Where to Search: Measure the Prior-Structured Search Space of LLM Agents
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914132096188416 |
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| author | Song, Zhuo-Yang |
| author_facet | Song, Zhuo-Yang |
| contents | The generate-filter-refine (iterative paradigm) based on large language models (LLMs) has achieved progress in reasoning, programming, and program discovery in AI+Science. However, the effectiveness of search depends on where to search, namely, how to encode the domain prior into an operationally structured hypothesis space. To this end, this paper proposes a compact formal theory that describes and measures LLM-assisted iterative search guided by domain priors. We represent an agent as a fuzzy relation operator on inputs and outputs to capture feasible transitions; the agent is thereby constrained by a fixed safety envelope. To describe multi-step reasoning/search, we weight all reachable paths by a single continuation parameter and sum them to obtain a coverage generating function; this induces a measure of reachability difficulty; and it provides a geometric interpretation of search on the graph induced by the safety envelope. We further provide the simplest testable inferences and validate them via two instantiation. This theory offers a workable language and operational tools to measure agents and their search spaces, proposing a systematic formal description of iterative search constructed by LLMs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_14846 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Where to Search: Measure the Prior-Structured Search Space of LLM Agents Song, Zhuo-Yang Artificial Intelligence Computation and Language Logic in Computer Science The generate-filter-refine (iterative paradigm) based on large language models (LLMs) has achieved progress in reasoning, programming, and program discovery in AI+Science. However, the effectiveness of search depends on where to search, namely, how to encode the domain prior into an operationally structured hypothesis space. To this end, this paper proposes a compact formal theory that describes and measures LLM-assisted iterative search guided by domain priors. We represent an agent as a fuzzy relation operator on inputs and outputs to capture feasible transitions; the agent is thereby constrained by a fixed safety envelope. To describe multi-step reasoning/search, we weight all reachable paths by a single continuation parameter and sum them to obtain a coverage generating function; this induces a measure of reachability difficulty; and it provides a geometric interpretation of search on the graph induced by the safety envelope. We further provide the simplest testable inferences and validate them via two instantiation. This theory offers a workable language and operational tools to measure agents and their search spaces, proposing a systematic formal description of iterative search constructed by LLMs. |
| title | Where to Search: Measure the Prior-Structured Search Space of LLM Agents |
| topic | Artificial Intelligence Computation and Language Logic in Computer Science |
| url | https://arxiv.org/abs/2510.14846 |