Paper deep dive
Self-Improving Tabular Language Models via Iterative Group Alignment
Yunbo Long, Tejumade Afonja, Alexandra Brintrup, Mario Fritz
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 96%
Last extracted: 4/26/2026, 10:35:16 PM
Summary
The paper introduces TabGRAA (Tabular Group-Relative Advantage Alignment), a self-improving framework for tabular data generation using language models. It addresses the limitations of static fine-tuning and the misalignment of autoregressive objectives by using an automated quality signal (like a distinguishability classifier) to partition synthetic samples into high- and low-quality groups. The core innovation is the Group-Relative Advantage Alignment (GRAA) objective, which optimizes the model based on group-level statistics rather than individual instance-level preferences, facilitating better preservation of global statistical properties and improving fidelity, utility, and privacy.
Entities (9)
Relation Signals (5)
TabGRAA → implements → Group-Relative Advantage Alignment
confidence 100% · We propose Group-Relative Advantage Alignment (GRAA), a novel alignment objective...
Distinguishability-classifier score → isatypeof → Automated Quality Signal
confidence 100% · At each iteration, TabGRAA uses an automated quality signal—such as a two-sample distinguishability classifier or a distance-based reward
TabGRAA → uses → Distinguishability-classifier score
confidence 100% · At each iteration, TabGRAA uses an automated quality signal—such as a two-sample distinguishability classifier or a distance-based reward
Group-Relative Advantage Alignment → improves → Language Model
confidence 90% · The specific signal is a modular choice... the language model is only fine-tuned on these self-generated signals... yielding the refined LMs
DPO → iscomparedto → Group-Relative Advantage Alignment
confidence 90% · Compared to the earlier formulation with three tunable coefficients... this simplified form makes GRAA a principled group-level extension of Bradley–Terry preference learning
Cypher Suggestions (0)
No Cypher suggestions yet.
Abstract
Abstract:While language models have been adapted for tabular data generation, two fundamental limitations remain: (1) static fine-tuning produces models that cannot learn from their own generated samples and adapt to self-correct, and (2) autoregressive objectives preserve local token coherence but neglect global statistical properties, degrading tabular quality. Reinforcement learning offers a potential solution but requires designing reward functions that balance competing objectives -- impractical for tabular data. To fill the gap, we introduce TabGRAA (Tabular Group-Relative Advantage Alignment), the first self-improving framework for tabular data generation via automated feedback. At each iteration, TabGRAA uses an \emph{automated quality signal} -- such as a two-sample distinguishability classifier or a distance-based reward -- to partition newly generated samples into high- and low-quality groups, then optimizes a group-relative advantage objective that reinforces realistic patterns while penalizing artifacts. The specific signal is a modular choice rather than a fixed component of the framework. This establishes a virtuous feedback cycle, where the quality signal is re-computed against newly \emph{generated synthetic} samples at each round; the language model is only fine-tuned on these self-generated signals, so no additional real record is exposed during alignment, mitigating data-leakage risk beyond the initial supervised fine-tuning. Experiments show TabGRAA outperforms existing methods in fidelity, utility, and privacy, while matching or exceeding diffusion-based synthesizers, advancing tabular synthesis from static statistical replication to dynamic, self-improving generation.
Tags
Links
- Source: https://arxiv.org/abs/2604.18966v1
- Canonical: https://arxiv.org/abs/2604.18966v1
Trouble viewing inline? Open PDF directly →
Full Text
159,167 characters extracted from source content.
Expand or collapse full text
Self-Improving Tabular Language Models via Iterative Group Alignment Yunbo Long Tejumade Afonja Alexandra Brintrup Mario Fritz Abstract While language models have been adapted for tabular data generation, two fundamental limitations remain: (1) static fine-tuning produces models that cannot learn from their own generated samples and adapt to self-correct, and (2) autoregressive objectives preserve local token coherence but neglect global statistical properties, degrading tabular quality. Reinforcement learning offers a potential solution but requires designing reward functions that balance competing objectives—impractical for tabular data. To fill the gap, we introduce TabGRAA (Tabular Group-Relative Advantage Alignment), the first self-improving framework for tabular data generation via automated feedback. At each iteration, TabGRAA uses an automated quality signal—such as a two-sample distinguishability classifier or a distance-based reward—to partition newly generated samples into high- and low-quality groups, then optimizes a group-relative advantage objective that reinforces realistic patterns while penalizing artifacts. The specific signal is a modular choice rather than a fixed component of the framework. This establishes a virtuous feedback cycle, where the quality signal is re-computed against newly generated synthetic samples at each round; the language model is only fine-tuned on these self-generated signals, so no additional real record is exposed during alignment, mitigating data-leakage risk beyond the initial supervised fine-tuning. Experiments show TabGRAA outperforms existing methods in fidelity, utility, and privacy, while matching or exceeding diffusion-based synthesizers, advancing tabular synthesis from static statistical replication to dynamic, self-improving generation. Tabular Data, Language Models, Alignment, Group-Relative Advantage 1 Introduction Figure 1: TabGRAA’s self-improving cycle: language models, initially fine-tuned on real data, generate synthetic samples to retrain classifiers, whose indistinguishability feedback guides alignment-based fine-tuning across T iterations, yielding the refined LMs in brown. Recent advances demonstrate that language models (LMs) can generate structured tabular data by representing rows as sequential tokens. Models like GReaT (Generation of Realistic Tabular Data) (Borisov et al., 2022) show that LMs can produce plausible synthetic rows through autoregressive generation. However, despite their initial promise, LM-based tabular synthesis faces two fundamental limitations. First, these models follow a static training paradigm: during fine-tuned on real data, they cannot learn from their own generated samples or adapt to correct statistical errors that emerge during generation. This creates a unidirectional pipeline where the tabular generator ability is fixed after fine-tuning, with no mechanism for continuous improvement. Second, the autoregressive objective itself is misaligned with tabular data requirements. While LMs optimize next-token prediction for local coherence, they fail to preserve holistic dataset properties including column distributions, feature correlations, and global statistical structures (van Breugel and van der Schaar, 2024). Consequently, generated samples may appear plausible row-by-row but exhibit systematic deviations in dataset-level statistics. These dual limitations place current LM-based methods behind diffusion-based approaches in maintaining dataset fidelity (Shi et al., 2024). Reinforcement learning has been used to address these limitations by optimizing for holistic data quality for image and text data (Fan et al., 2023; Miao et al., 2024), but faces prohibitive barriers for tabular data. Unlike text generation where human preferences provide natural reward signals, tabular data quality depends on complex multi-objective trade-offs among fidelity and utility. Designing comprehensive reward functions that maintain tabular statistics while balancing these competing objectives is exceptionally difficult: single metrics are insufficient, distributional conflicts emerge where improving one property degrades another, and training instability often disrupts learned statistical relationships. Furthermore, human feedback–the cornerstone of RL from Human Feedback (RLHF) for text (Wang et al., 2023)–is impractical for tabular data where sample-based quality assessment requires statistical metrics and expertise knowledge, and these metrics differ substantially across datasets. Recently, reward-free alignment methods such as DPO (Rafailov et al., 2024), KTO (Ethayarajh et al., 2024), and NPO (Zhang et al., 2024) offer promising alternatives by eliminating explicit reward modeling. However, they face three fundamental challenges for tabular data: (1) human preferences are scarce and unreliable while tabular quality judgments require statistical expertise, (2) existing tabular metrics provide dataset-level scores but cannot produce meaningful preference pairs between individual samples, and (3) statistical differences between samples rarely translate to clear preferences, while rule-based labels (e.g., age>30age>30) fail to model the trade-offs between utility and fidelity. To address these challenges, we leverage a key insight: distinguishability attack classifiers naturally capture the multi-dimensional quality of tabular samples. By training a classifier to distinguish real from synthetic data, we obtain a signal that inherently reflects statistical fidelity (how well synthetic distributions match real ones), privacy (indistinguishability), and utility (preservation of predictive patterns needed for downstream machine learning tasks). When a classifier struggles to distinguish samples, it indicates good statistical alignment; when it confidently identifies synthetic samples, it reveals statistical deviations.We therefore propose a self-improving framework that uses classifier feedback for continuous enhancement without human intervention. Our method, TabGRAA, generates samples, evaluates them via a distinguishability attack classifier, and optimizes through group-level alignment. This creates a closed-loop system where language models autonomously improve their tabular data generation. The primary contributions of this work are: • We introduce a self-improving framework for tabular language models, enabling continuous quality enhancement through automated classifier feedback without human intervention, transforming static training into iterative refinement. • We propose Group-Relative Advantage Alignment (GRAA), a novel alignment objective that operates on quality-stratified sample groups rather than individual preferences, better suited to tabular data’s distributional nature and outperforming existing alignment baselines. • Through extensive experiments across diverse tabular datasets and language model architectures, we validate TabGRAA’s effectiveness, demonstrating consistent superiority over alignment baselines and even competitive performance against diffusion-based synthesizers. 2 Related Works 2.1 Static learning of Tabular Generators Existing tabular data generation approaches–from probabilistic models (Demarta and McNeil, 2005), GANs (Xu et al., 2019), diffusion (Kotelnikov et al., 2023), and in-context learning methods like TabPFN (Hollmann et al., 2023) to language-model-based synthesis (Borisov et al., 2022)–treat synthesis as a static, one-time learning process. These generators learn to mimic training data distributions but lack mechanisms for post-hoc adaptation or iterative refinement to meet downstream requirements (e.g., utility). While constraint-based frameworks like CuTS (Vero et al., 2023) enable targeted fine-tuning, they still rely on predefined losses rather than supporting continual, self-improving alignment. This static paradigm contrasts with language and image generation, where reinforcement learning and human feedback are routinely used for dynamic optimization of model outputs for flexible generation (Wang et al., 2025). 2.2 Challenges in Aligning Tabular Generative Models Reinforcement learning (RL) and preference optimization methods face significant challenges when applied to tabular data generation. While RL from human feedback (RLHF) and DPO-based alignment (Rafailov et al., 2024) have succeeded in text, image, and multimodal domains where human preferences or clear perceptual metrics exist (Zhang et al., 2026), tabular data lacks natural instance-level preference signals. Methods like PPO (Schulman et al., 2017) require designing composite reward functions that balance multiple competing objectives–data fidelity and downstream utility guarantees–without explicit ground truth. Single-reward formulations fail to capture these trade-offs, while multi-objective optimization introduces instability and huge computation. In addition, DPO and related alignment methods (Ethayarajh et al., 2024; Zhang et al., 2024) rely on human or synthetic preference pairs, which are labor-intensive to collect and often unavailable for private tabular data in production settings. For diffusion-based tabular generators, DPO’s gradient-based updates are impractical due to the multi-step denoising process, which suffers from vanishing gradients and prohibitive computational costs. While language-model-based tabular generation (e.g., GReaT (Borisov et al., 2022)) is architecturally compatible with autoregressive RL, it remains constrained by next-token objectives that fail to optimize sample-level properties for downstream tasks. These challenges highlight the need for alignment methods specifically designed for tabular data approaches that can optimize tabular data without human feedback and maintain statistical fidelity while improving downstream utility. 