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Existing approaches usually improve either the instruction side or the tool side in isolation, which leaves unclear what should be updated after failure. We propose EGL-SCA, a verifier-centric dual-space framework that models a graph reasoning agent using two collaborative components: an instruction-side policy space for reasoning strategies, and a tool-side program space for executable algorithmic tools. Our central mechanism is structural credit assignment, which maps trajectory evidence to conditional updates, precisely routing failures to either prompt optimization or t","title":"EGL-SCA: Structural Credit Assignment for Co-Evolving Instructions and Tools in Graph Reasoning Agents","url":"https://arxiv.org/abs/2605.10366","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.10366v1 Announce Type: new \nAbstract: Graph reasoning agents operating from natural-language inputs must solve a coupled problem: they must reconstruct a structured graph instance from text, decide whether existing computational assets are sufficient, interact with tools under a strict execution protocol, and satisfy an external verifier that checks structured correctness rather than textual plausibility. Existing approaches usually improve either the instruction side or the tool side in isolation, which leaves unclear what should be updated after failure. 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