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REVIEW 4 major objections 6 minor 43 references

APAR: Modeling Irregular Target Functions in Tabular Regression via Arithmetic-Aware Pre-Training and Adaptive-Regularized Fine-Tuning

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper proposes APAR, a two-stage recipe that pre-trains a tabular encoder to predict arithmetic results on continuous labels and then fine-tunes it with adaptive gate-based augmentation, claiming RMSE gains of 9.43–20.37% over tree…

desk verdict The arithmetic-aware pre-training idea is genuinely novel and worth pursuing, but the headline RMSE gains are not believable until the authors disclose how they picked each dataset's arithmetic operator. read the letter →

arxiv 2412.10941 v1 pith:WWLKLNAX submitted 2024-12-14 cs.LG cs.AI

Hong-Wei Wu , Wei-Yao Wang , Kuang-Da Wang , Wen-Chih Peng This is my paper · ORCID
classification cs.LGcs.AI
keywords tabularregressionarithmetic-awarepre-trainingadaptiveregularizationcontinuouslabelsself-attentiongradient-boosteddecisiontreesdataaugmentationirregulartargetfunctions
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

APAR is a bet that the reason neural networks lose to gradient-boosted trees on tabular regression is not feature encoding but irregular target functions: small feature shifts that produce large label jumps. The paper proposes a two-stage cure: pre-train a self-attention encoder to predict the result of an arithmetic operation on the continuous labels of two randomly paired samples, then fine-tune it under a consistency regularizer that augments each sample with a feature gate sampled from a learnable correlated distribution. The claim is that this uses the continuous labels far more directly than reconstruction-based or contrastive pre-training, which either ignore labels or need discrete classes. On ten regression datasets spanning housing, emissions, elections, air quality, bike sharing, music, kernel performance, and flight prices, the paper reports RMSE improvements of 9.43% to 20.37% over GBDT-based, supervised neural, and pretrain-finetune neural baselines.

What carries the argument

Two mechanisms carry the argument. The arithmetic-aware pretext objective turns the continuous label into a supervised signal about sample relationships: from representations of two samples, the model must output $y_i \odot y_j$, so the encoder has to organize the representation space so that label arithmetic is readable from concatenated CLS tokens. The adaptive regularizer is a relaxed multivariate Bernoulli gate: $\tilde{Z}_i = Z_i \odot \tilde{m}$, with $\tilde{m}$ sampled under a correlation matrix $R$ and learnable inclusion probabilities $\pi$, trained so the augmented view and original view give consistent labels while $\sum \pi_i$ is penalized. This gives a differentiable, correlation-aware form of learned data augmentation.

What would settle it

Run the full APAR protocol again on the same ten datasets with the arithmetic operator selected for each dataset using only validation data, and compare average RMSE to the same baselines; if the advantage disappears or falls to within run-to-run variation, the headline gains came from test-set-dependent operator selection.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that arithmetic can act as a bridge between continuous labels and self-supervised representation learning. Pairs of samples are encoded; the concatenated CLS vectors must predict $y_i \odot y_j$ for a chosen operator $\odot \in \{+, -, \times, /\}$; after this pre-training, the model is fine-tuned by requiring the prediction from an augmented view—embeddings multiplied by a relaxed multivariate Bernoulli gate with learnable inclusion probabilities and a data-derived correlation matrix—to match the prediction from the original view. The paper argues that the first stage builds sample-wise awareness of label geometry, and the second stage keeps the model from latching onto uninformative features by letting the network learn which features to corrupt. The central evidence is that both stages contribute and that arithmetic pre-training beats reconstruction and mask pre-training on all ten datasets.

Load-bearing premise

The reported gains assume the arithmetic operation for each dataset was picked by a validation-based rule rather than by looking at test-set RMSE.

