# EGL-SCA: Structural Credit Assignment for Co-Evolving Instructions and Tools in Graph Reasoning Agents

arXiv: https://arxiv.org/abs/2605.10366 · HTML: https://mlsanity.com/paper/2605.10366/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 27 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 11 of 11)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning](https://mlsanity.com/paper/2507.19457/) (2025)
- [ART: Automatic multi-step reasoning and tool-use for large language models](https://mlsanity.com/paper/2303.09014/) (2023)
- [Graph-ToolFormer: To Empower LLMs with Graph Reasoning Ability via Prompt Augmented by ChatGPT](https://mlsanity.com/paper/2304.11116/) (2023)
- [GraphInstruct: Empowering Large Language Models with Graph Understanding and Reasoning Capability](https://mlsanity.com/paper/2403.04483/) (2024)
- [GraphArena: Evaluating and Exploring Large Language Models on Graph Computation](https://mlsanity.com/paper/2407.00379/) (2024)
- [Graph Meets LLMs: Towards Large Graph Models](https://mlsanity.com/paper/2308.14522/) (2023)
- [GraphOmni: A Comprehensive and Extensible Benchmark Framework for Large Language Models on Graph-theoretic Tasks](https://mlsanity.com/paper/2504.12764/) (2025)

## Built on by (most cited first, 4 of 4)

- [Coverage, Not Credit: Failure-Credit Routing of Zeroth-Order Perturbation Budgets Does Not Improve On-Pool Sample Efficiency for LLM Agents](https://mlsanity.com/paper/2608.28011/) (2026)
- [Are Large Language Models Suitable for Graph Computation? Progress and Prospects](https://mlsanity.com/paper/2606.06865/) (2026)
- [GRAIN: Bridging Name and Narrative Shifts in Real-World Graph Reasoning through Invariance-Rewarded Agentic RL](https://mlsanity.com/paper/2608.27142/) (2026)
- [GraphOPD: Graph-Augmented On-Policy Distillation for LLM Agents](https://mlsanity.com/paper/2610.08959/) (2026)

## Abstract (arXiv)

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. 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 tool synthesis and repair. To provide sufficient learning signals for dual-space adaptation, we introduce a training distribution stratified by task family, coupled with a Pareto-style retention strategy to balance success, generality, and parsimony. Experiments on four graph reasoning benchmarks show that EGL-SCA achieves a state-of-the-art 92.0% average success rate. By effectively co-evolving instructions and tools, our framework significantly outperforms both pure-prompting and fixed-toolbox baselines.