arXiv:2606.20625v2 Announce Type: replace Abstract: LLM agents are promising for alpha mining via combining financial priors, symbolic reasoning, executable factor generation, and feedback-driven refinement. Yet, they face a combinatorial search space, noisy non-stationary feedback, redundant discoveries, and overfitting risks from naively reusing past successes. To address these challenges, we propose AlphaMemo, a self-evolving alpha mining agent with Structured Search-Process Memory. Rather than memorizing only final factors or full trajectories, AlphaMemo records reusable evidence about which edit motifs work or fail under specific parent-factor contexts. It extracts motifs from Abstract Syntax Tree (AST) differences, applies confidence-gated residual memory on top of a search-ledger prior, and uses asymmetric veto control to suppress high-confidence failure patterns. Experiments on CSI 500 and S&P 500 show improved out-of-sample performance and fixed-budget discovery efficiency, with ablations validating the roles of residual learning, confidence gating, AST-diff motifs, and veto memory. Code is at https://github.com/jarrettyu/sspm.