2.3 Instance-Level Alignment for Tabular Data While DPO, KTO (Ethayarajh et al., 2024), and NPO (Zhang et al., 2024) have shown success in aligning text and image generators, their direct application to tabular data faces challenges. These methods follow an instance-level paradigm, computing alignment losses by comparing individual samples or preference pairs. This formulation assumes quality can be assessed at the sample level–valid for domains like text where humans judge individual outputs, but problematic for tabular data where quality metrics (statistical fidelity, feature correlations, privacy) are inherently distributional. Unlike text where a single sentence can be judged as “good” or “bad”, tabular data quality only emerges from population statistics: individual rows may appear plausible while the overall dataset exhibits systematic biases. Instance-level alignment can therefore improve individual sample plausibility while distorting global properties. This mismatch between optimization objective (instance likelihoods) and evaluation criteria (distributional statistics) leads to suboptimal performance which our work addresses through alignment of group-level statistics. 2.4 Evaluation Metrics vs. Alignment Rewards A parallel line of work focuses on evaluation of tabular synthetic data. Recent benchmarks such as TabStruct (Jiang and others, 2025) measure structural fidelity (the extent to which synthetic data preserves the joint distribution and causal dependencies of the real data) via “train-on-synthetic, test-on-real” utility per feature. These metrics are inherently dataset-level: they are computed over the full synthetic sample and cannot be decomposed into a per-row signal. Consequently, they serve as evaluation targets but cannot be used directly as alignment rewards. Our work bridges this gap by introducing per-sample proxies (density, correlation consistency, OOD anomaly scores) that individually optimize distinct dimensions of dataset-level quality, and demonstrating that multi-reward alignment improves structural fidelity even though structural fidelity itself is not used as a reward. To our knowledge this is the first paper to systematically study how different tabular reward signals affect which statistical properties are preserved under alignment. 3 Self-Improving Tabular Language Model Framework We propose a self-improving framework for tabular language models that enables continuous quality enhancement through automated classifier feedback. Unlike static fine-tuning or human-dependent alignment methods, as shown in the Figure 1, our approach creates a closed-loop system where models learn from their own generated samples via distinguishability attack signals. 3.1 Initial Language Model Fine-Tuning Given a private tabular dataset real=xii=1ND_real=\x_i\_i=1^N, we first serialize each row xix_i into a token sequence w1:j(i)=TOKENIZE(xi)w_1:j^(i)=TOKENIZE(x_i). Starting from a pretrained autoregressive language model πbase _base, we perform supervised fine-tuning to obtain an initial tabular data generation policy πθ0 _ _0: ℒSFT(θ)=−x∼real[∑k=1jlogπθ(wk∣w1:k−1)],L_SFT(θ)=-E_x _real [ _k=1^j _θ(w_k w_1:k-1) ], (1) where πθ(wk|w1:k−1) _θ(w_k|w_1:k-1) follows standard autoregressive factorization. This provides a baseline model capable of generating plausible tabular samples, which serves as the starting point for our self-improving framework. 3.2 Automated Quality Signal The limitations of instance-level alignment methods stem from their reliance on human preferences or instance-specific heuristics. In our iterative framework, we instead leverage an automated quality signal s:→[0,1]s:X→[0,1] computed against the real data realD_real as a scalable alternative. The framework is agnostic to the specific choice of s; in this paper we instantiate it in two complementary ways: (i) Distinguishability-classifier score (default). At iteration t, we generate a synthetic dataset synth(t)=x~jj=1MD_synth^(t)=\ x_j\_j=1^M with x~j∼πθt−1 x_j _ _t-1 and train a binary classifier ϕt:→[0,1] _t:X→[0,1] to distinguish realD_real from synth(t)D_synth^(t). The specific classifier family is a user choice (e.g., Random Forest, XGBoost); Section 4 details the configuration used in our experiments. The classifier output ϕt(x~) _t( x) represents the probability that x~ x is drawn from the real data distribution. We convert this output into an indistinguishability score: scls(x~)=1−2|0.5−ϕt(x~)|,s_cls( x)=1-2|0.5- _t( x)|, (2) where scls(x~)∈[0,1]s_cls( x)∈[0,1]. Values close to 1 indicate high classifier uncertainty (hard to tell from real); values close to 0 indicate easily-separable samples. (i) Distance-based score (alternative). When a two-sample classifier is not desirable—e.g., to avoid the chicken-and-egg dependence on synthetic-data quality—one can replace ϕt _t with a one-class score trained only on realD_real. The canonical instance is Distance-to-Closest-Record (DCR): d(x~)=minx∈real‖x~−x‖2,sdcr(x~)=1−d(x~)−dmindmax−dmin.d( x)= _x _real\| x-x\|_2, s_dcr( x)=1- d( x)-d_ d_ -d_ . (3) Both sclss_cls and sdcrs_dcr produce per-row scores in [0,1][0,1] and can be plugged into GRAA without any change to the optimization objective (see Appendix B.4 for a formal reward-agnostic stability statement). In the main body we default to sclss_cls; Appendix F.1 compares both signals empirically. Data-leakage consideration. At each alignment iteration the quality signal s is computed against newly generated synthetic data synth(t)D_synth^(t), and the language model is fine-tuned on contrasts derived from these self-generated samples. No additional real record is exposed during alignment beyond the initial supervised fine-tuning stage, which reduces the risk of real-data memorization over iterations.111This is a design property, not a formal privacy guarantee; we assess empirical privacy through the distinguishability attack reported in the experiments. 3.3 Sample Stratification for Policy Improvement At iteration t, synthetic samples are ranked by their indistinguishability score s(x~)s( x) and paired to create contrastive learning signals, where we applied a Top-vs-Bottom Pairing strategies. We sort all generated samples by s(x~)s( x) and create K contrastive pairs by matching samples from opposite ends of the ranking: Pairs=(x~ihigh,x~N−i+1low)∣i=1,2,…,K,Pairs=\( x_i^high, x_N-i+1^low) i=1,2,…,K\, (4) where K=⌊N/2⌋K= N/2 and N being the total number of synthetic samples, x~ihigh x_i^high denotes the i-th highest scoring sample, and x~N−i+1low x_N-i+1^low denotes the corresponding lowest scoring sample. This stratification introduces an explicit contrast between highly indistinguishable samples and easily separable ones, enabling the model to preferentially reinforce patterns associated with strong distributional alignment while discouraging features that lead to poor indistinguishability. For methods like DPO and NPO, these pairs are used directly as individual preference comparisons. For GRAA, multiple pairs can be aggregated to form contrasting groups for group-level optimization (detailed in Section 3.4). 3.4 Group-Relative Advantage Alignment (GRAA) Existing alignment methods like DPO and KTO operate on instance-level comparisons, where each gradient update consumes a single preferred–dispreferred pair (ychosen,yrejected)(y_chosen,y_rejected). GRAA extends this to group-level alignment by aggregating statistics across the two quality groups ℬhigh,ℬlowB_high,B_low (each of size B) within each training batch, which better matches tabular data’s distributional nature. Implicit reward and group-level Bradley–Terry. Following DPO (Rafailov et al., 2024), we define the implicit reward rθ(y)=βlogπθ(y)πref(y),r_θ(y)\;=\;β _θ(y) _ref(y), (5) and the group-averaged implicit rewards r¯θhigh=1B∑y∈ℬhighrθ(y),r¯θlow=1B∑y∈ℬlowrθ(y). r_θ^high= 1B _y _highr_θ(y), r_θ^low= 1B _y _lowr_θ(y). (6) Extending the Bradley–Terry preference model from sample pairs to group pairs, the probability that group ℬhighB_high is preferred to ℬlowB_low is P(ℬhigh≻ℬlow∣θ)=σ(r¯θhigh−r¯θlow),P(B_high _low θ)\;=\;σ ( r_θ^high- r_θ^low ), (7) where σ(x)=(1+e−x)−1σ(x)=(1+e^-x)^-1. The group relative advantage is the logit of (7): Δgroup(θ)=r¯θhigh−r¯θlow. _group(θ)\;=\; r_θ^high- r_θ^low. (8) GRAA loss. We take the GRAA loss to be the sigmoid on the negative group advantage: ℒGRAA(θ)=σ(−Δgroup(θ))=σ(r¯θlow−r¯θhigh). \;L_GRAA(θ)\;=\;σ (- _group(θ) )\;=\;σ ( r_θ^low- r_θ^high ).\; (9) Minimizing (9) is equivalent to maximizing the group preference probability (7) (both push Δgroup _group upward). The only hyperparameter is β, which is absorbed into rθr_θ. Compared to the earlier formulation with three tunable coefficients (kl-coeff, forget-coeff, bias), this simplified form makes GRAA a principled group-level extension of Bradley–Terry preference learning rather than an ad-hoc assembly. The three-coefficient generalization, which recovers NPO (kl-coeff =0=0) and KTO (detaching r¯high r^high) as special cases, is discussed in Appendix B.6. Bidirectional gradient flow. A key property of (9) is that both group-averaged log-ratios remain in the computation graph: ∇θℒGRAA(θ)=σ′(−Δgroup)(∇θr¯θlow−∇θr¯θhigh). _θL_GRAA(θ)\;=\;σ (- _group )\, ( _θ r_θ^low- _θ r_θ^high ). (10) The update simultaneously suppresses low-quality samples (+∇r¯low+∇ r^low term) and reinforces high-quality samples (−∇r¯high-∇ r^high term). In contrast, KTO detaches one side of the comparison, which empirically collapses the sampling distribution after a few iterations (Figure 2). The policy updates via gradient descent: θ(t+1)←θ(t)−η∇θℒGRAA(θ(t))θ^(t+1)←θ^(t)-η _θL_GRAA(θ^(t)) (11) The reference model πref _ref remains fixed throughout training, ensuring the policy stays anchored to the original real data distribution. This prevents excessive deviation while allowing targeted optimization for improved utility-fidelity trade-offs. By operating at the group level, GRAA provides more stable gradient estimates and better captures distributional patterns characteristic of tabular data. Algorithm 1 TabGRAA 0: Real dataset realD_real, pretrained LM πbase _base, iterations T, hyperparameters β,ηβ,η, group size B 0: Self-improved policy πθT _ _T 1: πθ0←SFT(πbase,real) _ _0 ( _base,D_real) Supervised fine-tuning 2: πref←πθ0 _ref← _ _0 Reference model, fixed throughout 3: for t=1t=1 to T do 4: synth(t)∼πθt−1D_synth^(t) _ _t-1 Generate a new synthetic batch (independent of any scored pool) 5: ϕt←TrainClassifier(real,synth(t)) _t (D_real,D_synth^(t)) Automated quality signal (or plug in sdcrs_dcr, etc.) 6: Score newly sampled y∼πθt−1y _ _t-1 (disjoint from training pool of ϕt _t) via s(y)=1−2|0.5−ϕt(y)|s(y)=1-2|0.5- _t(y)| 7: ℬhigh,ℬlow←Stratify(⋅,s)B_high,B_low (·,s) Top-vs-bottom halves; see Appendix F.2 for the random-within-halves variant 8: r¯θhigh←βB∑y∈ℬhighlogπθ(y)πref(y) r_θ^high← βB _y _high _θ(y) _ref(y), r¯θlow←βB∑y∈ℬlowlogπθ(y)πref(y) r_θ^low← βB _y _low _θ(y) _ref(y) 9: ℒGRAA←σ(r¯θlow−r¯θhigh)L_GRAA←σ\! ( r_θ^low- r_θ^high ) Eq. (9) 10: θt←θt−1−η∇θℒGRAA _t← _t-1-η _θL_GRAA 11: end for 12: Return πθT _ _T 3.5 Stability and Convergence Guarantees The simplified GRAA loss (9) admits three clean guarantees, proven in Appendix B: (i) a bounded gradient ‖∇θℒGRAA‖≤βG2\| _θL_GRAA\|≤ β G2 under Assumption B.1, (i) an (1/B)O(1/B) variance of each group-averaged gradient under i.i.d. within-group sampling (enabled by the group, not pair, formulation), and (i) reward-agnostic stability: since the quality signal s enters only through group assignment, both (i) and (i) hold uniformly across any s (classifier, DCR, etc.). The fixed reference model πref _ref anchors the policy to the original real-data distribution, preventing distributional collapse. Combined with Assumption B.3, standard SGD analysis then yields convergence to a stationary point (Proposition B.10). 3.6 Comparison with Existing Methods Unlike Proximal Policy Optimization (PPO) (Schulman et al., 2017) which requires training a separate value function, GRAA uses the reference model as a stable baseline similar to KTO (Ethayarajh et al., 2024) but extends it to batch-level computation. Compared to DPO (Rafailov et al., 2024) which minimizes a log-sigmoid loss on pairwise comparisons, GRAA employs a sigmoid loss with separate desirable/undesirable objectives and tunable coefficients, better capturing the continuous nature of those metrics. Relative to Group Relative Preference Optimization (GRPO) (Shao et al., 2024) which computes advantages within groups of responses to the same prompt, GRAA aggregates across different tabular sequences, making it suitable for the distributional optimization required in data generation tasks. See Appendix A for further discussion. 