arXiv:2610.32336v1 Announce Type: new Abstract: Retrieving the right skill from a large library is essential for LLM agents, yet requests and skills are written for different purposes and in different words. Existing retrievers narrow this request-skill gap with one or two representation choices each, so it is unknown whether their gains hold in combination. No prior work measures the gap itself, so it is also unclear which part of it each choice narrows. We define a representation design space by five choices -- encoder fine-tuning, query-side and document-side expansion, background projection and a lexical channel -- and evaluate them together for the first time, as modules of one retriever, SkillRep. With a 0.6B encoder and LLM expansion, SkillRep improves MRR@10 on SRA-Bench over the strongest same-size retriever by 7.02 points with the official skill pool and 8.79 with UniPool, a 111,247-skill pool we build from public registries, and is best on SkillsBench. The value of each choice depends on the others. Fine-tuning, for instance, reverses the ranking of the four training-free modules and turns them from complementary into overlapping. To understand why, we measure the gap with three quantities: background, the embedding component that does not separate skills; unsaid vocabulary, the gold skill's content a request leaves unsaid; and dilution, the information lost when a skill is encoded into a single vector. They show which part each module narrows and by what mechanism. This reveals that modules narrowing the same part compete for it, while those narrowing different parts complement each other.