LLM-Enhanced Random Forests in Orthogonal Hyperbolic Subspaces for Tabular Learning

Tabular data is widely applied in critical domains, where tree-based models remain dominant, yet their performance is often constrained by manual heuristic splitting criteria and limited ensemble diversity. While hyperbolic geometry naturally fits the hierarchical topology of tabular data, existing hyperbolic algorithms are hindered by complex Riemannian optimization and the difficulty of defining subtree priors in non-Euclidean spaces. To address these challenges, we propose HOT, a hyperbolic random forest framework based on data decoupling. First, we leverage intrinsic geometric structures and LLM reasoning to guide subtree construction, replacing traditional manual heuristics with geometric-semantic priors. Second, we introduce an orthogonal hyperbolic subspace projection mechanism via tangent space isometry, effectively decoupling feature dependencies and maximizing ensemble diversity. Finally, we establish an end-to-end collaborative training paradigm where gradient residuals from a graph network directly guide the growth of new hyperbolic trees, bypassing expensive iterative optimization. Experiments on 13 benchmark datasets demonstrate that HOT significantly outperforms state-of-the-art baselines in both computational efficiency and predictive performance.