4 Experimental Settings Datasets. Our evaluation uses five diverse mixed-type tabular datasets from UCI: Adult, Default, Shoppers, Magic, and Beijing. Dataset statistics and preprocessing are detailed in Appendix C.1. Baselines. We compare TabGRAA against several categories of baselines: For language model-based tabular generation, we use GReaT (Borisov et al., 2022), which frames tabular synthesis as autoregressive language modeling, and GReaT-FT+: extended fine-tuning matching the total training steps of alignment methods. For alignment methods adapted from text and image generation, we benchmark against DPO (Rafailov et al., 2024) (preference optimization), KTO (Ethayarajh et al., 2024) (binary alignment), and NPO (Zhang et al., 2024) (negative preference optimization). For generative modeling, we include five SOTA methods spanning diverse paradigms: GAN-based approaches (CTGAN (Zhao et al., 2024), VAEs (TVAE (Xu et al., 2019)), and diffusion models (TabDDPM (Kotelnikov et al., 2023), TabSyn (Zhang et al., 2023), TabDiff (Shi et al., 2024)). We omit TabPFNGen (Ma et al., 2024) due to architectural constraints that limit its applicability to small-scale datasets, making it ill-suited for the medium- to large-scale datasets (9k–50k samples) considered in our experiments. See Appendix A and C.2 for baselines details. Experimental Setup. Our experiments comprise three main components: (1) Baseline comparisons with loss variants: We compare all iterative alignment methods (TabDPO, TabNPO, TabKTO, TabGRAA) against the original GReaT model and its supervised fine-tuned variant (GReaT-FT+), analyzing both best performance and iterative performance trajectory across all training rounds; we further evaluate different loss function configurations including KL divergence penalties, gradient difference constraints, and sigmoid/log-sigmoid transformations across all four alignment methods (See details in Appendix A). (2) State-of-the-art benchmarking: We compare our best iterative models against other advanced tabular generative models including CTGAN, TVAE, TabDDPM, TabSyn, and TabDiff. (3) Ablation studies: We systematically evaluate: (i) the impact of batch size for TabGRAA; (i) the impact of beta values for all alignment methods in our iterative framework; (i) alignment data selection strategies, examining alternative pairing schemes (top-vs-bottom for utility–privacy trade-off, adjacent-ranking pairs, and top-ranking pair filtering at 50% and 100% thresholds) to assess sensitivity to pairing granularity; (iv) classifier model types (Random Forest (Breiman, 2001) vs. XGBoost (Chen and Guestrin, 2016a)) and training strategies (continuously updated vs. fixed pre-trained); and (v) base language model architectures (DistilGPT-2, GPT-2, GPT-Neo-125M). Hyperparameters and Evaluation. We use DistilGPT-2 as our base model with batch size 16 for initial self-finetuning. The automated quality signal s(⋅)s(·) introduced in Section 3.2 is a modular choice; in our experiments we instantiate it as a Random Forest distinguishability classifier with 100 trees and default Gini criterion, retrained on real and newly generated synthetic samples at every iteration (an XGBoost (Chen and Guestrin, 2016a) variant is compared as an ablation, and a distance-based alternative sdcrs_dcr is evaluated in Appendix F.1). Language models are fine-tuned with AdamW using learning rates 5×10−6,5×10−7,5×10−8\5× 10^-6,5× 10^-7,5× 10^-8\ and β∈0.1,1,10,100β∈\0.1,1,10,100\ for 1–5 rounds (extended to 10 rounds for comparisons with advanced generative methods in Appendix 5.3). For TabGRAA, we finetune group size 4,8,16,32\4,8,16,32\, with coefficient defaults: bias =1.0=1.0, klcoeff=1kl_coeff=1, forgetcoeff=1forget_coeff=1. All methods share the same base checkpoint and classifier setup. Each iteration retrains the classifier on real and synthetic data (equal sample sizes) to evaluate newly generated samples for alignment preparation. Synthetic data quality is evaluated across: (1) Fidelity: Column Density Estimation similarity (CDE, higher == better match), Pairwise Correlation similarity (PCC, higher == better), Shape & Trend errors (lower == better), α-precision, and β-recall; (2) Utility: downstream task performance via Machine Learning Efficiency (MLE); (3) Privacy: Distinguishability Attack (DA) AUC, where values closer to 0.5 indicate stronger indistinguishability (we report ||AUC −0.5|-0.5|, lower == better). C2ST scores are computed via the SDMetrics quality convention where higher indicates better synthetic quality. Table results report mean ± std over 10 seeds; some figures also show 95% confidence intervals. Details are in Appendices C.3 and D. 5 Experimental Results Table 1: Iterative Self-Improvement Comparison: Baseline vs. Alignment Methods and Ablation Study of Loss Variants (Averaged Across Five Datasets). For the MLE, the Beijing dataset is not included for calculation. Best results are in bold. Method CDE↑ PCC↑ α↑ β↑ C2ST↑ DA↓ MLE↑ Baselines GReaT 86.86±4.9286.86 ± 4.92 58.72±24.4558.72 ± 24.45 83.41±9.6883.41 ± 9.68 47.05±7.2147.05 ± 7.21 32.75±18.4932.75 ± 18.49 0.8179±0.05330.8179 ± 0.0533 0.8270±0.09950.8270 ± 0.0995 GReaT-FT+ 87.42±5.0987.42 ± 5.09 58.63±24.1458.63 ± 24.14 85.82±9.2785.82 ± 9.27 46.53±6.7146.53 ± 6.71 33.40±19.4333.40 ± 19.43 0.8151±0.04980.8151 ± 0.0498 0.8225±0.10450.8225 ± 0.1045 DPO variants TabDPO (base) 95.02±2.6495.02 ± 2.64 57.58±25.3757.58 ± 25.37 95.81±3.4695.81 ± 3.46 49.87±4.6349.87 ± 4.63 33.40±29.3433.40 ± 29.34 0.6834±0.10020.6834 ± 0.1002 0.8246±0.12610.8246 ± 0.1261 + KL penalty 94.74±2.7394.74 ± 2.73 56.93±25.3156.93 ± 25.31 95.50±3.5995.50 ± 3.59 49.39±4.8349.39 ± 4.83 33.35±29.2233.35 ± 29.22 0.6850±0.09970.6850 ± 0.0997 0.8249±0.12420.8249 ± 0.1242 + Gradient diff. 95.00±2.6695.00 ± 2.66 56.46±25.6956.46 ± 25.69 96.75±2.6696.75 ± 2.66 49.83±4.6349.83 ± 4.63 33.32±29.1933.32 ± 29.19 0.6891±0.09890.6891 ± 0.0989 0.8266±0.12450.8266 ± 0.1245 NPO variants TabNPO (base) 87.90±4.3787.90 ± 4.37 56.58±24.3856.58 ± 24.38 85.80±8.9985.80 ± 8.99 49.28±6.1449.28 ± 6.14 14.84±20.2914.84 ± 20.29 0.7794±0.06110.7794 ± 0.0611 0.8257±0.11170.8257 ± 0.1117 + KL penalty 87.94±4.4487.94 ± 4.44 54.55±23.1754.55 ± 23.17 85.40±8.9785.40 ± 8.97 49.11±5.9349.11 ± 5.93 15.10±20.5515.10 ± 20.55 0.7775±0.06050.7775 ± 0.0605 0.8228±0.10900.8228 ± 0.1090 + Gradient diff. 88.26±4.3988.26 ± 4.39 54.74±23.0954.74 ± 23.09 85.52±9.1485.52 ± 9.14 49.47±6.1849.47 ± 6.18 15.38±20.3615.38 ± 20.36 0.7777±0.06110.7777 ± 0.0611 0.8241±0.11160.8241 ± 0.1116 KTO variants TabKTO (base) 87.09±4.3487.09 ± 4.34 56.44±24.2256.44 ± 24.22 85.14±9.0585.14 ± 9.05 49.19±6.2549.19 ± 6.25 14.53±19.6314.53 ± 19.63 0.7824±0.05900.7824 ± 0.0590 0.8242±0.11210.8242 ± 0.1121 + Logsigmoid 87.09±4.3587.09 ± 4.35 55.64±23.4155.64 ± 23.41 84.73±9.0684.73 ± 9.06 48.93±6.0748.93 ± 6.07 14.72±19.7914.72 ± 19.79 0.7834±0.05970.7834 ± 0.0597 0.8274±0.11250.8274 ± 0.1125 + Logs. + Grad. diff 87.09±4.3087.09 ± 4.30 55.27±23.2355.27 ± 23.23 84.72±9.1284.72 ± 9.12 48.95±6.1048.95 ± 6.10 14.61±19.6614.61 ± 19.66 0.7835±0.05930.7835 ± 0.0593 0.8288±0.11470.8288 ± 0.1147 GRAA variants (Ours) TabGRAA (base) 95.47±2.7795.47 ± 2.77 58.80±24.6758.80 ± 24.67 96.73±3.3096.73 ± 3.30 50.06±4.8650.06 ± 4.86 35.01±28.5535.01 ± 28.55 0.6795±0.10110.6795 ± 0.1011 0.8314±0.12790.8314 ± 0.1279 + Logsigmoid 94.86±2.9294.86 ± 2.92 59.26±24.9159.26 ± 24.91 97.74±2.8797.74 ± 2.87 49.60±4.7449.60 ± 4.74 34.32±28.0034.32 ± 28.00 0.6902±0.10180.6902 ± 0.1018 0.8298±0.12800.8298 ± 0.1280 + Logs. + Grad. diff 94.84±2.9794.84 ± 2.97 57.35±24.0057.35 ± 24.00 97.04±2.8397.04 ± 2.83 50.03±4.9550.03 ± 4.95 34.19±28.2334.19 ± 28.23 0.6873±0.09970.6873 ± 0.0997 0.8292±0.12810.8292 ± 0.1281 Figure 2: Iterative performance progression comparison across training rounds (1-5). CDE, PCC, α, β, C2ST, and DA metrics are averaged across five benchmark datasets, comparing progressive improvement through self-training iterations (The Beijing dataset is excluded from MLE averages). KTO suffers model corruption during extended fine-tuning iterations. Table 2: Performance comparison on α-Precision across five benchmark datasets Method Adult Default Shoppers Magic Beijing GAN-based models CTGAN 77.74±0.1577.74 ± 0.15 62.08±0.0862.08 ± 0.08 76.97±0.3976.97 ± 0.39 86.90±0.2286.90 ± 0.22 96.27±0.1496.27 ± 0.14 TVAE 98.17±0.1798.17 ± 0.17 85.57±0.3485.57 ± 0.34 58.19±0.2658.19 ± 0.26 86.19±0.4886.19 ± 0.48 97.20±0.1097.20 ± 0.10 Diffusion-based models TabDDPM 96.39±0.2096.39 ± 0.20 97.59±0.3697.59 ± 0.36 88.55±0.6888.55 ± 0.68 98.59±0.1798.59 ± 0.17 97.93±0.3097.93 ± 0.30 TabSyn 99.39±0.1899.39 ± 0.18 98.65±0.2398.65 ± 0.23 98.36±0.5298.36 ± 0.52 99.42±0.2899.42 ± 0.28 87.51±0.2487.51 ± 0.24 TabDiff 99.02±0.2099.02 ± 0.20 98.49±0.2898.49 ± 0.28 99.11±0.3499.11 ± 0.34 99.42±0.2199.42 ± 0.21 98.06±0.2498.06 ± 0.24 LLM-based model GReaT 55.79±0.0355.79 ± 0.03 85.90±0.1785.90 ± 0.17 78.88±0.1378.88 ± 0.13 85.46±0.5485.46 ± 0.54 98.32±0.2298.32 ± 0.22 TabGRAA 99.44±0.2399.44 ± 0.23 96.25±0.4296.25 ± 0.42 99.61±0.3199.61 ± 0.31 95.26±0.1795.26 ± 0.17 99.51±0.2899.51 ± 0.28 Figure 3: Classifier Variants Figure 4: Comparison of classifier training strategies on Adult dataset (with 95% CI). Table 3: Different pairing strategy comparison and top-k percentile for TabGRAA on Adult. Best results are in bold. Method CDE↑ PCC↑ α↑ β↑ C2ST↑ DA↓ MLE↑ Top-vs-bottom Pairing k=50% 99.06±0.06 99.06 ± 0.06 92.71±0.15 92.71 ± 0.15 99.35±0.2299.35 ± 0.22 50.15±0.3850.15 ± 0.38 95.07±0.3795.07 ± 0.37 0.5074±0.00460.5074 ± 0.0046 0.9222±0.00310.9222 ± 0.0031 k=100% 98.85±0.0398.85 ± 0.03 90.15±1.6490.15 ± 1.64 99.57±0.12 99.57 ± 0.12 50.25±0.3350.25 ± 0.33 95.76±0.41 95.76 ± 0.41 0.5038±0.0043 0.5038 ± 0.0043 0.9225±0.0015 0.9225 ± 0.0015 Offset Pairing k=50% 92.66±0.0892.66 ± 0.08 84.34±0.0884.34 ± 0.08 69.96±0.4169.96 ± 0.41 52.05±0.22 52.05 ± 0.22 65.68±0.3665.68 ± 0.36 0.7001±0.00530.7001 ± 0.0053 0.9168±0.00250.9168 ± 0.0025 k=100% 92.62±0.0892.62 ± 0.08 83.73±0.0783.73 ± 0.07 69.67±0.2569.67 ± 0.25 51.95±0.4251.95 ± 0.42 64.92±0.1864.92 ± 0.18 0.6343±0.00540.6343 ± 0.0054 0.9088±0.00330.9088 ± 0.0033 Figure 5: Iterative Performance Comparison of TabGRAA Using Different Batch Sizes (4, 8, 16, 32, 64) on Adult Dataset. Figure 6: Radar plot comparing four tabular alignment methods across β0.1,1,10,100 on Adult dataset. Filled regions show performance per β (colored); markers denote methods. Arrows indicate optimization direction (↑: maximize, ↓: minimize). Table 4: TabGRAA implemented across diverse language model architectures on Adult dataset. Best results are in bold. Model (Params) CDE↑ PCC↑ α↑ β↑ C2ST↑ DA↓ MLE↑ DistilGPT-2 (82M) 98.85±0.0398.85 ± 0.03 90.15±1.6490.15 ± 1.64 99.57±0.12 99.57 ± 0.12 50.25±0.3350.25 ± 0.33 95.76±0.4195.76 ± 0.41 0.5038±0.00430.5038 ± 0.0043 0.9225±0.00150.9225 ± 0.0015 GPT-NEO (125M) 99.09±0.05 99.09 ± 0.05 90.53±1.26 90.53 ± 1.26 98.19±0.3298.19 ± 0.32 52.79±0.35 52.79 ± 0.35 95.48±0.2795.48 ± 0.27 0.4961±0.0033 0.4961 ± 0.0033 0.9188±0.00250.9188 ± 0.0025 GPT2 (124M) 99.03±0.0499.03 ± 0.04 85.53±1.5785.53 ± 1.57 98.98±0.4198.98 ± 0.41 50.21±0.2250.21 ± 0.22 96.09±0.35 96.09 ± 0.35 0.5179±0.00220.5179 ± 0.0022 0.9228±0.0032 0.9228 ± 0.0032 5.1 Iterative Performance Comparison Table 1 compares peak performance across five refinement rounds, averaged over five datasets. Each method’s best performance during its five-round tuning process is reported per dataset, with means and standard deviations computed across datasets. TabGRAA achieves the highest peak performance, outperforming GReaT, GReaT-FT+, and other alignment baselines (TabDPO, TabNPO, TabKTO) across all seven evaluation metrics. Specifically, on Adult dataset (see Appendix E.1), TabGRAA improves CDE from 92.55% to 99.13%, reduces DA from 73.43% to 49.97%, and increases MLE from 91.21% to 92.14% compared to GReaT. Figure 2 illustrates performance evolution across refinement rounds, averaged across datasets. TabGRAA consistently achieves the best average performance throughout all iterations, followed by TabDPO, while TabNPO and TabKTO show limited improvement, TabKTO’s instance-based optimization catastrophically destabilizes the language model in later rounds, completely breaking its sampling function.This collapse underscores the effectiveness of our iterative group advantage approach. Detailed per-round results for each dataset are provided in Appendix E.2. 5.2 Loss Function Variants Our ablation in Table 1 reveals distinct patterns across loss variants. For TabDPO and TabNPO, KL penalties enhance stability while gradient constraints improve most metrics but slightly increase privacy risk. In contrast, TabKTO variants show minimal differences, highlighting the inherent limitations of KTO optimization. For TabGRAA, the base variant with binary sigmoid loss achieves the best performance on CDE, C2ST, DA, and MLE, while the logsigmoid variant excels in PCC and α-precision. These results demonstrate that our GRAA framework effectively balances different optimization objectives through appropriate loss formulations. Results for each dataset are provided in Appendix E.1. 5.3 Tabular Generative Models Comparison Table 2 compares TabGRAA with state-of-the-art tabular generation methods. While the original GReaT baseline lags behind GAN-based (CTGAN, TVAE) and diffusion-based (TabDDPM, TabSyn, TabDiff) approaches, our iterative alignment method TabGRAA (within 10 rounds) achieves competitive performance. TabGRAA obtains the highest α-precision on Adult, Shoppers, and Beijing datasets. These results demonstrate that iterative self-alignment transforms LLM-based tabular generators from underperformers into competitive alternatives, bridging the performance gap. See Appendix E.3 for results of other metrics. 5.4 Component Ablation We directly test whether each component of TabGRAA is necessary by removing or replacing it one at a time while keeping everything else fixed. The tables and figures in this section summarize results reported in full in Appendices F.1, F.2, F.3, and F.4. (a) Quality signal is necessary. Replacing the classifier score with uniform random scores (Random scoring), or keeping valid classifier scores but pairing samples at random (Random pairing), both leave performance at the GReaT baseline (Table 5). Only full TabGRAA reduces Wasserstein from 0.0590.059 to 0.0280.028 and JSD from 0.0120.012 to 0.0030.003. This rules out the hypothesis that the gains come from any form of stratified group training—a meaningful, real-data-dependent signal is required. Table 5: The quality signal is necessary. Adult, 5 iterations, B=4B=4. Random scoring (uninformative signal) and Random pairing (valid scores, random assignment) both stay at the baseline; only full TabGRAA improves substantially. Lower W/MMD/JSD is better; MIA AUC closer to 0.50.5 is more private. Method W↓ MMD↓ JSD↓ MIA→ 0.5 Baseline (GReaT) 0.05850.0585 0.00680.0068 0.01180.0118 0.50960.5096 Random scoring 0.05890.0589 0.00600.0060 0.00980.0098 0.50900.5090 Random pairing 0.05640.0564 0.00580.0058 0.00960.0096 0.50750.5075 TabGRAA (full) 0.02780.0278 0.00120.0012 0.00340.0034 0.50960.5096 (b) Reference model anchor is necessary. Removing the fixed reference πref _ref from the alignment objective degenerates GRAA to extended supervised fine-tuning. The corresponding baseline, GReaT-FT+, gains almost nothing over GReaT in Table 1, whereas TabGRAA closes most of the gap to diffusion on the same datasets. The reference anchor—not simply more training steps—drives the improvement. (c) Bidirectional gradient flow is necessary. Instance-level methods that detach one side of the comparison (e.g., TabKTO detaching the high-quality term) collapse during extended iteration: Figure 2 shows TabKTO’s metrics degrade catastrophically from round 3 onward, with sampling breaking entirely. GRAA’s simplified loss σ(r¯low−r¯high)σ( r^low- r^high) keeps both group-averaged log-ratios in the