用大模型生成+机器学习优化，让特征转换更稳定准确

Feature transformation enhances data representation by deriving new features from the original data. Generative AI offers potential for this task, but faces challenges in stable generation (consistent outputs) and valid generation (error-free sequences). Existing methods--traditional MLs' low validity and LLMs' instability--fail to resolve both. We find that LLMs ensure valid syntax, while ML's gradient-steered search stabilizes performance. To bridge this gap, we propose a teaming framework combining LLMs' symbolic generation with ML's gradient optimization. This framework includes four steps: (1) golden examples generation, aiming to prepare high-quality samples with the ground knowledge of the teacher LLM; (2) feature transformation sequence embedding and search, intending to uncover potentially superior embeddings within the latent space; (3) student LLM feature transformation, aiming to distill knowledge from the teacher LLM; (4) LLM-ML decoder teaming, dedicating to combine ML and the student LLM probabilities for valid and stable generation. The experiments on various datasets show that the teaming policy can achieve 5\% improvement in downstream performance while reducing nearly half of the error cases. The results also demonstrate the efficiency and robustness of the teaming policy. Additionally, we also have exciting findings on LLMs' capacity to understand the original data.