Tabular More vs. Fewer Loss: Insights

• Tabular More vs. Fewer Loss is a conceptual framework that modulates loss aggregation in tabular models to enhance expressivity and robustness.
• It explores methodologies from self-supervised adversarial encoding and multi-observation elicitation to ranking and monotonicity losses in multimodal settings.
• Adaptive strategies like TabMoFe and close-k losses provide practical benefits by balancing robustness, computational cost, and handling missing or imbalanced data.

Tabular More vs. Fewer Loss

Tabular More vs. Fewer Loss encompasses a diverse class of methodological choices and architectural innovations centered on controlling the amount, the nature, and the aggregation mode of losses employed in supervised, self-supervised, and multimodal learning with tabular data. Across representation learning, property elicitation, and robust multimodal fusion, allocating "more" or "fewer" losses—whether in terms of loss-terms, attributes, observations, or examples—directly impacts model expressivity, optimization, robustness, and interpretability. Recent literature systematically compares single- versus multi-term loss formulations, explores multi-observation loss elicitation, develops ranking losses for missingness-robust fusion, and introduces adaptive aggregate losses emphasizing decision-critical cases.

1. Reconstruction and Regularization: Single vs. Multi-Term Losses in Self-Supervised Tabular Encoders

Self-supervised learning for tabular data departs from image-centric paradigms due to heterogeneity and the lack of generic augmentations. The MET (Masked Encoding for Tabular Data) framework contrasts "fewer" (single-term) and "more" (dual-term) loss designs for unsupervised encoder training (Majmundar et al., 2022). The standard masked reconstruction loss

$\Lrec^{\rm std}(\theta, \phi) = \sum_{i=1}^{N_u} \| x_i - h_\phi(f_\theta((S_i, x_i^{S_i}))) \|_2^2$

trains the encoder-decoder solely on masked input reconstruction. MET augments this with an adversarial loss term

$\Lrec^{\rm adv}(\theta, \phi) = \sum_{i=1}^{N_u} \max_{\|\delta\|_2 \le \epsilon} \| x_i - h_\phi(f_\theta((S_i, x_i^{S_i} + \delta))) \|_2^2$

where each example undergoes worst-case perturbation to maximize reconstruction error. The full objective is

$\Ltotal(\theta, \phi) = \Lrec^{\rm std}(\theta, \phi) + \lambda \Lrec^{\rm adv}(\theta, \phi).$

Empirical comparisons reveal that incorporating the adversarial term ("more" loss) enhances downstream classification accuracy across diverse tabular benchmarks, with performance improvements up to several percentage points over the "fewer" loss regime, at the expense of increased computational overhead and an extra hyperparameter (Majmundar et al., 2022).

2. Tabular More vs. Fewer (TabMoFe) Loss for Monotonic Robustness with Missing Data

The TabMoFe loss addresses the challenge of learning multimodal vision-tabular models where tabular attribute availability is variable, such as in clinical settings with sparse measurements (Hasny et al., 22 Dec 2025). For each image-tabular pair, two nested subsets of available attributes ($t^-$ and $t^+$, with $t^- \subset t^+$) are fused, and the model is penalized only when access to "more" attributes yields worse loss: $$\mathcal{L}_{\rm TabMoFe} = \max\{\mathcal{L}_{\rm task}(i, t^+) - \mathcal{L}_{\rm task}(i, t^-), 0\}.$$ The overall fine-tuning objective combines the task losses for both attribute sets with a weighted TabMoFe hinge term. This enforces a monotonicity constraint: model performance should not degrade as more information becomes available. Integrated within the RoVTL framework—featuring gated cross-attention fusion and Disentangled Gradient Learning (DGL) to stabilize optimization—TabMoFe yields improved robustness to missing tabular input without sacrificing unimodal performance (Hasny et al., 22 Dec 2025).

