Enhancing Tabular Regression with Supervised Manifold-Guided Graph Neural Networks

Standard deep neural networks exhibit suboptimal convergence in tabular regression, particularly under sparse distribution and high heterogeneity. We hypothesize that this limitation arises from the absence of an explicit inductive bias to enforce intrinsic geometric continuity on the target function in standard point-wise loss functions. Although graph neural networks offer a potential remedy, existing approaches rely on static neighborhood topologies that fail to adapt to spatially varying feature densities, inducing a suboptimal bias-variance trade-off. We propose a supervised manifold-guided framework that unifies differentiable topology inferences with geometric representation learning. Our framework introduces a neural k -Predictor that dynamically estimates point-wise optimal neighborhood sizes by minimizing local label variance through an exhaustive oracle-guided meta-loss. Crucially, we established an end-to-end training pipeline via straight-through estimation, enabling geometric gradients from a novel supervised manifold loss to backpropagate through discrete graph structures and regularize the baseline feature extractor. Extensive experiments on eight heterogeneous benchmarks demonstrate that our method restores convergence in sparse, high-dimensional scenarios where standard baselines fail, recovering Insurance R 2 from −63.38% to 86.53%, approaching XGBoost’s 87.12%. Ablation studies confirmed the following: Adaptive geometric inductive bias is essential for stabilizing the optimization in sparse, high-curvature data manifolds. • Proposed a Supervised Manifold-Guided Framework for tabular regression. • Neural k -Predictor dynamically infers optimal neighborhood sizes. • Supervised Manifold Loss enforces geometric continuity on embeddings. • End-to-end training is achieved via Straight-Through Estimator (STE). • The method outperforms XGBoost in high-dimensional sparse regimes.