SkillProj: Skill Retrieval by Projection onto Requirement Subspaces

Skill-based recursive self-improvement (RSI) relies on retrieving accumulated procedures as task requirements evolve. Whole-request encoding compresses multiple needs into one direction, while maximum per-requirement similarity retains only the strongest individual match. We introduce SkillProj, which represents complete active requirements by their vector span and retrieves skills through projection, requirement-level reranking, and residual diversity. We extend public SkillRouter, SkillRet, and R3-Skill resources into three trajectory benchmarks with 429 five-turn dialogues and libraries of up to 79,141 skills. With GPT-5.6 Luna, SkillProj achieves the highest Recall@10 and full coverage among eight methods on all three benchmarks. Averaged equally across benchmarks, its Recall@10 exceeds the strongest baseline by 8.16, 5.30, and 5.95 percentage points under GPT-5.6 Luna, DeepSeek V4.1 Flash, and GLM-5.3-Flash, respectively. With DeepSeek V4.1 Flash and GLM-5.3-Flash, it uses 33–34% fewer generation tokens than SkillDreamer. Agents using SkillProj also achieve the highest content accuracy in 1,128 end-to-end executions. Matched ablations support representing active requirements as a subspace and retaining requirement-level matching during reranking.