SymboLLM-FE: LLM-Accelerated Symbolic Regression for Automated Feature Engineering on Tabular Data

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.

In clinical tabular prediction, classical machine learning models with feature engineering often outperform neural methods. LLMs are increasingly used to automate this process, acting as domain experts that propose diverse feature transformations to boost downstream performance. However, the feature generation process of existing LLM-based methods is agnostic to the downstream learner: the LLM receives no signal about which features currently drive predictions or where the model's representational capacity falls short, so proposals are neither targeted to promising regions of the feature space nor tailored to the learner's inductive bias. This shortcoming is amplified in healthcare data, which simultaneously exhibits class imbalance, heterogeneous feature spaces, and strict interpretability requirements. In this paper, we propose MedFeat, the first feature engineering framework inspired by the workflow of machine learning practitioners, leveraging model-awareness and feature importance signals to iteratively guide feature discovery for clinical tabular learning. We evaluate MedFeat on a broad range of challenging real-world clinical tasks and show that it statistically significantly outperforms state-of-the-art baselines, with an average F1 improvement of more than 10% over the baseline across models with distinct inductive biases.

We introduce an iterative framework that automates the extraction of interpretable, schema-bound categorical features from unstructured text for tabular prediction models. To navigate the feature space, a generator LLM proposes semantic definitions, a separate extractor LLM materializes the features, and a downstream tabular model evaluates their predictive performance. We optimize this search by translating explicit model errors, such as AUC ranking inversions, into natural-language feedback, steering the LLM to resolve specific predictive failures. Evaluated across three public datasets, this error-driven loop accelerates feature discovery by up to $3\times$ compared to unguided search. Empirically, the generated features demonstrate strong multi-view complementarity, strictly outperforming any subset when combined with TF-IDF and dense embeddings. Finally, the framework guarantees instance-level interpretability: the discovered features dominate SHAP importance rankings and provide a fully transparent, semantic audit trail for every prediction.