Editorial extensions

If this is right

  • Pretrain-finetune neural methods can move from classification-style tabular benchmarks to regression without discarding continuous label information.
  • Using the arithmetic pretext task in place of feature-reconstruction or mask-reconstruction pre-training improves RMSE on all ten datasets tested.
  • The adaptive correlated gate is what turns fine-tuning into a regularized problem: without it, performance degrades across all datasets.
  • Addition and multiplication are the safe pre-training operators; subtraction is weaker and division often fails to converge, so practitioners can default to one of the two.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The per-operator study implies that no single arithmetic operator is always best; a validation-based selector for $\odot$ is the most direct extension, and its success would make the method less dependent on human choice.
  • Because the pre-training signal only needs pairs of continuous labels, the same objective could be attached to different tabular encoders or combined with reconstruction tasks; the ablations suggest arithmetic and reconstruction capture different information.
  • The paper motivates 'irregular target functions' without defining them quantitatively; a formal irregularity measure could predict which datasets benefit most from APAR.
  • The learned gate probabilities $\pi$ can be read as feature-importance estimates; comparing them with tree-based importances would test whether the adaptive regularizer is discovering the same features that drive predictions.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes APAR, a two-stage framework for tabular regression. In pre-training, pairs of samples are encoded by a Transformer with a feature tokenizer, and the model predicts the result of an arithmetic operation (addition, subtraction, multiplication, or division) applied to the two labels. In fine-tuning, the model is regularized by enforcing prediction consistency between an original sample and a version augmented with a gate vector drawn from a relaxed multivariate Bernoulli distribution, with a sparsity penalty on the gate. The method is evaluated on 10 tabular regression datasets against GBDT, supervised neural, and pretrain-finetune baselines, reporting average RMSE improvements of 9.43% to 20.37%, with ablations for the pre-training task, the adaptive regularization, and the choice of arithmetic operator.

Significance. If the reported gains are robust, APAR is a practically relevant recipe: it provides a simple arithmetic pretext task that uses continuous labels, an adaptive and structure-aware augmentation scheme, and a consistent empirical pipeline across 10 datasets with public code and data. The paper also includes ablations that isolate the pre-training task and the regularization component. However, the central benchmark claim is not yet fully supported because the per-dataset arithmetic operator is chosen without a stated protocol, no standard deviations are reported despite the stated use of 5 seeds, and several table entries for APAR itself are inconsistent across tables. These issues must be fixed before the headline 'consistently superior' claim can be accepted.

major comments (4)
  1. [§4.2, Algorithm 1, §5.5] The per-dataset arithmetic operator is the most load-bearing unstated choice. The footnote in §4.2 says 'We empirically chose arithmetic operations in our experiments,' and Algorithm 1 line 2 says 'Select an appropriate arithmetic operation' without defining the selection rule. Table 4 shows that the best operator varies by dataset and, for ER, Multiplication achieves 0.0266 while the APAR entry in Table 2 is 0.0338 (the Addition value). If the operator was selected after inspecting test-set results, the reported gains are a post-selected maximum over four choices, not the performance of a single pre-specified method. The authors must specify a pre-registered or validation-based selection rule, report the operator chosen for each dataset, and present the resulting numbers; otherwise the headline 9.43–20.37% improvement is not established.
  2. [§5.1, Tables 2–5] The paper states that 'All the results are the average of 5 different random seeds' but reports no standard deviations, per-seed values, or significance tests anywhere. Many adjacent entries in Table 2 differ by under 1% (e.g., BD: APAR 0.2397 vs. TabNet 0.2404), so without variance information the 'consistently superior' ranking claim cannot be distinguished from noise. Please report mean ± std or equivalent, and ideally a paired significance test or rank stability analysis across seeds.
  3. [§5.4, Table 3] The RQ3 discussion claims that removing adaptive-regularized fine-tuning 'degrades the performance across all datasets.' This is contradicted by Table 3: on ER, both w/o AR and APAR report 0.0266, so the improvement is exactly zero there. The claim should be revised to reflect the actual per-dataset differences, and the ER row should be discussed explicitly.
  4. [Tables 2, 3, and 5] The APAR results are internally inconsistent across tables. Table 2 lists APAR as ER=0.0338, BS=0.0139, PM=0.5239; Table 3 lists the same APAR row as ER=0.0266; and Table 5 lists APAR as ER=0.034, BS=0.014, PM=0.524. If these are different runs or configurations, this must be stated; otherwise the reported numbers should be unified. This discrepancy directly affects the reproducibility of the main result.
minor comments (6)
  1. [Abstract and §5.2] The phrase 'outperforms ... in RMSE (+9.43% ∼ 20.37%)' is ambiguous about direction; since lower RMSE is better, please write 'reduces RMSE by 9.43%–20.37%.'
  2. [Related Work] There is a typo: 'supervised lavels' should be 'supervised labels.'
  3. [Table 2] The notation 'TabNet*' and 'TabNet' is confusing: the group is titled 'NN-based with a Pretrain-Finetune,' but the footnote says '* denotes without pre-training,' and TabNet appears both starred and unstarred. Please clarify which TabNet variant is in which group.
  4. [§5.2] The phrase 'arithmetic-related pertaining tasks' should be 'arithmetic-related pre-training tasks.'
  5. [Eq. (8)] The division operator yi/yj has no guard for yj = 0; please clarify whether the log-scaled labels are always positive or how zero labels are handled.
  6. [§5.2] The sentence 'achieving an average RMSE improvement of 9.18% compared to the second-best ranking method' is not directly derivable from Table 2; please specify which baseline is used for each dataset and how the average is computed.