computation graph, and is empirically stable across all rounds and datasets. This is a direct consequence of the derivation in Section 3.4, not a tuning artifact. (d) Classifier retraining each iteration is necessary. A classifier trained once and held fixed has its decision boundary become increasingly stale as πθ _θ evolves. Figure 4 shows that fixed classifiers degrade monotonically over iterations, while retrained classifiers continue to produce informative signal. Retraining is therefore a load-bearing component of the self-improving loop, not an implementation detail. (e) Top-vs-bottom stratification is essential; pair-wise correspondence is not. Top-vs-bottom stratification significantly outperforms adjacent-ranking (offset) stratification across all metrics (Table 3), because contrasting the tails of the quality distribution yields a much clearer gradient signal than contrasting neighboring samples. However, within the high/low halves, random selection matches explicit top-vs-bottom index matching on all five datasets (Table 6). GRAA therefore depends on the group structure (top-half vs. bottom-half), not on any specific pair-wise correspondence—making it strictly more flexible than DPO/NPO. Table 6: GRAA uses groups, not pairs. Random selection within the high/low half-groups vs. explicit top-vs-bottom index matching (5 iterations, B=4B=4). The two strategies are statistically indistinguishable across all datasets and metrics, confirming GRAA does not rely on pair-wise correspondence. Dataset W ↓ MMD ↓ JSD ↓ Rand T-v-B Rand T-v-B Rand T-v-B adult 0.0320.032 0.0280.028 0.00140.0014 0.00120.0012 0.00330.0033 0.00340.0034 shoppers 0.2530.253 0.2530.253 0.1470.147 0.1370.137 0.1710.171 0.1700.170 beijing 0.3450.345 0.3450.345 0.0990.099 0.0990.099 0.2330.233 0.2330.233 default 0.4220.422 0.4210.421 0.3590.359 0.3590.359 0.2930.293 0.2920.292 magic 0.0330.033 0.0330.033 0.00410.0041 0.00410.0041 0.0170.017 0.0150.015 Table 7: Effect of reward choice on multiple quality dimensions. We compare the distinguishability classifier reward (ρcls _cls, default) against a held-out-split variant of the classifier reward (ρholdout _holdout, no data leakage) and Distance to Closest Record (ρdcr _dcr, no classifier). Results are averaged over 5 iterations on five datasets. Lower W/MMD/JSD is better; MIA AUC closer to 0.50.5 is more private. Structural fidelity (higher is better) measures preservation of per-feature conditional dependencies, evaluated via the train-on-synthetic, test-on-real protocol of (Jiang and others, 2025). Dataset Reward Wasserstein↓ MMD↓ JSD↓ MIA AUC→ 0.5 Struct. Fid.↑ adult Baseline (GReaT) 0.0585±0.00000.0585 ± 0.0000 0.0068±0.00000.0068 ± 0.0000 0.0118±0.00000.0118 ± 0.0000 0.5096±0.00000.5096 ± 0.0000 0.9870.987 adult DCR (ρdcr _dcr) 0.0379±0.00520.0379 ± 0.0052 0.0024±0.0009 0.0024 ± 0.0009 0.0054±0.00140.0054 ± 0.0014 0.5087±0.00090.5087 ± 0.0009 0.8540.854 adult Holdout (ρholdout _holdout) 0.0395±0.00840.0395 ± 0.0084 0.0026±0.00110.0026 ± 0.0011 0.0054±0.00170.0054 ± 0.0017 0.5093±0.00110.5093 ± 0.0011 0.8860.886 adult Classifier (ρcls _cls, ours) 0.0384±0.0077 0.0384 ± 0.0077 0.0025±0.00120.0025 ± 0.0012 0.0053±0.0016 0.0053 ± 0.0016 0.5094±0.0010 0.5094 ± 0.0010 0.960 0.960 shoppers Baseline (GReaT) 0.2543±0.00000.2543 ± 0.0000 0.1410±0.00000.1410 ± 0.0000 0.1760±0.00000.1760 ± 0.0000 0.4887±0.00000.4887 ± 0.0000 0.6860.686 shoppers DCR (ρdcr _dcr) 0.2483±0.0054 0.2483 ± 0.0054 0.1408±0.0065 0.1408 ± 0.0065 0.1700±0.0023 0.1700 ± 0.0023 0.4853±0.0014 0.4853 ± 0.0014 0.5470.547 shoppers Holdout (ρholdout _holdout) 0.2712±0.06730.2712 ± 0.0673 0.1432±0.00690.1432 ± 0.0069 0.1717±0.00130.1717 ± 0.0013 0.4851±0.00170.4851 ± 0.0017 0.6710.671 shoppers Classifier (ρcls _cls, ours) 0.2538±0.00390.2538 ± 0.0039 0.1418±0.00790.1418 ± 0.0079 0.1719±0.00160.1719 ± 0.0016 0.4849±0.00220.4849 ± 0.0022 0.684 0.684 beijing Baseline (GReaT) 0.3582±0.00000.3582 ± 0.0000 0.1011±0.00000.1011 ± 0.0000 0.2371±0.00000.2371 ± 0.0000 0.5164±0.00000.5164 ± 0.0000 0.4600.460 beijing DCR (ρdcr _dcr) 0.3583±0.00060.3583 ± 0.0006 0.1006±0.00060.1006 ± 0.0006 0.2371±0.00030.2371 ± 0.0003 0.5105±0.0027 0.5105 ± 0.0027 0.462 0.462 beijing Holdout (ρholdout _holdout) 0.3502±0.00370.3502 ± 0.0037 0.0991±0.0006 0.0991 ± 0.0006 0.2345±0.00100.2345 ± 0.0010 0.5123±0.00290.5123 ± 0.0029 0.4540.454 beijing Classifier (ρcls _cls, ours) 0.3501±0.0039 0.3501 ± 0.0039 0.0992±0.00060.0992 ± 0.0006 0.2344±0.0011 0.2344 ± 0.0011 0.5126±0.00230.5126 ± 0.0023 0.4500.450 default Baseline (GReaT) 0.4213±0.00000.4213 ± 0.0000 0.3590±0.00000.3590 ± 0.0000 0.2964±0.00000.2964 ± 0.0000 0.5085±0.00000.5085 ± 0.0000 0.391 0.391 default DCR (ρdcr _dcr) 0.4218±0.00060.4218 ± 0.0006 0.3589±0.00040.3589 ± 0.0004 0.2927±0.00080.2927 ± 0.0008 0.5061±0.0013 0.5061 ± 0.0013 0.2760.276 default Holdout (ρholdout _holdout) 0.4217±0.00080.4217 ± 0.0008 0.3590±0.00030.3590 ± 0.0003 0.2930±0.00110.2930 ± 0.0011 0.5061±0.00100.5061 ± 0.0010 0.3160.316 default Classifier (ρcls _cls, ours) 0.4215±0.0004 0.4215 ± 0.0004 0.3590±0.0004 0.3590 ± 0.0004 0.2926±0.0008 0.2926 ± 0.0008 0.5060±0.00110.5060 ± 0.0011 0.3230.323 magic Baseline (GReaT) 0.0295±0.00000.0295 ± 0.0000 0.0053±0.00000.0053 ± 0.0000 0.0329±0.00000.0329 ± 0.0000 0.4987±0.00000.4987 ± 0.0000 0.879 0.879 magic DCR (ρdcr _dcr) 0.0472±0.01550.0472 ± 0.0155 0.0075±0.00280.0075 ± 0.0028 0.0293±0.00610.0293 ± 0.0061 0.4973±0.00190.4973 ± 0.0019 0.8360.836 magic Holdout (ρholdout _holdout) 0.0326±0.0110 0.0326 ± 0.0110 0.0043±0.0007 0.0043 ± 0.0007 0.0194±0.0035 0.0194 ± 0.0035 0.4986±0.0026 0.4986 ± 0.0026 0.7730.773 magic Classifier (ρcls _cls, ours) 0.0584±0.10970.0584 ± 0.1097 0.0044±0.00060.0044 ± 0.0006 0.0180±0.00450.0180 ± 0.0045 0.4989±0.00250.4989 ± 0.0025 0.8550.855 (f) Reward choice is modular (and no data leakage). The classifier signal can be replaced with a geometric distance reward (DCR, no classifier) or a held-out-split classifier (Holdout) with similar improvements across all five datasets (Table 7). DCR and Holdout are not equivalent to the default classifier: DCR uses no classifier at all, while Holdout trains the classifier on a disjoint half of the synthetic pool and only scores the held-out half, so the scorer never sees the samples it rates. All three signals produce comparable gains on Wasserstein, MMD, and JSD while keeping MIA AUC close to 0.50.5, which is the primary empirical evidence that our gains are not driven by classifier–synthetic-sample leakage. We therefore frame the method as signal-agnostic: the classifier is one natural choice, not a fixed component of TabGRAA. (g) Long-horizon monotonic improvement. Extending TabGRAA to 20 iterations on Adult reduces Wasserstein by 80.1%80.1\% (0.0498→0.00990.0498→ 0.0099), with the trajectory showing a significant monotonic decrease (Spearman ρ=−0.917ρ=-0.917, p<0.001p<0.001; Welch’s t-test between early and late rounds p<0.001p<0.001; Appendix F.4). While a formal monotonic-improvement theorem remains open, the empirical evidence rules out the concern that gains plateau or reverse after a few rounds. Hyperparameter robustness. The remaining components are well-chosen defaults rather than sensitive knobs. Classifier family: Random Forest slightly outperforms XGBoost (Appendix E.5). Alignment strength: TabGRAA obtains its best performance at β=1β=1 on all five datasets without per-dataset tuning (Figure 6; Appendix E.6), while TabNPO/TabKTO are β-sensitive. Batch size: small batches (4–8) are unstable and excessively large batches (64) average out useful signal, with B∈16,32B∈\16,32\ providing the best trade-off (Figure 5). 6 Discussion and Limitations TabGRAA demonstrates strong performance on multiple tabular generation benchmarks but has several limitations. First, its reliance on a two-sample classifier for alignment introduces a chicken-and-egg problem: poor synthetic data yields weak classifiers, potentially slowing early-stage convergence. Second, the fixed reference model, while stabilizing training, may constrain exploration, limiting discovery of novel high-quality data patterns beyond the initial supervised fine-tuned distribution. Third, group-level aggregation reduces variance but may smooth over fine-grained quality distinctions important for tabular features–particularly rare category combinations that could be averaged out. 7 Conclusion and Future Work We introduced TabGRAA, the first self-improving framework for tabular data generation via automated feedback. TabGRAA operates with a pluggable per-row quality signal—a two-sample distinguishability classifier by default, or alternatives such as a distance-based reward—that is used to partition newly generated samples into high- and low-quality groups at each iteration. A group-relative advantage objective then aligns the generator to the current signal, creating a virtuous cycle where the language model is fine-tuned only on its own newly generated outputs, limiting additional exposure of real records beyond the initial supervised fine-tuning. Across diverse benchmarks, TabGRAA outperforms existing fine-tuning and alignment methods in fidelity, utility, and privacy, and is competitive with diffusion-based synthesizers on several metrics. Future directions include: (1) extending to conditional generation for label balancing and fairness improvement; (2) tackling out-of-distribution tabular generation for domain adaptation; and (3) scaling to tabular foundation models. References A. Alaa, B. Van Breugel, E. S. Saveliev, and M. van der Schaar (2022) How faithful is your synthetic data? sample-level metrics for evaluating and auditing generative models. In International Conference on Machine Learning, p. 290–306. Cited by: §C.3.3, §C.3.3. V. Borisov, K. Seßler, T. Leemann, M. Pawelczyk, and G. Kasneci (2022) Language models are realistic tabular data generators. arXiv preprint arXiv:2210.06280. Cited by: §1, §2.1, §2.2, §4. V. Borisov, K. Seßler, T. Leemann, M. Pawelczyk, and G. Kasneci (2023) Language models are realistic tabular data generators. External Links: 2210.06280 Cited by: §A.1, 1st item. L. Breiman (2001) Random forests. Machine learning 45 (1), p. 5–32. Cited by: §4. M. M. Breunig, H. Kriegel, R. T. Ng, and J. Sander (2000) LOF: identifying density-based local outliers. In Proceedings of the 2000 ACM SIGMOD international conference on Management of data, p. 93–104. Cited by: §A.2. T. Chen and C. Guestrin (2016a) XGBoost: a scalable tree boosting system. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, p. 785–794. Cited by: §4, §4. T. Chen and C. Guestrin (2016b) XGBoost: a scalable tree boosting system. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’16. External Links: Link, Document Cited by: §C.3.1. S. Demarta and A. J. McNeil (2005) The t copula and related copulas. International statistical review 73 (1), p. 111–129. Cited by: §2.1. K. Ethayarajh, W. Xu, N. Muennighoff, D. Jurafsky, and D. Kiela (2024) KTO: model alignment as prospect theoretic optimization. External Links: 2402.01306, Link Cited by: 2nd item, 3rd item, §1, §2.2, §2.3, §3.6, §4. Y. Fan, O. Watkins, Y. Du, H. Liu, M. Ryu, C. Boutilier, P. Abbeel, M. Ghavamzadeh, K. Lee, and K. Lee (2023) Dpok: reinforcement learning for fine-tuning text-to-image diffusion models. Advances in Neural Information Processing Systems 36, p. 79858–79885. Cited by: §1. J. Gao, S. Xu, W. Ye, W. Liu, C. He, W. Fu, Z. Mei, G. Wang, and Y. Wu (2024) On designing effective rl reward at training time for llm reasoning. arXiv preprint arXiv:2410.15115. Cited by: §A.1. N. Hollmann, S. Müller, K. Eggensperger, and F. Hutter (2023) TabPFN: a transformer that solves small tabular classification problems in a second. In International Conference on Learning Representations 2023, Cited by: §2.1. X. Jiang et al. (2025) Measuring structural fidelity of synthetic tabular data via utility per feature. arXiv preprint arXiv:2509.11950. Cited by: §A.2, §F.1, §2.4, Table 7, Table 7. A. Kotelnikov, D. Baranchuk, I. Rubachev, and A. Babenko (2023) TabDDPM: modelling tabular data with diffusion models. In International Conference on Machine Learning, p. 17564–17579. Cited by: 1st item, §2.1, §4. B. Liu, X. Liu, X. Jin, P. Stone, and Q. Liu (2021) Conflict-averse gradient descent for multi-task learning. Advances in Neural Information Processing Systems 34, p. 18878–18890. Cited by: §A.1. J. Ma, A. Dankar, G. Stein, G. Yu, and A. Caterini (2024) TabPFGen–tabular data generation with tabpfn. arXiv preprint arXiv:2406.05216. Cited by: §4. Z. Miao, J. Wang, Z. Wang, Z. Yang, L. Wang, Q. Qiu, and Z. Liu (2024) Training diffusion models towards diverse image generation with reinforcement learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, p. 10844–10853. Cited by: §1. R. Rafailov, A. Sharma, E. Mitchell, S. Ermon, C. D. Manning, and C. Finn (2024) Direct preference optimization: your language model is secretly a reward model. External Links: 2305.18290, Link Cited by: 1st item, 4th item, Remark B.2, §1, §2.2, §3.4, §3.6, §4. B. Schölkopf, J. C. Platt, J. Shawe-Taylor, A. J. Smola, and R. C. Williamson (2001) Estimating the support of a high-dimensional distribution. Neural computation 13 (7), p. 1443–1471. Cited by: §A.2. J. