libraries. GoS constructs an executable skill graph offline from skill packages, then retrieves a bounded, dependency-aware bundle through hybrid semantic-lexical seeding, reverse-aware Personalized PageRank, and context-budgeted hydration. Across SkillsBench and ALFWorld, with three model families (Claude Sonnet 4.5, MiniMax M2.7, and GPT-5.2 Codex), GoS attains the highest average reward in all six model-benchmark blocks, at a fraction of the token cost of loading the full library. On SkillsBench with GPT-5.2 Codex it raises average reward by 7.0 absolute points over full skill loading, a 25.6% relative gain, while cutting total tokens by 56.7%. Ablations isolate the mechanism: replacing reverse traversal with forward propagation costs 9.1 reward points, a larger loss than removing the graph altogether. The gain thus comes from traversing dependencies backwards, not from graph diffusion as such. A budget-matched retrieval study holding seeding, reranking, hydration, and context budget fixed reproduces the same ordering, with dependency-pair co-recovery falling from 0.654 to 0.362. Code is available at https://github.com/davidliuk/graph-of-skills

Large skill libraries are now standard equipment for LLM agents, and which subset reaches the prompt decides what the agent can do. Enumeration and top-$K$ embedding retrieval both treat skills as independent documents, assuming relevance is a property of one skill at a time. It is not: skills depend on, conflict with, specialize, and duplicate one another, so the closest match to a task can name it while omitting a prerequisite it needs. Graph retrieval encodes these relations but spends them in a fixed pipeline, handing the agent an opaque bundle. We present SkillDAG, which exposes a typed skill graph to the LLM as an agent-callable interface rather than consuming it for the agent: search returns vector matches, typed-edge neighbors, and conflict signals, and a propose-then-commit protocol lets it register execution-backed edges as it works. Across two benchmarks and three model families, SkillDAG outperforms full-library prompting, vector retrieval, and Graph-of-Skills, gaining +14.3 points of ALFWorld success and tying only at ceiling; its ranking holds flat across a $10\times$ pool expansion that degrades the fixed pipeline. Inter-skill structure, these results suggest, is worth more to an agent that can query and revise it than to a retriever that consumes it.

Skill ecosystems for LLM agents have matured rapidly, yet recent benchmarks show that providing agents with more skills does not monotonically improve performance -- focused sets of 2-3 skills outperform comprehensive documentation, and excessive skills actually hurt. The bottleneck has shifted from skill availability to skill orchestration: agents need not more skills, but a structural mechanism to select, compose, and execute them with explicit causal dependencies. We propose GraSP, the first executable skill graph architecture that introduces a compilation layer between skill retrieval and execution. GraSP transforms flat skill sets into typed directed acyclic graphs (DAGs) with precondition-effect edges, executes them with node-level verification, and performs locality-bounded repair through five typed operators -- reducing replanning from O(N) to O(d^h). Across ALFWorld, ScienceWorld, WebShop, and InterCode with eight LLM backbones, GraSP outperforms ReAct, Reflexion, ExpeL, and flat skill baselines in every configuration, improving reward by up to +19 points over the strongest baseline while cutting environment steps by up to 41%. GraSP's advantage grows with task complexity and is robust to both skill over-retrieval and quality degradation, confirming that structured orchestration -- not larger skill libraries -- is the key to reliable agent execution.