AlphaS${}^2$: Semantic–Symbolic Co-Evolution for Alpha Mining with Coding Agents

Quantitative alpha mining aims to discover predictive signals that generalize under noisy and non-stationary markets. Large language model (LLM) agents provide a promising direction by combining financial reasoning with executable factor generation. However, existing methods primarily evolve complete alpha expressions within a fixed representation or search space. As a result, knowledge discovered through expensive LLM exploration is largely reused only at the level of individual factors, rather than being distilled into reusable structures that can reshape subsequent search. Our key insight is that effective alpha discovery should co-evolve both the semantic hypotheses being explored and the symbolic language used to express and search them. We introduce \tool, a semantic-symbolic co-evolution framework for alpha mining with coding agents. A semantic LLM agent generates and evolves executable alphas from financial hypotheses, while an operator-construction agent distills recurring relations from successful factors into typed symbolic operators. These operators expand the grammar of a genetic-programming miner, enabling efficient recombination into new factors. Selected symbolic descendants are then returned to the LLM archive, closing a bidirectional co-evolution loop: semantic exploration evolves the symbolic search space, while symbolic exploration broadens future semantic discovery. Across CSI300, CSI500, and CSI1000, \tool achieves strong predictive and economic performance, with ICIRs of 0.3549, 0.2092, and 0.517 and annualized excess returns of 9.08%, 13.22%, and 16.58%, respectively. These results demonstrate that co-evolving semantic knowledge and symbolic representations provides an effective mechanism for scalable, reusable, and adaptive alpha discovery.