SIGMA: SHAP-Guided Implicit-Trajectory Generation for Metadata-Free LLM-Based AutoFE

Automatic feature engineering (AutoFE) for tabular data requires discovering informative transformations from a large program space. Existing approaches suffer from three limitations: classical methods rely on fixed operator libraries with limited expressivity, LLM-based methods generate proposals from static prompts without retaining search experience, and evolutionary methods use fixed migration policies that ignore task-specific cross-family transfer utility. We introduce TOPOFE, a framework that formulates AutoFE as graph-structured multi-island evolutionary program search. The transformation space is partitioned into semantically coherent families, each explored by an island through LLM-guided mutation and crossover. Each island maintains a Prompt Adaptation Memory that accumulates accept/reject feedback to steer proposals toward productive regions without parameter updates. To coordinate global exploration, TOPOFE dynamically learns a directed topology graph whose edge weights encode transfer utility between transformation families. Cross-island transfer is triggered by adaptive saturation detection and performed through LLM-mediated hybrid synthesis, enabling discovery of compositional feature programs that cannot emerge from isolated local search. Experiments on 29 tabular datasets show that TOPOFE consistently outperforms most state-of-the-art AutoFE methods on classification and regression tasks. Beyond predictive performance, TOPOFE produces feature sets with lower redundancy and higher representational coverage, while the learned topology graph acquires meaningful task-specific transfer structure correlated with downstream gains. The discovered feature programs transfer reliably across diverse predictors and LLM backbones, demonstrating that improvements arise from TOPOFE's structured search and adaptive coordination rather than backbone-specific generation capability.

Tabular data, as a core data format in machine learning, often lacks the discriminative power needed for high-performance modeling due to insufficient feature informativeness. Automated Feature Engineering (AutoFE) overcomes this by automating feature generation and selection, ensuring both model performance and operational efficiency. However, traditional AutoFE often yield features with poor interpretability because they rely on blind mathematical transformations, while large language models (LLM)-based AutoFE faces challenges in requiring costly multi-round iterations to generate high-utility features to effectively enhance model performance, compounded by inherent risks of bias and hallucination. In this paper, we combine symbolic regression with LLMs for feature engineering (SymboLLM-FE) to solve these challenges. We extract mathematically expressive formulas strongly correlated with the target via symbolic regression, which can enhance model performance, then refine them by LLMs with rich prior knowledge to ensure interpretability. Empirical results on six real-world datasets and four Kaggle competitions demonstrate that SymboLLM-FE outperforms existing AutoFE. SymboLLM-FE also addresses the dual challenges of poor interpretability and numerous iterations by employing a statistical prior-grounded LLM refinement mechanism and single-digit LLM calls.

Automated feature generation extracts informative features from raw tabular data without manual intervention and is crucial for accurate, generalizable machine learning. Traditional methods rely on predefined operator libraries and cannot leverage task semantics, limiting their ability to produce diverse, high-value features for complex tasks. Recent Large Language Model (LLM)-based approaches introduce richer semantic signals, but still suffer from a restricted feature space due to fixed generation patterns and from the absence of feedback from the learning objective. To address these challenges, we propose a Memory-Augmented LLM-based Multi-Agent System (MALMAS) for automated feature generation. MALMAS decomposes the generation process into agents with distinct responsibilities, and a Router Agent activates an appropriate subset of agents per iteration, further broadening exploration of the feature space. We further integrate a memory module comprising procedural memory, feedback memory, and conceptual memory, enabling iterative refinement that adaptively guides subsequent feature generation and improves feature quality and diversity. Extensive experiments on multiple public datasets against state-of-the-art baselines demonstrate the effectiveness of our approach. The code is available at https://github.com/fxdong24/MALMAS