CosmosAlpha: Multi-Relational Graph Search with Pareto-Guided Exploration for LLM-Driven Alpha Mining

Discovering predictive alpha factors from noisy financial data is a fundamental yet challenging problem in quantitative finance. LLM-driven formulaic alpha mining offers an attractive paradigm by combining interpretable symbolic expressions with iterative generation and refinement guided by quantitative feedback. However, existing generation-centric and tree-based search strategies primarily organize factors through generation lineage, leaving structural and statistical relationships across search branches underutilized. Consequently, information remains localized along parent--child trajectories, which can confine exploration to redundant regions. Moreover, effective factor discovery must account for multiple distinct objectives that cannot be adequately captured by a single search criterion. We introduce CosmosAlpha, a graph-based LLM factor-mining framework that represents discovered factors as a multi-relational graph encoding generation lineage, expression-structure similarity, and cross-sectional exposure correlation. A Graph Flow mechanism propagates search utilities across the graph, allowing each factor to be assessed using relational evidence from nearby factors rather than in isolation. Pareto-guided selection jointly considers quality, fertility and diversity, explicitly modeling their trade-offs within a multi-objective search framework. Across CSI 300 and CSI 500, CosmosAlpha-Graph achieves the best mean rank over seven predictive and portfolio metrics and outperforms its controlled CosmosAlpha-MCTS counterpart on every reported metric, showing a consistent advantage for relational graph search in LLM-driven factor mining. The source code is available at https://github.com/wzhmtldswz/CosmosAlpha