Language models (LMs) and classical machine learning methods offer complementary strengths for predictive modeling, yet their fundamentally different representations and training paradigms hinder effective integration: LMs 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 LM 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 LM, whose embeddings augment the RF feature space, while calibrated RF probability estimates provide feedback signals that guide reinforcement learning updates of the LM. Experiments across three medical datasets, evaluated with both a domain-adapted clinical encoder (ClinicalBERT) and a larger instruction-tuned language model (Qwen2-7B-Instruct), demonstrate consistent performance gains for both model components. Ablation analyses indicate that iterative refinement, hybrid reward design, and dimensionality control jointly contribute to these gains. SHAP analysis further confirms that LM-derived representations are among the most important inputs to the RF predictions. The proposed framework provides a general mechanism that allows incompatible model families to leverage each other's strengths through bidirectional adaptation.

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