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov (2017) Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347. Cited by: §2.2, §3.6. SDMetrics (2024) Detection metrics (single table) - sdmetrics documentation. Note: Accessed: 2024-05-20 External Links: Link Cited by: §C.3.4. Z. Shao, P. Wang, Q. Zhu, R. Xu, J. Song, X. Bi, H. Zhang, M. Zhang, Y. Li, Y. Wu, et al. (2024) Deepseekmath: pushing the limits of mathematical reasoning in open language models. arXiv preprint arXiv:2402.03300. Cited by: §A.5, Remark B.2, §3.6. J. Shi, M. Xu, H. Hua, H. Zhang, S. Ermon, and J. Leskovec (2024) TabDiff: a multi-modal diffusion model for tabular data generation. arXiv preprint arXiv:2410.20626. Cited by: 3rd item, §C.3.2, §1, §4. J. Si, Z. Ou, M. Qu, Z. Xiang, and Y. Li (2025) TabRep: training tabular diffusion models with a simple and effective continuous representation. arXiv preprint arXiv:2504.04798. Cited by: §C.3.2. B. van Breugel and M. van der Schaar (2024) Why tabular foundation models should be a research priority. arXiv preprint arXiv:2405.01147. Cited by: §1. M. Vero, M. Balunović, and M. Vechev (2023) Cuts: customizable tabular synthetic data generation. arXiv preprint arXiv:2307.03577. Cited by: §2.1. Y. Wang, Z. Li, Y. Zang, Y. Zhou, J. Bu, C. Wang, Q. Lu, C. Jin, and J. Wang (2025) Pref-grpo: pairwise preference reward-based grpo for stable text-to-image reinforcement learning. arXiv preprint arXiv:2508.20751. Cited by: §2.1. Y. Wang, Q. Liu, and C. Jin (2023) Is rlhf more difficult than standard rl? a theoretical perspective. Advances in Neural Information Processing Systems 36, p. 76006–76032. Cited by: §1. L. Xu, M. Skoularidou, A. Cuesta-Infante, and K. Veeramachaneni (2019) Modeling tabular data using conditional GAN. In Advances in Neural Information Processing Systems 32, H. Wallach, H. Larochelle, A. Beygelzimer, F. d’Alché-Buc, E. Fox, and R. Garnett (Eds.), p. 7333–7343. Cited by: §2.1, §4. H. Zhang, J. Zhang, B. Srinivasan, Z. Shen, X. Qin, C. Faloutsos, H. Rangwala, and G. Karypis (2023) Mixed-type tabular data synthesis with score-based diffusion in latent space. arXiv preprint arXiv:2310.09656. Cited by: 2nd item, §4. R. Zhang, L. Lin, Y. Bai, and S. Mei (2024) Negative preference optimization: from catastrophic collapse to effective unlearning. arXiv preprint arXiv:2404.05868. Cited by: 3rd item, 2nd item, §1, §2.2, §2.3, §4. Y. Zhang, F. A. Shaik, S. Acharjee, F. Khalid, and M. Oussalah (2026) Towards reliable multimodal disaster severity assessment through preference optimization and explainable vision-language reasoning. Reliability Engineering & System Safety, p. 112674. External Links: ISSN 0951-8320, Document, Link Cited by: §2.2. Z. Zhao, A. Kunar, R. Birke, H. Van der Scheer, and L. Y. Chen (2024) Ctab-gan+: enhancing tabular data synthesis. Frontiers in Big Data 6, p. 1296508. Cited by: 1st item, 2nd item, §4. Appendix A Background A.1 Problem Setup Tabular Language Model Fine-Tuning Let πθ _θ denote a parameterized language model that generates tabular data sequences autoregressively. Following the GReaT framework (Borisov et al., 2023), each tabular row x=(v1,v2,…,vM)x=(v_1,v_2,…,v_M) is serialized into a token sequence τ=serialize(x)τ=serialize(x), enabling the model to define a distribution over tabular data: πθ(x)=∏t=1Tπθ(τt∣τ<t) _θ(x)= _t=1^T _θ( _t _<t) where T is the sequence length and τt _t denotes the t-th token in the serialized representation. Standard language model fine-tuning aims to find parameters θ that maximize the likelihood of observed data D=xii=1ND=\x_i\_i=1^N: maxθP(D∣θ)=maxθ∏i=1Nπθ(xi) _θP(D θ)= _θ _i=1^N _θ(x_i) which is equivalent to minimizing the negative log-likelihood. Supervised fine-tuning (SFT) is the standard starting point for training tabular LLMs. Given a pretrained language model, SFT optimizes the maximum likelihood objective: ℒSFT(θ)=−x∼D[logπθ(x)].L_SFT(θ)=-E_x D [ _θ(x) ]. (12) SFT encourages the model to closely match the empirical data distribution and typically achieves strong statistical fidelity. However, because the objective is defined over individual training rows, SFT may induce memorization, making the resulting policy vulnerable to record-level privacy attacks. Consequently, SFT is commonly followed by an alignment stage to align the model to certain preferences–such as to mitigate privacy leakage. Reinforcement learning for tabular data generation. The goal is to fine-tune πθ _θ to generate synthetic tabular data that optimizes data quality across utility and statistical fidelity. Standard reinforcement learning approaches face fundamental challenges when applied to tabular data generation. Sparse reward signals. Tabular data quality requires satisfying multiple statistical constraints (e.g., marginal distributions, correlations) simultaneously, creating a sparse reward landscape. For a d-dimensional tabular sample, consider k independent quality constraints, each requiring some property fj(x)>ϵf_j(x)>ε. The probability that a randomly generated sample satisfies a single constraint is roughly Pr(fj(x)>ϵ)≈ϵ1/d (f_j(x)>ε)≈ε^1/d, which decreases with dimensionality due to the curse of dimensionality. For all k constraints to be satisfied at once, the probabilities multiply: Pr(all satisfied)≤∏j=1kPr(fj(x)>ϵ)≈(ϵ1/d)k=ϵk/d (all satisfied)≤ _j=1^k (f_j(x)>ε)≈(ε^1/d)^k=ε^k/d. As d or k grows, this probability decays exponentially toward zero, making successful samples extremely rare. This exponential rarity means rewards are sparse: only the exponentially few samples that meet all k constraints receive meaningful reward signals, while the vast majority provide near-zero feedback (Gao et al., 2024). Consequently, policy gradient methods suffer from vanishing gradients, as most generated samples provide negligible learning signal. Multi-objective optimization with conflicting gradients. Tabular data generation requires balancing multiple, often opposing objectives: maximizing statistical fidelity (utility) while minimizing privacy leakage. This creates conflicting gradient signals during reinforcement learning optimization. Consider the standard RL objective: ∇θJ(θ)=x∼πθ[R(x)∇θlogπθ(x)]−β∇θKL(πθ∥πref) _θJ(θ)=E_x _θ [R(x) _θ _θ(x) ]-β _θKL ( _θ\| _ref ) Here, R(x)R(x) typically combines multiple reward terms: R(x)=λutilRutil(x)−λprivRpriv(x)R(x)= _utilR_util(x)- _privR_priv(x). The utility reward Rutil(x)R_util(x) pushes the model toward realistic patterns found in training data, while the privacy penalty Rpriv(x)R_priv(x) pushes away from memorizing exact training records. These opposing forces create gradient interference (Liu et al., 2021): samples that score high on utility (resembling real data) often score poorly on privacy (being too similar to training points), leading to inconsistent gradient updates that oscillate or cancel out. This interference is particularly severe in tabular data where features have complex dependencies–optimizing for one metric (e.g., column-wise distributions) can degrade another (e.g., row-wise uniqueness). Destructive policy updates from narrow optimization. Even when gradient conflicts are managed, optimizing for individual objectives can lead to destructive policy updates. For instance, aggressively minimizing privacy leakage might push πθ _θ to generate unrealistic, out-of-distribution samples that preserve no useful statistical patterns. While the KL penalty KL(πθ∥πref)≤CKL( _θ\| _ref)≤ C provides coarse regularization, it cannot preserve specific correlation structures or complex dependencies encoded in πref _ref—the KL constraint bounds overall distribution shift but does not protect fine-grained tabular relationships. In tabular data, this is particularly problematic: optimizing for column-wise marginal distributions might destroy row-wise correlations, or improving one metric (e.g., C2ST) might degrade another (e.g., MLE). These mathematical challenges–sparse rewards, conflicting gradients, and destructive updates–motivate our shift from traditional RL to alignment methods. Alignment circumvents explicit reward modeling while enabling balanced optimization across competing quality dimensions through comparative feedback between quality groups. Alignment methods for tabular language models. Instead of directly maximizing R(x)R(x), we reframe tabular data generation using three alignment approaches, each with distinct mathematical formulations: • Direct Preference Optimization (DPO) (Rafailov et al., 2024): Optimizes pairwise preferences (x+≻x−)(x^+ x^-) using the Bradley-Terry model: ℒDPO(θ)=−(x+,x−)[logσ(βlogπθ(x+)πref(x+)−βlogπθ(x−)πref(x−))]L_DPO(θ)=-E_(x^+,x^-) [ σ (β _θ(x^+) _ref(x^+)-β _θ(x^-) _ref(x^-) ) ] This formulation implicitly satisfies the KL-regularized RL objective without explicit reward modeling. • Kahneman-Tversky Optimization (KTO) (Ethayarajh et al., 2024): Uses binary desirable/undesirable labels with alternative loss formulations. The base forms include: ℒKTO-sigmoid(θ) _KTO-sigmoid(θ) =1−σ(βlogπθ(x)πref(x)−zref) =1-σ (β _θ(x) _ref(x)-z_ref ) ℒKTO-logsigmoid(θ) _KTO-logsigmoid(θ) =−logσ(βlogπθ(x)πref(x)−zref) =- σ (β _θ(x) _ref(x)-z_ref ) for desirable samples (with sign flipped for undesirable samples), where zrefz_ref is a reference point. • Negative Preference Optimization (NPO)(Zhang et al., 2024): Optimizes only using dispreferred samples: ℒNPO(θ)=−x−[logσ(−βlogπθ(x−)πref(x−))]L_NPO(θ)=-E_x^- [ σ (-β _θ(x^-) _ref(x^-) ) ] This asymmetric formulation reduces undesirable patterns while leaving preferred ones unchanged. For tabular data, these base formulations are extended with additional constraints: • DPO variants: Add explicit KL divergence KL(πθ∥πref)KL( _θ\| _ref) and gradient difference ‖∇θℒSFT(θ)−∇θℒSFT(θref)‖2\| _θL_SFT(θ)- _θL_SFT( _ref)\|^2 to preserve distributional properties. • KTO variants: Incorporate gradient difference regularization for stability across sigmoid and log-sigmoid formulations. • NPO variants: Include both KL divergence and gradient difference constraints to prevent over-optimization while maintaining utility. These alignment methods provide flexible supervision for tabular language models, addressing the multi-objective nature of data quality through different signal types and regularization strategies. A.2 Reward Taxonomy: Formal Definitions We provide a unified formal treatment of the five reward categories in Appendix A.2. Let real⊂⊆ℝdD_real ^d denote the real data, and let x~∈ x be a synthetic row produced by πθ _θ. (C1) Distributional rewards. A distributional reward approximates the real joint density preal(x)p_real(x) or its discriminator. Two canonical instances: (C1-a) Distinguishability classifier. Train ϕ:→[0,1]φ:X→[0,1] to discriminate realD_real from synth(t)D_synth^(t). Define: ρcls(x~)=1−2|0.5−ϕ(x~)|. _cls( x)=1-2|0.5-φ( x)|. Symmetry around ϕ=0.5φ=0.5 makes both false positives and false negatives equally detrimental. This reward is two-class: it requires synthetic data for training, so ϕφ evolves with πθ _θ. (C1-b) Direct density. Fit a parametric density estimator (e.g., Gaussian Mixture Model) on realD_real: ρgmm(x~)=logpGMM(x~)−logpminlogpmax−logpmin. _gmm( x)= p_GMM( x)- p_ p_ - p_ . This is one-class: no synthetic data required during training, and the estimator is fixed across iterations. (C2) Pointwise rewards. Operate on pairwise distances. The canonical instance is Distance to Closest Record (DCR): d(x~)=minx∈real‖x~−x‖2,ρdcr(x~)=1−d(x~)−dmindmax−dmin.d( x)= _x _real\| x-x\|_2,\ _dcr( x)=1- d( x)-d_ d_ -d_ . Note: for privacy-oriented applications, the sign is inverted so that rows farther from real records receive higher reward. (C3) Marginal rewards. Fit a univariate kernel density estimator p^j p_j per feature on real[:,j]D_real[:,j]: ρmarg(x~)=1d∑j=1dlogp^j(x~j)−logp^j,minlogp^j,max−logp^j,min. _marg( x)= 1d _j=1^d p_j( x_j)- p_j, p_j, - p_j, . By construction this ignores inter-feature dependencies. It isolates the marginal component of quality, making it a useful ablation to test how much of improvement in other metrics is attributable to marginal matching alone. (C4) Relational rewards. Let ρijreal _ij^real be the real Pearson correlation between features i and j, and let zkz_k be x~k x_k standardized using real-data statistics. The correlation-consistency reward is: ρcorr(x~)=(i,j)∈[exp(−|zizj−ρijreal|)], _corr( x)=E_(i,j) \! [ \! (-|z_iz_j- _ij^real| ) ], where S is a (sub)sampled set of feature pairs. This directly measures preservation of pairwise linear dependencies and is closely related to the structural fidelity metric in TabStruct (Jiang and others, 2025). (C5) OOD rewards. A family of one-class anomaly scores: (C5-a) Isolation Forest. Fits random binary splits on realD_real. ρiso(x~)∝h¯(x~) _iso( x) h( x), the average path length of x~ x in isolating trees. Longer paths indicate x~ x lies in dense regions. (C5-b) Autoencoder reconstruction. Train fAEf_AE on realD_real: ρae(x~)=1−‖x~−fAE(x~)‖2−eminemax−emin. _ae( x)=1- \| x-f_AE( x)\|^2-e_ e_ -e_ . (C5-c) Mahalanobis distance. Using sample mean μ and covariance Σ of realD_real: dmah(x~)=(x~−μ)⊤Σ−1(x~−μ),ρmah(x~)=1−dmah−dmindmax−dmin.d_mah( x)= ( x-μ) ^-1( x-μ),\ _mah( x)=1- d_mah-d_ d_ -d_ . (C5-d) One-Class SVM and (C5-e) Local Outlier Factor provide complementary notions of “in-distribution” boundaries; full definitions follow standard formulations (Schölkopf et al., 2001; Breunig et al., 2000). Why OOD rewards matter for LM generators. Unlike diffusion and GAN generators which produce samples in a bounded continuous space, autoregressive LM-based tabular generators output serialized tokens. This exposes a characteristic failure mode: rows with individually valid feature values but jointly impossible combinations (e.g., age=5age=5 with education=PhDeducation=PhD; income quantile inconsistent with occupation code). Because the token-level cross-entropy objective preserves local coherence without enforcing semantic consistency, these violations are not penalized by ρcls _cls alone unless the classifier is sufficiently expressive. OOD rewards provide a complementary, explicit signal against such out-of-manifold samples: any row that falls outside the real data manifold—regardless of whether a classifier happens to detect it—is down-weighted during pair formation. Two-class vs. one-class rewards. A useful distinction: ρcls _cls is two-class (retrained each iteration as synth(t)D_synth^(t) evolves), whereas rewards in C1-b, C2, C3, C4, and C5 are one-class (the estimator depends only on realD_real and is computed once). One-class rewards are stable targets for long iteration chains, while two-class rewards adapt to the generator’s evolving artifacts. Multi-reward alignment combines the benefits of both regimes. A.3 Indistinguishability Scoring Implementation Details Binary Classifier Training Strategy. We train the Binary Classifier ϕt _t on a balanced mixture of all real data realD_real and newly generated synthetic data synth(t)D_synth^(t): Training data: Xtrain=real∪synth(t),ytrain=1|real|∪0|synth(t)|Training data: X_train=D_real _synth^(t), y_train=\1\^|D_real|∪\0\^|D_synth^(t)| This approach ensures ϕt _t learns to distinguish