Circularity Check

1 steps flagged · score 5.0 of 10

APAR's headline RMSE gain is partly a per-dataset selection over empirically tried arithmetic operators, whose selection rule is never specified.

  1. fitted input called prediction [Section 4.2, footnote 1; Algorithm 1 line 2; Section 5.5 Table 4; Section 5.2 Table 2]
    "Footnote 1: "We empirically chose arithmetic operations in our experiments (See Sec. 5.5 for detailed analyses)." Algorithm 1: "Select an appropriate arithmetic operation ∨ ∈ {+, -, ×, /}." Section 5.5: "These results highlight the adaptability of the arithmetic-aware pre-training method that is able to benefit different regression scenarios from various arithmetic operators.""

    The final APAR method is not a single pre-specified algorithm: the arithmetic operator is chosen "empirically" per dataset, and no validation-based selection rule is stated. Comparing the APAR row in Table 2 with the four per-operator rows in Table 4 shows that for 9 of 10 datasets the reported APAR RMSE equals the best (minimum) value among the four operators for that dataset (e.g., BD 0.2397 = Multiplication, PM 0.5239 = Addition, BS 0.0139 = Multiplication). The claimed "outperforms" results are therefore at least partly a selected maximum over empirically tried choices rather than the test performance of a fixed pipeline; if selection used the test set, the headline improvement is a fitted result.

full rationale

Apart from the arithmetic-operator selection, APAR's derivation is self-contained: the pre-training objective (Eqs. 6-9) and fine-tuning losses (Eqs. 14-18) are specified, the ablations in Table 3 provide independent evidence that the pre-training task and adaptive regularization contribute, and no load-bearing self-citation or imported uniqueness theorem is used. The circularity concern is concentrated on the operator choice. Because the paper says the operations were "empirically chose[n]" and Algorithm 1 just instructs to "Select an appropriate arithmetic operation" without a protocol, the reported per-dataset results can coincide with the best of four empirical configurations. If the choice was made on validation data the issue is mild model-selection bias; as written, the test-set protocol is unspecified, so the headline gain is not guaranteed to be the performance of one pre-registered method. This warrants a moderate circularity score rather than a high one, since the framework itself still has independent, falsifiable content.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The framework rests on tuned loss weights (β and γ), a per-dataset categorical operator choice, and four unproven modeling assumptions about the copula, arithmetic pre-training, consistency regularization, and log-scaling. No new physical or conceptual entities are introduced beyond the training objective and gate mechanism.

