Revisiting Tabular Deep Regression: Objectives and the Limits of Global Early Stopping

Large-scale, high-dimensional tabular regression remains challenging: tree-based models are robust but lack end-to-end representation learning, while deep models enable flexible feature learning but often incur costly interaction modeling and sensitivity to noisy or redundant features. We propose TabNSM, a scalable regression framework that extends our earlier sparse-attention and mixer architectures. At its core, the Adaptive Sparse Interaction Module (ASIM) integrates foreground feature discovery, sparse local interaction encoding, and Feature-Token Mixing, providing near-linear complexity under fixed sparse configurations. For regression, TabNSM introduces three complementary components: a Multi-Stage Regression Head for progressive prediction refinement; GridLoss, an ordinal-aware soft-binning objective that incorporates target structure into representation learning; and RISE (Reweighted Instance Sampling by Error), a difficulty-aware sampling strategy based on loss-quantile bins. Across nine real-world regression benchmarks, TabNSM delivers strong predictive performance and practical scalability, with particularly consistent gains on high-dimensional and heterogeneous datasets. These results demonstrate that selective interaction modeling, structured regression supervision, and difficulty-aware sampling provide an effective and scalable approach to deep tabular regression.

Recent tabular learning benchmarks increasingly show a tight performance cluster rather than a clear hierarchy among leading methods, spanning gradient boosted decision trees, attention-based architectures, and implicit ensembles such as TabM. As benchmark gains plateau, a complementary goal is to understand and control the mechanisms that make simple neural tabular models competitive. We propose LoMETab, a rank-$r$ generalization of multiplicative implicit ensembles. LoMETab lifts the rank-1 BatchEnsemble/TabM modulation to a rank-$r$ identity-residual Hadamard family by parameterizing each member weight as $W_k = W \odot (1 + A_kB_k^\top)$, where $W$ is shared and $(A_k, B_k)$ are member-specific low-rank factors. This exposes two practical diversity-control axes: the adapter rank $r$ and the initialization scale $σ_{\mathrm{init}}$, and we prove that for $r \ge 2$ this generalization strictly enlarges BatchEnsemble's hypothesis class. Empirically, we show that this added capacity manifests as measurable predictive diversity after training: on representative classification datasets, LoMETab sustains higher pairwise KL than an additive low-rank ablation, and $(r, σ_{\mathrm{init}})$ provides broad control over pairwise KL, varying by up to several orders of magnitude across configurations. The induced diversity is reflected in task-appropriate output-level measures: argmax disagreement for classification and ambiguity for regression, indicating that the control extends beyond pairwise KL to decision- and output-level member variation. Finally, experiments sweeping over adapter rank $r$ and initialization scale $σ_{\mathrm{init}}$ reveal that predictive performance is dataset-dependent over the $(r, σ_{\mathrm{init}})$ grid, supporting LoMETab as a controllable family of implicit ensembles rather than a fixed rank-1 construction.

Deep tabular generative models are benchmarked on datasets with tens of thousands of rows; clinical datasets have hundreds. We preregistered and ran a size-ladder benchmark to find where the two regimes diverge: 8 public datasets subsampled from 200 to 20,000 training rows, seven generators (independent marginals, Gaussian copula, SMOTE, unconditional SMOTE, CTGAN, TVAE, TabDDPM) with a fixed 20-trial tuning budget and 5 evaluation seeds, plus 4 natively small clinical datasets at true size, for 2,220 committed runs in total. The primary metric is the AUROC of fixed classifiers trained on synthetic and tested on real data. In 23 of 24 (dataset, deep model) pairs no deep model ever beats the best trivial baseline by more than seed noise, at any training size we measured. The best baseline wins 40 of 49 (dataset, size) cells. Our preregistered prediction that the deep models' ranking would be unstable at small sizes is falsified: mean Kendall tau between adjacent rungs below 5,000 rows is 0.806, above our 0.8 threshold, and stability is highest at the smallest sizes rather than lowest. One caveat bounds all of this: in 81% of cells the gap between the top two methods is smaller than the variation between seeds. Finally, method rankings on natively small clinical datasets agree only moderately with rankings on subsampled large ones (mean tau 0.57 to 0.64), which questions whether a subsampled large dataset can stand in for a small one. All 2,220 result files, the preregistration and its hash, and the code that regenerates every figure and number from those files are public.