arXiv:2604.16378v1 Announce Type: new Abstract: Large language models (LLMs) and classical machine learning methods offer complementary strengths for predictive modeling, yet their fundamentally different representations and training paradigms hinder effective integration: LLMs rely on gradient-based optimization over textual data, whereas models such as Random Forests (RF) employ non-differentiable feature partitioning. This work introduces a reciprocal co-training framework that couples an LLM with an RF classifier via reinforcement learning, creating an iterative feedback loop in which each model improves using signals from the other. Tabular data are reformulated into standardized textual representations for the LLM, whose embeddings augment the RF feature space, while calibrated RF probability estimates provide feedback signals that guide reinforcement learning updates of the LLM. Experiments across three medical datasets demonstrate consistent performance gains for both models, with particularly strong effects for the LLM. Ablation analyses show that iterative refinement, hybrid reward design, and dimensionality control jointly contribute to these gains. The proposed framework provides a general mechanism that allows incompatible model families to leverage each other's strengths through bidirectional adaptation.