free parameters (3)
  • β (regularization loss weight) = per dataset, value not reported
    Selected from {0.010, 0.025, 0.050, 0.075, 0.1, 0.2, 0.3, 0.4, 0.5} using the validation set (Appendix B); final per-dataset values are not listed.
  • γ (sparsity loss weight) = per dataset, value not reported
    Same configuration set and selection procedure as β; final values are not reported.
  • arithmetic operator per dataset = not reported per dataset
    Section 4.2 says operators were 'empirically chosen'; Section 5.5 compares addition, subtraction, multiplication, and division but does not state how the final choice was made. This categorical choice can affect reported RMSE.
assumptions (4)
  • domain assumption The Gaussian copula with a correlation matrix computed from all features can represent the joint distribution of tabular features well enough for masking (Eq. 10-12).
    Invoked in Section 4.3 to generate correlated gate vectors; mixed categorical and numeric features may not follow this copula, and no diagnostic is given.
  • ad hoc to paper Predicting arithmetic combinations of labels (Eq. 8) is a useful pretext for learning representations for downstream regression.
    Core modeling assumption of the proposed method, stated in Section 4.2; justified only by downstream empirical gains, not by theory.
  • ad hoc to paper Enforcing prediction consistency between original and gate-augmented versions of a sample reduces overfitting without discarding target-relevant signal.
    Used in the fine-tuning loss, Eq. 17-18; no proof that the learned gate preserves the information needed for the downstream task.
  • domain assumption Log-scaling features and labels is an appropriate space for both the arithmetic pretext and RMSE comparisons.
    Continuous features and labels were log-transformed in Section 5.1; the effect of this transform on the interpretation of arithmetic operations and reported RMSE is not analyzed.

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Pith. "Pith review of APAR: Modeling Irregular Target Functions in Tabular Regression via Arithmetic-Aware Pre-Training and Adaptive-Regularized Fine-Tuning." pith.science (2026). https://pith.science/paper/WWLKLNAX

@misc{pith2026241210941,
  author       = {Pith},
  title        = {Pith review of: APAR: Modeling Irregular Target Functions in Tabular Regression via Arithmetic-Aware Pre-Training and Adaptive-Regularized Fine-Tuning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WWLKLNAX}},
  note         = {Machine review of arXiv:2412.10941}
}
abstract

Tabular data are fundamental in common machine learning applications, ranging from finance to genomics and healthcare. This paper focuses on tabular regression tasks, a field where deep learning (DL) methods are not consistently superior to machine learning (ML) models due to the challenges posed by irregular target functions inherent in tabular data, causing sensitive label changes with minor variations from features. To address these issues, we propose a novel Arithmetic-Aware Pre-training and Adaptive-Regularized Fine-tuning framework (APAR), which enables the model to fit irregular target function in tabular data while reducing the negative impact of overfitting. In the pre-training phase, APAR introduces an arithmetic-aware pretext objective to capture intricate sample-wise relationships from the perspective of continuous labels. In the fine-tuning phase, a consistency-based adaptive regularization technique is proposed to self-learn appropriate data augmentation. Extensive experiments across 10 datasets demonstrated that APAR outperforms existing GBDT-, supervised NN-, and pretrain-finetune NN-based methods in RMSE (+9.43% $\sim$ 20.37%), and empirically validated the effects of pre-training tasks, including the study of arithmetic operations. Our code and data are publicly available at https://github.com/johnnyhwu/APAR.

Figures

Figures reproduced from arXiv: 2412.10941 by the authors.

Figure 1
Figure 1. Illustrations of the impacts of irregular target functions commonly found in tabular regression tasks for finance (stock [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Illustration of the Arithmetic-Aware Pre-Train phase of APAR. Sample pairs are processed through the Feature Tok￾enizer and Feature Encoder, the outputs of which are concatenated for arithmetic prediction, enabling the model to understand inter-sample relationships in tabular regression. larization during the fine-tuning stage. 3 Problem Formulation In this paper, we focus on regression tasks within the tabular doma… view at source ↗
Figure 3
Figure 3. Illustration of the Adaptive Regularization Fine-Tuning phase of APAR. In this phase, an input sample is processed through the Feature Tokenizer to generate feature embeddings, which are augmented using a dynamically adaptive gate vector. The model is trained to predict consistent labels from varying inputs, which enhances the model’s robustness to uninformative features and performance on the target task. 4.2 Arith… view at source ↗

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Reviewed August 11, 2026 · model on record in the stance chip above.