3. Multi-Observation Losses: Reducing Elicitation Complexity via "More" Data Points Per Loss

In the property elicitation literature, the use of "more" (multi-observation) loss functions enables efficient estimation of statistical properties with reduced report-space dimension (Casalaina-Martin et al., 2017). A loss $L_m(r, y_1, \dots, y_m)$ measures the discrepancy between a report $r$ and $m$ jointly observed outcomes. While traditional (single-observation) losses require report dimension scaling with the complexity of the statistic (e.g., two parameters for variance), increasing the number of observations per loss to $m$ may allow the property to be elicited with a single-dimensional report. For instance, the variance can be estimated directly with a two-observation loss: $$L_2(r, y_1, y_2) = (r - \tfrac{1}{2}(y_1 - y_2)^2)^2$$ with $d=1$, bypassing the need for separate $E[Y]$ and $E[Y^2]$ estimates. A trade-off arises between per-sample cost (need for i.i.d. bundles) and model complexity (smaller hypothesis classes), as summarized in Table 1 below.

Observations (m)	Report Dim (d)	Elicited Property
1	2	$(E[Y], E[Y^2])$ (variance via two reports)
2	1	$E[\tfrac{1}{2}(y_1 - y_2)^2]$ (variance direct)
n	1	$n$th moment (high-order statistics)

This approach enables direct, lower-dimensional regression for complex statistics when multiple, jointly observed outcomes per input can be acquired (Casalaina-Martin et al., 2017).

4. Aggregate Losses: Focusing on More vs. Fewer Examples for Tabular Classification

In supervised classification, standard practice is to minimize the average per-example loss across the dataset. However, in tabular domains with class imbalance, outliers, or ambiguous points, blindly aggregating "more" examples can dilute learning signal, while focusing on "fewer" (most extreme) losses can bias the optimization. The close-$k$ loss interpolates these extremes by adaptively minimizing losses on the $k$ examples nearest the decision boundary: $$L_{\rm close\textrm{-}k}(\theta) = \sum_{i=1}^n \begin{cases} \ell_{[i]}(\theta), & \text{if } i \le k,\ 0, & \text{if } i>k \text{ and example is correctly classified}, \ M, & \text{if } i>k \text{ and misclassified}, \end{cases}$$ with $\ell_{[i]}$ sorted by distance to threshold. Theoretical guarantees ensure classification calibration for $k=1$, with suboptimality bounded by $k-1$ for generic $k$, and robust empirical gains on tabular datasets (up to $\geq2\%$ accuracy improvement in 20–25\% of cases) (He et al., 2018). A staged annealing schedule—decaying $k$ from $n$ to $k^*$—balances convexity for optimization with focused discrimination near the boundary.

5. Practical Trade-Offs, Guidelines, and Recommendations

The selection of "more" versus "fewer" losses displays multifaceted trade-offs:

• In self-supervised representation learning (e.g., MET), adding adversarial loss terms strengthens robustness and feature separability but increases computational burden (Majmundar et al., 2022).
• In multimodal learning, TabMoFe enforces the intuitive and practically critical monotonicity that access to more tabular information must not degrade task performance. Its integration with DGL orthogonalizes gradient flows and stabilizes training (Hasny et al., 22 Dec 2025).
• In property elicitation, multi-observation losses offer low-complexity models when multiple outputs per input are available, though this may increase sample complexity requirements (Casalaina-Martin et al., 2017).
• In classification, close-$k$ losses promote robustness to imbalance and dataset pathologies, but require careful $k$ selection; annealing or validation-based hyperparameter selection is recommended (He et al., 2018).

A unified principle is that dynamically controlling the amount or aggregation of loss—either by increasing loss terms (adversarial, multi-observation, ranking regularizers) or by adaptively focusing the aggregate (close-$k$)—enables a balance between robustness, representation quality, computational tractability, and practical model complexity.

6. Research Directions and Implications

The consistent empirical superiority of "more" complex loss formulations in numerous benchmarks, as well as the theoretical reductions in hypothesis complexity with multi-observation losses, suggest further exploration in the following areas:

• Automating the selection of loss aggregation hyperparameters (e.g., $k$, or loss weightings $\lambda$) in a data-driven fashion.
• Extending ranking or monotonicity-based regularizers like TabMoFe to other domains and modalities with missing or partial observations.
• Generalizing multi-observation loss frameworks to structured prediction and non-i.i.d. data regimes.
• Investigating further combinations of self-supervised objectives (masking, adversarial, multi-observation) in the tabular domain, especially for transfer and robustness under covariate shift.

A plausible implication is that fine-grained, context-dependent balancing of "more" versus "fewer" loss contributions can form a central guideline for designing loss functions in modern tabular data modeling.