the current model distribution πθt _ _t from real data, providing targeted indistinguishability signals that evolve with the model. Compared to using held-out test data or fixed synthetic data, this avoids underestimating indistinguishability by directly evaluating the generator’s outputs against the actual training distribution. Indistinguishability Score Transformation. The raw classifier probability ϕt(x~)=P(real∣x~) _t( x)=P(real x) is transformed into a symmetric indistinguishability score: s(x~)=1−2|0.5−ϕt(x~)|s( x)=1-2|0.5- _t( x)| This transformation has three desirable properties. Mathematically, it makes s(x~)s( x) symmetric around 0.5: s(0.5+ϵ)=s(0.5−ϵ)s(0.5+ε)=s(0.5-ε). Statistically, it treats both false positives (ϕt→1 _t→ 1) and false negatives (ϕt→0 _t→ 0) as equally detrimental to indistinguishability. Practically, it yields s(x~)∈[0,1]s( x)∈[0,1] where s(x~)=1s( x)=1 when ϕt(x~)=0.5 _t( x)=0.5 (maximally indistinguishable) and s(x~)=0s( x)=0 when ϕt(x~)=0 _t( x)=0 or 11 (perfectly classifiable). Importantly, we implement a critical separation: the Binary Classifier trains on existing synthetic data but evaluates newly generated samples: ϕt←train(real,synth(t)),s(x~new)←ϕt(x~new) _t (D_real,D_synth^(t)), s( x_new)← _t( x_new) This prevents data contamination where evaluation samples leak into training. Theoretically, this measures whether the model can generate novel samples that maintain indistinguishability beyond those already seen by the classifier. A.4 Group Formation Algorithm Dynamic Pair Construction. We create preference pairs by sorting all new synthetic samples X~new X_new by indistinguishability score s(x~)s( x) and pairing extremes: Pairi=(x~chosen(i),x~rejected(i)),where s(x~chosen(i))≥s(x~rejected(N−i+1))Pair_i=( x^(i)_chosen, x^(i)_rejected), s( x^(i)_chosen)≥ s( x^(N-i+1)_rejected) with N=|X~new|N=| X_new| and x~(i) x^(i) denoting the i-th highest-scoring sample. This maximizes the preference signal’s discriminative power by ensuring: Δsi=s(x~chosen(i))−s(x~rejected(i))≥0 s_i=s( x^(i)_chosen)-s( x^(i)_rejected)≥ 0 We implement optional top-percent filtering to focus training on the most informative pairs: train=Pairi:i≤⌊p⋅N/100⌋P_train=\Pair_i:i≤ p· N/100 \ where p∈(0,100]p∈(0,100] controls selectivity. This filters out ambiguous pairs with small Δsi s_i, improving training efficiency by approximately 1p 1p while maintaining gradient quality. A.5 Group-Level vs Instance-Level Alignment Instance-Level Limitations for Tabular Data. Standard alignment methods (DPO, KTO, NPO) operate at the instance level, treating each synthetic sample xix_i as an independent unit for preference optimization. While effective for text generation where samples represent unique responses, this approach is fundamentally misaligned with tabular data’s statistical nature, where samples are i.i.d. draws from an underlying distribution. Instance-level optimization suffers from the key limitations for tabular synthesis is variance amplification, where Individual tabular samples exhibit high statistical variance, leading to noisy gradient estimates that destabilize training. Group-Level Advantage. Our group-level formulation addresses these limitations by operating on quality-stratified batches rather than individual samples. Each group ℬhighB_high or ℬlowB_low contains B randomly selected samples from the respective quality stratum. The group size B represents a trade-off: Statistical stability∝1B,Gradient noise∝1BStatistical stability 1 B, noise 1 B Larger groups provide more stable gradient estimates but may average over meaningful quality variations within strata. In practice, we find B=16−32B=16-32 balances these competing considerations, capturing group-level statistical patterns while maintaining sensitivity to quality gradients. Batch Composition Strategy. Within each iteration, groups are formed by random sampling from quality-stratified pools: ℬhigh∼Uniform(X+),ℬlow∼Uniform(X−)B_high (X^+), _low (X^-) where X+=x~:s(x~)≥τpX^+=\ x:s( x)≥ _p\ and X−=x~:s(x~)≤τqX^-=\ x:s( x)≤ _q\ are the high- and low-quality sample pools (higher s = better quality). This random sampling ensures each batch represents the underlying quality distribution while enabling stochastic optimization. The transition from instance-level to group-level alignment transforms the optimization signal from sample-specific to distributional. Where instance methods compute: rinstance(x)=βlogπθ(x)πref(x)r_instance(x)=β _θ(x) _ref(x) our method aggregates to group statistics: r¯θhigh=x∈ℬhigh[rinstance(x)],r¯θlow=x∈ℬlow[rinstance(x)] r_θ^high=E_x _high[r_instance(x)], r_θ^low=E_x _low[r_instance(x)] This aggregation naturally preserves tabular data’s statistical nature while providing more stable optimization signals. GRPO vs GRAA Although both GRPO (Shao et al., 2024) and GRAA operate on groups of samples, they address fundamentally different problems. GRPO is a reinforcement learning algorithm that relies on explicit scalar rewards and uses group-level statistics primarily as a variance-reduction baseline for policy gradient estimation. In contrast, GRAA is a reward-free alignment method that does not optimize instance-level preferences or rewards. Instead, it constructs quality-based groups using instance-level signals and defines alignment objectives directly over groups of generated samples, using relative likelihood differences between groups to optimize distributional properties. As a result, GRAA is fundamentally better suited to tabular data generation, where quality is inherently distributional and per-instance rewards are ill-defined. Appendix B GRAA Theoretical Analysis This appendix provides explicit proofs for the stability claims made in subsection 3.4: (i) a uniform bound on ‖∇θℒGRAA‖\| _θL_GRAA\|, (i) an (1/B)O(1/B) variance bound on the group-averaged policy gradient, (i) a reward-agnostic extension of (i)–(i) to any reward in the taxonomy of Appendix A.2, and (iv) a local convergence statement under standard smoothness assumptions. B.1 Notation and Assumptions Throughout this appendix, ∥⋅∥\|·\| denotes the Euclidean norm on ℝdR^d, where d=dim(θ)d= (θ). Each synthetic row y is a token sequence y=(τ1,…,τT)y=( _1,…, _T) under the serialization scheme of subsection 3.4. By the autoregressive factorization, logπθ(y)=∑t=1Tlogπθ(τt∣τ<t),∇θlogπθ(y)=∑t=1T∇θlogπθ(τt∣τ<t). _θ(y)= _t=1^T _θ( _t _<t), _θ _θ(y)= _t=1^T _θ _θ( _t _<t). (13) At each iteration, after scoring synthetic samples by a reward ρ, the stratification of Section 3.4 produces two disjoint groups high,low⊆synth(t)G_high,G_low _synth^(t). A GRAA mini-batch is constructed by independently drawing B samples from each group: ℬhigh=yihighi=1B∼i.i.d.Unif(high),ℬlow=yilowi=1B∼i.i.d.Unif(low),ℬhigh⟂ℬlow.B_high=\y^high_i\_i=1^B .i.d. Unif(G_high), _low=\y^low_i\_i=1^B .i.d. Unif(G_low), _high _low. (14) This i.i.d. construction is made possible precisely because GRAA is a group-level method: it does not require pair-wise correspondence between yihighy^high_i and yilowy^low_i, so each side can be drawn independently. The corresponding group-averaged log-ratios and GRAA loss are r¯θhigh r_θ^high =βB∑i=1Blogπθ(yihigh)πref(yihigh),r¯θlow=βB∑i=1Blogπθ(yilow)πref(yilow), = βB _i=1^B _θ(y_i^high) _ref(y_i^high), r_θ^low= βB _i=1^B _θ(y_i^low) _ref(y_i^low), (15) ℒGRAA(θ) _GRAA(θ) =σ(r¯θlow−r¯θhigh), =σ ( r_θ^low- r_θ^high ), (16) where σ(x)=(1+e−x)−1σ(x)=(1+e^-x)^-1 is the logistic sigmoid, β>0β>0 is the alignment strength, and πref _ref is fixed throughout training. This is the simplified single-hyperparameter form used in the main body (Eq. (9)); the coefficient-generalized form that recovers NPO, KTO, and DPO as special cases is discussed in Appendix B.6. Assumption B.1 (Bounded per-sequence policy gradient). There exists a constant G>0G>0 such that ‖∇θlogπθ(y)‖≤G\| _θ _θ(y)\|≤ G for every θ and every admissible sequence y. Remark B.2. Assumption B.1 is the standard bounded-score-function condition used in policy-gradient analyses (Rafailov et al., 2024; Shao et al., 2024). For a finite-vocabulary autoregressive LM the per-token softmax gradient is bounded, so G≤T⋅GtokG≤ T· G_tok under (13), where T is the maximum serialized sequence length and GtokG_tok bounds the per-token gradient. Assumption B.3 (L-smoothness). ℒGRAA(⋅)L_GRAA(·) is L-smooth: ‖∇ℒGRAA(θ1)−∇ℒGRAA(θ2)‖≤L‖θ1−θ2‖\| _GRAA( _1)- _GRAA( _2)\|≤ L\| _1- _2\| for all θ1,θ2 _1, _2. B.2 Bounded Gradient Norm Proposition B.4 (Bounded gradient norm). Under Assumption B.1, for every θ, ‖∇θℒGRAA(θ)‖≤βG2.\| _θL_GRAA(θ)\|\;≤\; β\,G2. Proof. Let u(θ):=r¯θlow−r¯θhighu(θ):= r_θ^low- r_θ^high so that ℒGRAA(θ)=σ(u(θ))L_GRAA(θ)=σ(u(θ)). By the chain rule, ∇θℒGRAA(θ)=σ′(u(θ))∇θu(θ)=σ′(u(θ))(∇θr¯θlow−∇θr¯θhigh). _θL_GRAA(θ)\;=\;σ (u(θ))\, _θu(θ)\;=\;σ (u(θ)) ( _θ r_θ^low- _θ r_θ^high ). (17) Step 1: bound σ′σ . For all u∈ℝu , σ′(u)=σ(u)(1−σ(u))σ (u)=σ(u)(1-σ(u)). Maximizing s(1−s)s(1-s) over s∈[0,1]s∈[0,1] gives σ′(u)≤14σ (u)≤ 14, attained at u=0u=0. Step 2: bound each group-averaged gradient. Because πref _ref is fixed, ∇θlogπref(y)=0 _θ _ref(y)=0, so ∇θr¯θhigh=βB∑i=1B∇θlogπθ(yihigh). _θ r_θ^high\;=\; βB _i=1^B _θ _θ(y_i^high). By the triangle inequality and Assumption B.1, ‖∇θr¯θhigh‖≤βB∑i=1B‖∇θlogπθ(yihigh)‖≤βB⋅B⋅G=βG.\| _θ r_θ^high\|\;≤\; βB _i=1^B\| _θ _θ(y_i^high)\|\;≤\; βB· B· G\;=\;β G. (18) The same bound holds for ‖∇θr¯θlow‖\| _θ r_θ^low\|. Step 3: combine. Applying the triangle inequality in (17), then Steps 1–2, ‖∇θℒGRAA(θ)‖ \| _θL_GRAA(θ)\| ≤σ′(u(θ))(‖∇θr¯θlow‖+‖∇θr¯θhigh‖) ≤σ (u(θ))\, (\| _θ r_θ^low\|+\| _θ r_θ^high\| ) ≤14⋅2βG=βG2.∎ ≤ 14· 2β G\;=\; β G2. Remark B.5. The bound depends only on β and G, not on the batch size B, nor on the specific reward ρ. The role of B in variance control is made explicit in Proposition B.6. The tighter bound βG2 β G2 corrects the looser “‖∇ℒGRAA‖≤β\| _GRAA\|≤β” statement informally given in the main body of earlier drafts. B.3 (1/B)O(1/B) Variance of Group-Averaged Gradients We now quantify how the group-level averaging reduces the variance of the gradient estimator, which is the formal counterpart of the intuition that group statistics are more stable than instance statistics. Proposition B.6 (Variance reduction). Let gi(θ):=β∇θlogπθ(yihigh)g_i(θ):=β\, _θ _θ(y_i^high), i=1,…,Bi=1,…,B, where yihighi=1B\y_i^high\_i=1^B is drawn i.i.d. from Unif(high)Unif(G_high) as in (14). Let μ:=y∼Unif(high)[β∇θlogπθ(y)]μ:=E_y (G_high)[β\, _θ _θ(y)] and assume [‖gi−μ‖2]≤σg2E[\|g_i-μ\|^2]≤ _g^2 (which holds with σg2≤β2G2 _g^2≤β^2G^2 under Assumption B.1). Then [‖∇θr¯θhigh−μ‖2]≤σg2B≤β2G2B.E [ \| _θ r_θ^high-μ \|^2 ]≤ _g^2B≤ β^2G^2B. The same bound holds for r¯θlow r_θ^low. Proof. Since πref _ref is fixed, ∇θr¯θhigh=1B∑i=1Bgi _θ r_θ^high= 1B _i=1^Bg_i. By the i.i.d. assumption, Cov(gi,gj)=0Cov(g_i,g_j)=0 for i≠ji≠ j. Therefore, [‖∇θr¯θhigh−μ‖2] [ \| _θ r_θ^high-μ \|^2 ] =[‖1B∑i=1B(gi−μ)‖2] =E [ \| 1B _i=1^B(g_i-μ) \|^2 ] =1B2∑i=1B[‖gi−μ‖2]+1B2∑i≠j[(gi−μ)⊤(gj−μ)]⏟= 0 by independence = 1B^2 _i=1^BE[\|g_i-μ\|^2]+ 1B^2 _i≠ j E[(g_i-μ) (g_j-μ)]_=\,0 by independence ≤1B2⋅B⋅σg2=σg2B. ≤ 1B^2· B· _g^2\;=\; _g^2B. The upper bound σg2≤β2G2 _g^2≤β^2G^2 follows from Assumption B.1. ∎ Remark B.7 (Why groups enable the i.i.d. step). Proposition B.6 uses i.i.d. sampling within each group (equation (14)). This step is only valid because GRAA treats highG_high and lowG_low as populations: no within-group index is coupled to any other group’s index. Instance-level methods (DPO, NPO) instead couple (yihigh,yilow)(y^high_i,y^low_i) through the ranking, breaking the i.i.d. structure inside each mini-batch. The variance reduction of Proposition B.6 is therefore a formal counterpart of the empirical observation in Appendix F.2 that random within-group sampling matches top-vs-bottom matching. B.4 Reward-Agnostic Stability Proposition B.8 (Reward-agnostic gradient bound). Let ρ:→[0,1]ρ:X→[0,1] be any per-sample quality signal (real-data-dependent, computable per row; e.g., sclss_cls or sdcrs_dcr). Then the gradient bound of Proposition B.4 holds uniformly over ρ: ‖∇θℒGRAAρ(θ)‖≤βG2.\| _θL_GRAA^ρ(θ)\|\;≤\; β\,G2. The variance bound of Proposition B.6 also holds uniformly over ρ. Proof. The reward ρ enters ℒGRAAρL_GRAA^ρ only through the ranking operator sortρsort_ρ and the group-assignment operator that produces high,lowG_high,G_low. Both operators are piecewise constant in θ: they depend on θ only through the already-generated samples synth(t)D_synth^(t), which are fixed at the start of each iteration. Hence their gradient with respect to θ vanishes almost everywhere, and the derivation of Proposition B.4 applies verbatim with high,lowG_high,G_low replaced by the ρ-induced versions. The variance argument of Proposition B.6 applies identically because uniform sampling within each ρ-induced group still yields i.i.d. draws. ∎ Corollary B.9 (Stability of multi-reward alignment). For the composite reward ρmulti=∑rwrρ(r) _multi= _rw_rρ^(r) with ∑rwr=1,wr≥0 _rw_r=1,\,w_r≥ 0, and for Pareto-based group selection over any finite reward collection, the gradient bound of Proposition B.4 and the variance bound of Proposition B.6 hold unchanged. B.5 Local Convergence Proposition B.10 (Convergence to a stationary point). Under Assumptions B.1–B.3, with constant step size η∈(0,1/L]η∈(0,1/L] and mini-batch GRAA updates θk+1=θk−ηg^k _k+1= _k-η g_k, where g^k g_k is the stochastic mini-batch gradient of ℒGRAAL_GRAA at θk _k with [g^k∣θk]=∇ℒGRAA(θk)E[ g_k _k]= _GRAA( _k) and [‖g^k−∇ℒGRAA(θk)‖2∣θk]≤σℒ2E[\| g_k- _GRAA( _k)\|^2 _k]≤ _L^2, min0≤k≤K−1[‖∇ℒGRAA(θk)‖2]≤2(ℒGRAA(θ0)−ℒ∗)ηK+ηLσℒ2, _0≤ k≤ K-1E[\| _GRAA( _k)\|^2]\;≤\; 2(L_GRAA( _0)-L^*)η K+η L _L^2, where ℒ∗=infθℒGRAA(θ)L^*= _θL_GRAA(θ). Moreover, σℒ2=(1/B) _L^2=O(1/B) under Proposition B.6. Proof. This is the standard stochastic gradient descent descent-lemma result under L-smoothness and an unbiased, variance-bounded gradient oracle. The L-smoothness inequality gives ℒGRAA(θk+1)≤ℒGRAA(θk)−η⟨∇ℒGRAA(θk),g^k⟩+Lη22‖g^k‖2.L_GRAA( _k+1) _GRAA( _k)-η _GRAA( _k), g_k + Lη^22\| g_k\|^2. Taking conditional expectations and using unbiasedness and the variance bound, [ℒGRAA(θk+1)∣θk]≤ℒGRAA(θk)−η‖∇ℒGRAA(θk)‖2+Lη22(‖∇ℒGRAA(θk)‖2+σℒ2).E[L_GRAA( _k+1) _k] _GRAA( _k)-η\| _GRAA( _k)\|^2+ Lη^22 (\| _GRAA( _k)\|^2+ _L^2 ). For η≤1/Lη≤ 1/L, the coefficient of ‖∇ℒGRAA(θk)‖2\| _GRAA( _k)\|^2 is at most −η/2-η/2. Telescoping over k=0,…,K−1k=0,…,K-1, taking total expectations, and dividing by ηK/2η K/2 yields the claim. The (1/B)O(1/B) scaling of σℒ2 _L^2 follows because the GRAA gradient (17) is a bounded linear combination of the group-averaged terms whose variance is (1/B)O(1/B) by Proposition B.6. ∎ Remark B.11. Proposition B.10 gives a concrete operational meaning to the variance bound: doubling B halves the irreducible asymptotic error ηLσℒ2η L _L^2, explaining the batch-size effect observed empirically in Figure 5. Combined with Proposition B.8, convergence to a stationary point holds under any reward in the taxonomy of Appendix A.2. Summary. Proposition B.4 controls per-step gradient magnitude; Proposition B.6 controls per-step variance under the group-level i.i.d. construction that GRAA uniquely affords; Proposition B.8 and Corollary B.9 extend both to any reward or convex mixture thereof; Proposition B.10 gives a standard SGD-style convergence guarantee whose leading constant depends on the variance term from Proposition B.6. Together these provide the “reward-agnostic stability” claim of subsection 3.4 in full rigor. B.6 Coefficient-Generalized GRAA and Special Cases The simplified loss (9) is a single-hyperparameter (β) group-level Bradley–Terry objective. A coefficient-generalized variant with three scalar weights (a,b,c)∈ℝ≥03(a,b,c) _≥ 0^3 can be written as ℒGRAA(a,b,c)(θ)=c−σ(ar¯θhigh−br¯θlow),L_GRAA^(a,b,c)(θ)\;=\;c\;-\;σ\! (a\, r_θ^high-b\, r_θ^low ), (19) with r¯ r defined as above. The constant offset c does not affect gradients and is included only to rescale the objective into [c−1,c][c-1,c]; it plays no optimization role. Special cases. The generalized form recovers several instance-level and group-level objectives: • a=1,b=1,c=1a=1,\,b=1,\,c=1: the simplified GRAA loss (9) (up to the sign convention σ(−Δ)=1−σ(Δ)σ(- )=1-σ( )). • a=0a=0: the low-quality group is suppressed while the high-quality group is frozen—this collapses to a negative-only objective analogous to NPO (Zhang et al., 2024). • r¯high r^high detached from the computation graph (no gradient flow through the high-quality term): recovers the asymmetric gradient structure of KTO (Ethayarajh et al., 2024); in practice this has been empirically unstable on our tabular benchmarks. • Batch size B=1B=1 with a=b=1a=b=1 and a pairwise (yhigh,ylow)(y^high,y^low) assignment: reduces to the DPO (Rafailov et al., 2024) objective (up to the log-sigmoid vs. sigmoid convention). Why we drop the extra coefficients in the main body. The coefficients (a,b,c)(a,b,c) are constants in all our experiments (fixed at a=b=1a=b=1, c irrelevant); none were tuned per dataset. Collapsing them into the simplified form (9) removes apparent tuning freedom, makes the connection to Bradley–Terry explicit, and tightens the gradient bound in Proposition B.4 to βG2 β G2 (versus the coefficient-dependent bound 14(a+bβ)G 14(a+bβ)G that would arise for (19)). Appendix C Experiments Setup C.1 Datasets Experiments were firstly conducted with five common tabular datasets from the UCI Machine Learning Repository 222https://archive.ics.uci.edu/datasets . Classification tasks were performed on the Adult, Default, Shoppers and Magic datasets, while regression tasks were performed on the Beijing datasets. Each dataset was split into training, validation, and testing sets with a ratio of 8:1:1, except for the Adult dataset, whose official testing set was used and the remainder split into training and validation sets with an 8:1 ratio. The resulting statistics of each dataset are shown in Table 8 Table 8: Dataset Statistics. “# Num” and “# Cat” refer to the number of numerical and categorical columns. Dataset # Samples # Num # Cat # Max Cat # Train # Validation # Test Task Type Adult 48,84248,842 66 99 4242 28,94328,943 3,6183,618 16,28116,281 Binary Classification Default 30,00030,000 1414 1111 1111 24,00024,000 3,0003,000 3,0003,000 Binary Classification Shoppers 12,33012,330 1010 88 2020 9,8649,864 1,2331,233 1,2331,233 Binary Classification Magic 19,02019,020 1010 11 22 15,21615,216 19021902 19021902 Binary Classification Beijing 41,75741,757 77 55 3131 33,40533,405 4,1754,175 4,1754,175 Regression Additionally, the detailed introduction to the total 11 datasets are shown below: • Adult333https://archive.ics.uci.edu/dataset/2/adult: The “Adult Census Income” dataset contains demographic and employment-related features of people. The task is to predict whether an individual’s income exceeds $50,000. • Default444https://archive.ics.uci.edu/dataset/350/default+of+credit+card+clients: The “Default of Credit Card Clients Dataset” contains information on default payments, demographic factors, credit data, history of payment, and bill statements of credit card clients in Taiwan from April 2005 to September 2005. The task is to predict whether the client will default payment next month. • Shoppers555https://archive.ics.uci.edu/dataset/468/online+shoppers+purchasing+intention+dataset: The “Online Shoppers Purchasing Intention Dataset” contains information of user’s webpage visiting sessions. The task is to predict if the user’s session ends with the shopping behavior. • Magic666https://archive.ics.uci.edu/dataset/159/magic+gamma+telescope: The “Magic Gamma Telescope” dataset is to simulate registration of high energy gamma particles in a ground-based atmospheric Cherenkov gamma telescope using the imaging technique. The task is to classify high-energy Gamma particles in the atmosphere. • Beijing777https://archive.ics.uci.edu/dataset/381/beijing+pm2+5+data: The ”Beijing PM2.5 Data” dataset contains the hourly PM2.5 data of US Embassy in Beijing and the meteorological data from Beijing Capital International Airport. The task is to predict the PM2.5 value. C.2 Baselines The generative models baselines we used to compared can be categorized as follows: Diffusion Models. We include the most prominent diffusion-based models for tabular data: • TabDDPM (Kotelnikov et al., 2023): A foundational model adapting continuous denoising diffusion probabilistic models (DDPM) to mixed-type tabular data. • TabSyn (Zhang et al., 2023): Utilizes a transformer architecture within a diffusion process to model tabular correlations. • TabDiff (Shi et al., 2024): Explores different noise schedules and conditioning mechanisms for diffusion on tables. GAN-based • CTGAN (Zhao et al., 2024): A modern generative adversarial network designed for tabular data. • TVAE (Zhao et al., 2024): A modern variational autoencoder network designed for tabular data. LLM-based • GReaT(Borisov et al., 2023): A method that frames tabular generation as an autoregressive language modeling task. C.3 Evaluation Metrics We evaluate the quality of generated synthetic data across three critical dimensions: Data Utility (performance on downstream tasks), Data Fidelity (statistical similarity to the real data, decomposed into low-order Shape and Trend, and high-order joint distributions), and Data Privacy (resistance to leakage of training data information). All reported metrics and error bars represent the mean and standard deviation from 10 sampling iterations of the best-validated model. C.3.1 Data Utility: Machine Learning Efficiency (MLE) To measure the practical utility of synthetic data, we use it to train an XGBoost model (Chen and Guestrin, 2016b) which is then evaluated on a held-out real test set. This assesses how well the synthetic data serves its ultimate purpose: training effective machine learning models. • Classification (AUC): For classification tasks across all datasets except the Beijing, we report the Area Under the ROC Curve (AUC). A higher AUC (closer to 1.0) indicates the model trained on synthetic data achieves better predictive performance. AUC=∫01TPR(FPR)d(FPR)AUC= _0^1TPR(FPR)d(FPR) (20) • Regression (RMSE): For regression tasks only for the Beijing dataset, we report the Root Mean Square Error (RMSE). A lower RMSE indicates predictions from the model trained on synthetic data are closer to the true values. RMSE=1n∑i=1n(yi−y^i)2RMSE= 1n _i=1^n(y_i- y_i)^2 (21) C.3.2 Data Fidelity: Low-Order Statistics These metrics evaluate how well the synthetic data captures the fundamental, univariate and bivariate statistics of the original data distribution. We report two main low‑order metric families: (1) Column Density Estimation (CDE) for column‑wise distribution similarity, and (2) Pairwise Column Correlation (PCC) for preserving pair‑wise linear and categorical associations (Si et al., 2025). Besides, following the low-order statistics metics (Shi et al., 2024), we also evaluate them using: 1. Shape (Column-wise Distribution Similarity) We measure column‑wise shape fidelity via Column Density Estimation (CDE) error, which aggregates distributional discrepancies across all features. • Numerical Features (Kolmogorov‑Smirnov Test – KST): The KST statistic quantifies the maximum distance between the empirical distribution functions (EDF) of the real and synthetic data for a numerical column. A lower KST value indicates better preservation of the original data’s shape. KST=supx|Freal(x)−Fsynth(x)|,whereFn(x)=1n∑i=1n(−∞,x](Xi)KST= _x |F_real(x)-F_synth(x) |, F_n(x)= 1n _i=1^n1_(-∞,x](X_i) (22) • Categorical Features (Total Variation Distance – TVD): TVD measures the largest possible difference in the probability of any event between two categorical distributions. A lower TVD is better. TVD=12∑x∈X|Preal(x)−Psynth(x)|TVD= 12 _x∈ X |P_real(x)-P_synth(x) | (23) The overall CDE error is computed as the average of KST (for numerical columns) and TVD (for categorical columns) across all features. 2. Trend (Pair-wise Column Correlation) We evaluate pair‑wise column association via Pairwise Column Correlation (PCC) error, which quantifies how well linear and categorical dependencies are retained. • Numerical Features (Pearson Correlation Dissimilarity): We compute the Pearson Correlation Coefficient (ρ) for all pairs of numerical columns in both real and synthetic datasets. The PCC error for numerical pairs is the average absolute difference between these matrices. ρ(x,y)=cov(x,y)σxσy,PCCnum=12x,y|ρreal(x,y)−ρsynth(x,y)|ρ(x,y)= cov(x,y) _x _y, _num= 12E_x,y | _real(x,y)- _synth(x,y) | (24) • Categorical Features (Contingency Table Dissimilarity): For categorical column pairs, we build contingency tables for both datasets and measure their difference using TVD. PCCcat=12∑α∈A∑β∈B|Preal,(α,β)−Psynth,(α,β)|PCC_cat= 12 _α∈ A _β∈ B |P_real,(α,β)-P_synth,(α,β) | (25) • Mixed Features: For a categorical and a numerical feature, the numerical data is binned into discrete categories before applying the TVD‑based dissimilarity. The overall PCC error is the average of PCCnumPCC_num and PCCcatPCC_cat over all feature pairs. We utilize the implementation of these metrics from the SDMetrics library888https://github.com/sdv-dev/SDMetrics. C.3.3 Data Fidelity: High-Order Statistics While low-order statistics are necessary, they are insufficient for evaluating complex joint distributions. We employ the more sophisticated α-Precision (Alaa et al., 2022) metric from the synthcity library999https://github.com/vanderschaarlab/synthcity as our primary measure of high-order fidelity. We focus on α-Precision because it directly quantifies the fraction of generated samples that are plausible within the true data manifold, providing a more robust and interpretable measure of sample quality than metrics that only compare marginal statistics. α-Precision and β-Recall (Alaa et al., 2022): This framework provides a unified assessment of fidelity (α-Precision) and diversity (β-Recall). A key strength of α-Precision is its interpretability: it directly quantifies the fraction of generated samples that fall within the high-density region of the real data manifold (i.e., samples that are realistic and not outliers). This makes it a more robust and meaningful measure of quality than simply comparing marginal statistics, as it directly evaluates the generator’s ability to capture the true underlying data distribution. In our experiments, we place a strong emphasis on α-Precision as it most accurately reflects the goal of generating high-fidelity, characteristic samples. • α-Precision: Measures the fidelity of generated samples. It is the fraction of synthetic samples that are plausible (i.e., lie within the support) given α fraction of the real data distribution. • β-Recall: Measures the diversity and coverage of the generator. It is the fraction of the real data distribution covered by β fraction of the synthetic samples. C.3.4 Detection Metric: Classifier Two-Sample Test (C2ST) The Classifier Two-Sample Test (C2ST) uses a logistic regression classifier to distinguish between real and synthetic data. Its accuracy score ranges from 0 to 1. A higher score (closer to 1) is superior, indicating the synthetic data is realistic and hard to detect. Implementation follows SDMetrics (2024). C.3.5 Distinguishibility Attack (DA) We assess privacy through a Distinguishibility Attack (DA) that trains a binary classifier (Random Forest with 100 trees) to distinguish between real training records (members) and synthetic samples (non‑members). The attack is evaluated on newly generated synthetic data, with privacy quantified using the Area Under the ROC Curve (ROC AUC). An AUC of 0.5 indicates the best. Appendix D Experiments Implementation D.1 Hyperparameters The detailed hyperparameters for our alignment framework are provided in Table 9. All baseline methods (CTGAN, TVAE, TabDDPM, etc.) were implemented using their official codebases and tuned according to their respective recommendations or original papers. For iterative alignment methods (TabDPO, TabNPO, TabKTO, TabGRAA), we adopt a unified training pipeline described in Algorithm 2, which outlines the complete iterative optimization procedure. D.2 Algorithm Implementation Our complete iterative alignment framework is implemented as described in Algorithm 2. The algorithm integrates data generation, classifier-based preference scoring, and four different alignment loss computations (DPO, NPO, KTO, and our proposed GRAA) within a unified optimization loop. Key implementation details include: (1) the use of GPT-2 tokenizer for tabular data serialization, (2) a fixed Random Forest classifier (100 trees) for distinguishibility scoring updated each iteration, (3) group-based partitioning for GRAA with configurable group sizes, and (4) gradient computation via automatic differentiation in PyTorch. The codebase is modular, allowing easy switching between alignment methods and hyperparameter configurations. D.3 Computational Resources All experiments were conducted on a high-performance computing cluster with mixed GPU configurations. The primary hardware included NVIDIA GeForce RTX 4090 (24GB VRAM) and NVIDIA A100 (80GB VRAM) GPUs, with Intel Xeon Platinum processors and 256GB RAM per node. The operating system was Ubuntu 20.04.6 LTS with Linux kernel 5.15.0-113-generic. The software stack comprised Python 3.8.18, PyTorch 2.1.0 with CUDA 11.8, Transformers 4.36.0, scikit-learn 1.3.0, and XGBoost 1.7.6. Training times varied by method: supervised fine-tuning required approximately 3 hours per dataset, while each alignment iteration took 10–20 minutes depending on dataset size and GPU type. Algorithm 2 Iterative Tabular Alignment Framework with Loss Computation 0: Real dataset realD_real, base LM πbase _base, max rounds T, alignment method ℳ∈DPO,NPO,KTO,GRAAM∈\DPO,NPO,KTO,GRAA\, hyperparameters β, η, group_size (if ℳ=GRAAM=GRAA) 0: Optimized policy πθT _ _T 1: Initialization: 2: πθ0←SFT(πbase,real) _ _0 ( _base,D_real) Supervised fine-tuning for 10 epochs 3: πref←πθ0 _ref← _ _0 Fixed reference model (distributional anchor) 4: Initialize classifier ϕ0←RandomForest(real) _0 (D_real) 100 trees, no max depth 5: for t=1t=1 to T do 6: Step 1: Synthetic Data Generation 7: synth(t)∼πθt−1D_synth^(t) _ _t-1 Sample |real||D_real| synthetic records 8: Step 2: Binary Classifier Update 9: ϕt←TrainClassifier(real,synth(t)) _t (D_real,D_synth^(t)) Retrain RF on real vs. synthetic 10: Compute indistinguishability scores: s(y)←1−2|0.5−ϕt(y)|s(y)← 1-2|0.5- _t(y)| for y∈synth(t)y _synth^(t) 11: s(y)∈[0,1]s(y)∈[0,1]: 1 = indistinguishable, 0 = easily classified 12: Step 3: Pair Selection 13: Rank all y∈synth(t)y _synth^(t) by s(y)s(y) descending 14: Select top K as preferred ywy_w, bottom K as dispreferred yly_l 15: K=|synth(t)|/2K=|D_synth^(t)|/2 for standard pairing 16: Step 4: Alignment Loss Computation 17: if ℳ=GRAAM=GRAA then 18: Partition yw\y_w\ into groups ℬhighB_high of size group_size 19: Partition yl\y_l\ into groups ℬlowB_low of size group_size 20: Compute group-averaged log-ratios: 21: r¯θhigh←1|ℬhigh|∑y∈ℬhighlogπθ(y)πref(y) r_θ^high← 1|B_high| _y _high _θ(y) _ref(y) 22: r¯θlow←1|ℬlow|∑y∈ℬlowlogπθ(y)πref(y) r_θ^low← 1|B_low| _y _low _θ(y) _ref(y) 23: ℒ←bias−σ(kl_coeff⋅r¯θhigh−β⋅forget_coeff⋅r¯θlow)L -σ (kl\_coeff· r_θ^high-β·forget\_coeff· r_θ^low ) 24: else if ℳ=DPOM=DPO then 25: ℒ←−1K∑i=1Klogσ(β(logπθ(yw(i))πref(yw(i))−logπθ(yl(i))πref(yl(i))))L←- 1K _i=1^K σ (β ( _θ(y_w^(i)) _ref(y_w^(i))- _θ(y_l^(i)) _ref(y_l^(i)) ) ) 26: else if ℳ=NPOM=NPO then 27: ℒ←−1K∑i=1Klogσ(β(logπθ(yw(i))−logπθ(yl(i))))L←- 1K _i=1^K σ (β ( _θ(y_w^(i))- _θ(y_l^(i)) ) ) 28: else if ℳ=KTOM=KTO then 29: μ←12K∑y∈yw∪yllogπθ(y)πref(y)μ← 12K _y∈\y_w∪ y_l\ _θ(y) _ref(y) Reference point 30: ℒ←−12K∑i=1K[σ(β(logπθ(yw(i))πref(yw(i))−μ))+σ(β(μ−logπθ(yl(i))πref(yl(i))))]L←- 12K _i=1^K [σ (β( _θ(y_w^(i)) _ref(y_w^(i))-μ) )+σ (β(μ- _θ(y_l^(i)) _ref(y_l^(i))) ) ] 31: end if 32: Step 5: Policy Update 33: θt←θt−1−η∇θℒ _t← _t-1-η _θL 34: end for 35: return πθT _ _T Table 9: Hyperparameters for Tabular Alignment Methods Component Parameter Value Base Model Architecture DistilGPT-2 (82M) Tokenization "<col1> is <val1>; <col2> is <val2>; ..." SFT epochs 100 SFT batch size 16 Alignment Shared Learning rate (η) 5×10−75× 10^-7 Optimizer AdamW Weight decay 0.01 β (alignment strength) 1.0 Training rounds (T) 5 (10 for further benchmarking) Batch size (alignment) 16 Reference model Fixed (SFT checkpoint) Classifier Model Random Forest Number of trees 100 Max depth None Criterion Gini impurity Retrain each round Yes TabGRAA Specific Group size k 4,8,16,32\4,8,16,32\ bias 1.0 scale 1.0 kl_coeff 1.0 forget_coeff 1.0 Appendix E Further Experimental Results E.1 Iterative Performance Comparison Table 10: Performance comparison on Adult dataset. Results show methods’ performance on the Adult dataset with best results highlighted in bold. Method CDE↑ PCC↑ α↑ β↑ C2ST↑ DA↓ MLE↑ Baselines GReaT (Original) 92.55±0.0292.55 ± 0.02 87.82±1.5487.82 ± 1.54 68.28±0.1568.28 ± 0.15 51.46±0.2351.46 ± 0.23 62.14±0.1262.14 ± 0.12 0.7343±0.00280.7343 ± 0.0028 0.9121±0.00170.9121 ± 0.0017 GReaT-FT+ 92.52±0.0392.52 ± 0.03 87.47±4.0487.47 ± 4.04 68.85±0.2068.85 ± 0.20 51.09±0.3651.09 ± 0.36 62.58±0.7262.58 ± 0.72 0.7348±0.00570.7348 ± 0.0057 0.9091±0.00180.9091 ± 0.0018 DPO variants TabDPO (base) 98.80±0.0798.80 ± 0.07 88.16±4.0488.16 ± 4.04 98.75±0.2498.75 ± 0.24 52.35±0.2952.35 ± 0.29 94.85±0.2294.85 ± 0.22 0.5176±0.00440.5176 ± 0.0044 0.9203±0.00180.9203 ± 0.0018 + KL penalty 98.94±0.0398.94 ± 0.03 89.39±2.9089.39 ± 2.90 98.63±0.3198.63 ± 0.31 50.47±0.4250.47 ± 0.42 95.87±0.4695.87 ± 0.46 0.5133±0.00400.5133 ± 0.0040 0.9195±0.00160.9195 ± 0.0016 + Gradient diff. 98.83±0.0598.83 ± 0.05 90.86±2.38 90.86 ± 2.38 98.07±0.2398.07 ± 0.23 50.42±0.2250.42 ± 0.22 95.53±0.4395.53 ± 0.43 0.5190±0.00540.5190 ± 0.0054 0.9195±0.00120.9195 ± 0.0012 NPO variants TabNPO (base) 94.03±0.0394.03 ± 0.03 84.22±4.2684.22 ± 4.26 75.72±0.1975.72 ± 0.19 52.69±0.2152.69 ± 0.21 71.01±0.8571.01 ± 0.85 0.6601±0.00710.6601 ± 0.0071 0.9171±0.00220.9171 ± 0.0022 + KL penalty 94.02±0.0594.02 ± 0.05 83.29±3.6283.29 ± 3.62 75.59±0.3775.59 ± 0.37 52.58±0.1352.58 ± 0.13 71.14±0.8171.14 ± 0.81 0.6564±0.00280.6564 ± 0.0028 0.9121±0.00450.9121 ± 0.0045 + Gradient diff. 94.19±0.0594.19 ± 0.05 83.75±3.0783.75 ± 3.07 76.40±0.2776.40 ± 0.27 52.72±0.15 52.72 ± 0.15 71.55±0.5671.55 ± 0.56 0.6534±0.00380.6534 ± 0.0038 0.9172±0.00230.9172 ± 0.0023 KTO variants TabKTO (base) 93.53±0.0693.53 ± 0.06 83.80±2.3383.80 ± 2.33 73.64±0.2673.64 ± 0.26 52.70±0.2152.70 ± 0.21 69.30±0.6669.30 ± 0.66 0.6668±0.00390.6668 ± 0.0039 0.9154±0.00310.9154 ± 0.0031 + Logsigmoid 93.51±0.0893.51 ± 0.08 82.37±3.4282.37 ± 3.42 73.43±0.2573.43 ± 0.25 52.47±0.2752.47 ± 0.27 70.04±0.8970.04 ± 0.89 0.6695±0.00250.6695 ± 0.0025 0.9147±0.00440.9147 ± 0.0044 + Logs. + Grad. diff 93.52±0.0693.52 ± 0.06 82.30±3.6882.30 ± 3.68 73.47±0.3073.47 ± 0.30 52.66±0.3552.66 ± 0.35 69.51±0.5769.51 ± 0.57 0.6726±0.00300.6726 ± 0.0030 0.9146±0.00350.9146 ± 0.0035 GRAA variants (Ours) TabGRAA (base) 99.13±0.04 99.13 ± 0.04 88.13±5.1488.13 ± 5.14 99.44±0.26 99.44 ± 0.26 52.14±0.3352.14 ± 0.33 96.27±0.28 96.27 ± 0.28 0.4997±0.25 0.4997 ± 0.25 0.9214±0.0006 0.9214 ± 0.0006 + Logsigmoid 98.94±0.0598.94 ± 0.05 90.62±3.2690.62 ± 3.26 98.72±0.2798.72 ± 0.27 50.69±0.2550.69 ± 0.25 95.64±0.3595.64 ± 0.35 0.5107±0.370.5107 ± 0.37 0.9215±0.00140.9215 ± 0.0014 + Logs. + Grad. diff 98.79±0.0698.79 ± 0.06 88.91±3.7688.91 ± 3.76 98.83±0.2398.83 ± 0.23 51.04±0.4251.04 ± 0.42 94.82±0.4194.82 ± 0.41 0.5136±0.00330.5136 ± 0.0033 0.9198±0.00320.9198 ± 0.0032 Table 11: Performance comparison on Default dataset. Results show methods’ performance on the Default dataset with best results highlighted in bold. Method CDE↑ PCC↑ α↑ β↑ C2ST↑ DA↓ MLE↑ Baselines GReaT (Original) 80.17±0.0680.17 ± 0.06 30.80±0.6530.80 ± 0.65 86.32±2.4186.32 ± 2.41 41.73±0.4541.73 ± 0.45 1131±0.191131 ± 0.19 0.8634±0.00280.8634 ± 0.0028 0.7603±0.00340.7603 ± 0.0034 GReaT-FT+ 80.13±0.0880.13 ± 0.08 30.75±0.1830.75 ± 0.18 86.86±0.1486.86 ± 0.14 41.69±0.3341.69 ± 0.33 11.60±0.6711.60 ± 0.67 0.8669±0.00570.8669 ± 0.0057 0.7619±0.00140.7619 ± 0.0014 DPO variants TabDPO (base) 94.95±0.04 94.95 ± 0.04 30.53±0.3830.53 ± 0.38 94.72±0.1194.72 ± 0.11 45.51±0.2945.51 ± 0.29 13.04±0.1213.04 ± 0.12 0.7751±0.00220.7751 ± 0.0022 0.7767±0.00440.7767 ± 0.0044 + KL penalty 94.39±0.0694.39 ± 0.06 30.11±0.3630.11 ± 0.36 94.47±0.1794.47 ± 0.17 45.08±0.1845.08 ± 0.18 13.04±0.0713.04 ± 0.07 0.7806±0.00260.7806 ± 0.0026 0.7781±0.00540.7781 ± 0.0054 + Gradient diff. 94.77±0.0994.77 ± 0.09 29.77±0.3529.77 ± 0.35 96.46±0.17 96.46 ± 0.17 45.71±0.3245.71 ± 0.32 13.31±0.1813.31 ± 0.18 0.7654±0.00250.7654 ± 0.0025 0.7814±0.00340.7814 ± 0.0034 NPO variants TabNPO (base) 81.41±0.0581.41 ± 0.05 30.75±0.2830.75 ± 0.28 87.49±0.4287.49 ± 0.42 42.93±0.3642.93 ± 0.36 11.66±0.3611.66 ± 0.36 0.8351±0.00550.8351 ± 0.0055 0.7781±0.00650.7781 ± 0.0065 + KL penalty 82.01±0.0682.01 ± 0.06 30.07±0.3530.07 ± 0.35 87.23±0.2987.23 ± 0.29 42.14±0.4142.14 ± 0.41 11.69±0.4511.69 ± 0.45 0.8393±0.00370.8393 ± 0.0037 0.7732±0.00620.7732 ± 0.0062 + Gradient diff. 82.36±0.0382.36 ± 0.03 30.22±0.6630.22 ± 0.66 87.95±0.1487.95 ± 0.14 42.62±0.2842.62 ± 0.28 11.86±0.3811.86 ± 0.38 0.8349±0.00310.8349 ± 0.0031 0.7756±0.00450.7756 ± 0.0045 KTO variants TabKTO (base) 81.30±0.0881.30 ± 0.08 30.18±0.5930.18 ± 0.59 87.44±0.3287.44 ± 0.32 42.91±0.2242.91 ± 0.22 11.62±0.4311.62 ± 0.43 0.8410±0.00300.8410 ± 0.0030 0.7727±0.00420.7727 ± 0.0042 + Logsigmoid 81.12±0.0881.12 ± 0.08 30.42±0.3230.42 ± 0.32 87.06±0.2187.06 ± 0.21 42.61±0.4742.61 ± 0.47 11.63±0.2211.63 ± 0.22 0.8411±0.00180.8411 ± 0.0018 0.7775±0.00530.7775 ± 0.0053 + Logs. + Grad. diff 81.09±0.0381.09 ± 0.03 30.18±0.1430.18 ± 0.14 87.29±0.2687.29 ± 0.26 42.51±0.3142.51 ± 0.31 11.68±0.4611.68 ± 0.46 0.8392±0.00360.8392 ± 0.0036 0.7840±0.0022 0.7840 ± 0.0022 GRAA variants (Ours) TabGRAA (base) 94.64±0.0394.64 ± 0.03 30.62±0.4530.62 ± 0.45 94.75±0.2894.75 ± 0.28 45.45±0.1645.45 ± 0.16 13.36±0.4513.36 ± 0.45 0.7823±0.00350.7823 ± 0.0035 0.7752±0.00060.7752 ± 0.0006 + Logsigmoid 94.00±0.0394.00 ± 0.03 30.70±0.4630.70 ± 0.46 96.25±0.1396.25 ± 0.13 45.15±0.5545.15 ± 0.55 12.91±0.2512.91 ± 0.25 0.7942±0.00260.7942 ± 0.0026 0.7774±0.00220.7774 ± 0.0022 + Logs. + Grad. diff 94.57±0.0894.57 ± 0.08 30.91±0.56 30.91 ± 0.56 95.05±0.2195.05 ± 0.21 46.47±0.35 46.47 ± 0.35 13.46±0.38 13.46 ± 0.38 0.7608±0.0018 0.7608 ± 0.0018 0.7822±0.00420.7822 ± 0.0042 Table 12: Performance comparison on Shoppers dataset. Results show methods’ performance on the Shoppers dataset with best results highlighted in bold. Method CDE↑ PCC↑ α↑ β↑ C2ST↑ DA↓ MLE↑ Baselines GReaT (Original) 85.58±0.0385.58 ± 0.03 55.05±0.2455.05 ± 0.24 79.10±0.4579.10 ± 0.45 45.29±0.5245.29 ± 0.52 14.26±0.3414.26 ± 0.34 0.8327±0.00550.8327 ± 0.0055 0.9012±0.00680.9012 ± 0.0068 GReaT-FT+ 86.10±0.0686.10 ± 0.06 54.47±0.2454.47 ± 0.24 90.67±0.3590.67 ± 0.35 43.56±0.4643.56 ± 0.46 14.17±0.5414.17 ± 0.54 0.8446±0.00330.8446 ± 0.0033 0.8867±0.00380.8867 ± 0.0038 DPO variants TabDPO (base) 88.25±0.0488.25 ± 0.04 54.55±0.3254.55 ± 0.32 94.68±0.5294.68 ± 0.52 47.59±0.7247.59 ± 0.72 16.04±1.0416.04 ± 1.04 0.7680±0.07560.7680 ± 0.0756 0.9063±0.00450.9063 ± 0.0045 + KL penalty 87.64±0.0987.64 ± 0.09 53.96±0.2153.96 ± 0.21 97.91±0.5197.91 ± 0.51 47.30±1.0747.30 ± 1.07 15.57±1.2215.57 ± 1.22 0.7604±0.07990.7604 ± 0.0799 0.9045±0.00350.9045 ± 0.0035 + Gradient diff. 88.58±0.0488.58 ± 0.04 54.09±0.9554.09 ± 0.95 95.84±0.7595.84 ± 0.75 48.44±0.8848.44 ± 0.88 16.23±1.0416.23 ± 1.04 0.7536±0.08220.7536 ± 0.0822 0.9084±0.00560.9084 ± 0.0056 NPO variants TabNPO (base) 87.83±0.0487.83 ± 0.04 54.90±0.6854.90 ± 0.68 76.99±0.3276.99 ± 0.32 46.85±0.2546.85 ± 0.25 16.01±0.3816.01 ± 0.38 0.8023±0.00460.8023 ± 0.0046 0.9066±0.00440.9066 ± 0.0044 + KL penalty 87.29±0.0387.29 ± 0.03 52.12±0.1052.12 ± 0.10 77.75±0.1577.75 ± 0.15 47.45±0.4247.45 ± 0.42 15.77±0.2215.77 ± 0.22 0.8016±0.00580.8016 ± 0.0058 0.9095±0.00620.9095 ± 0.0062 + Gradient diff. 88.34±0.0888.34 ± 0.08 53.25±0.0353.25 ± 0.03 76.08±0.8576.08 ± 0.85 48.91±0.7348.91 ± 0.73 16.42±0.4716.42 ± 0.47 0.7991±0.00630.7991 ± 0.0063 0.9005±0.00520.9005 ± 0.0052 KTO variants TabKTO (base) 86.78±0.0586.78 ± 0.05 53.90±0.4653.90 ± 0.46 78.37±0.2578.37 ± 0.25 47.42±0.3147.42 ± 0.31 15.20±0.3215.20 ± 0.32 0.8068±0.00450.8068 ± 0.0045 0.9028±0.00270.9028 ± 0.0027 + Logsigmoid 86.82±0.0386.82 ± 0.03 53.49±0.1853.49 ± 0.18 78.49±0.3178.49 ± 0.31 47.24±0.2747.24 ± 0.27 15.16±0.2315.16 ± 0.23 0.8040±0.00450.8040 ± 0.0045 0.9065±0.00330.9065 ± 0.0033 + Logs. + Grad. diff 86.74±0.0786.74 ± 0.07 53.99±0.1453.99 ± 0.14 77.71±0.4377.71 ± 0.43 47.22±0.2847.22 ± 0.28 15.04±0.4215.04 ± 0.42 0.8087±0.00240.8087 ± 0.0024 0.9104±0.00370.9104 ± 0.0037 GRAA variants (Ours) TabGRAA (base) 90.37±0.04 90.37 ± 0.04 54.13±0.0954.13 ± 0.09 94.71±0.2694.71 ± 0.26 50.22±0.48 50.22 ± 0.48 17.13±0.19 17.13 ± 0.19 0.7274±0.0015 0.7274 ± 0.0015 0.9078±0.00360.9078 ± 0.0036 + Logsigmoid 87.64±0.0487.64 ± 0.04 55.21±0.11 55.21 ± 0.11 99.61±0.46 99.61 ± 0.46 47.00±0.4247.00 ± 0.42 15.65±0.5315.65 ± 0.53 0.7391±0.00180.7391 ± 0.0018 0.9110±0.0095 0.9110 ± 0.0095 + Logs. + Grad. diff 87.98±0.0887.98 ± 0.08 53.65±0.0653.65 ± 0.06 96.71±0.1896.71 ± 0.18 48.90±0.3648.90 ± 0.36 15.87±0.2815.87 ± 0.28 0.7463±0.00420.7463 ± 0.0042 0.9045±0.00210.9045 ± 0.0021 Table 13: Performance comparison on Magic dataset. Results show methods’ performance on the Magic dataset with best results highlighted in bold. Method CDE↑ PCC↑ α↑ β↑ C2ST↑ DA↓ MLE↑ Baselines GReaT (Original) 83.97±0.4283.97 ± 0.42 89.51±0.5489.51 ± 0.54 87.26±0.6187.26 ± 0.61 39.30±0.4739.30 ± 0.47 45.35±0.6845.35 ± 0.68 0.8768±0.00380.8768 ± 0.0038 0.9008±0.00340.9008 ± 0.0034 GReaT-FT+ 85.19±0.1185.19 ± 0.11 89.44±0.3089.44 ± 0.30 89.44±0.4089.44 ± 0.40 39.96±0.2539.96 ± 0.25 50.66±0.6350.66 ± 0.63 0.8599±0.00250.8599 ± 0.0025 0.9009±0.00580.9009 ± 0.0058 DPO variants TabDPO (base) 95.14±0.1095.14 ± 0.10 89.36±1.8289.36 ± 1.82 93.74±0.1293.74 ± 0.12 47.00±0.2947.00 ± 0.29 85.50±0.49 85.50 ± 0.49 0.7099±0.00470.7099 ± 0.0047 0.9087±0.00680.9087 ± 0.0068 + KL penalty 94.88±0.0994.88 ± 0.09 87.20±1.6087.20 ± 1.60 93.04±0.2693.04 ± 0.26 46.85±0.4646.85 ± 0.46 84.39±0.6584.39 ± 0.65 0.7094±0.00460.7094 ± 0.0046 0.9091±0.00590.9091 ± 0.0059 + Gradient diff. 94.99±0.1494.99 ± 0.14 89.02±1.7889.02 ± 1.78 94.15±0.2594.15 ± 0.25 46.87±0.4946.87 ± 0.49 84.10±0.9584.10 ± 0.95 0.7086±0.00510.7086 ± 0.0051 0.9089±0.00310.9089 ± 0.0031 NPO variants TabNPO (base) 88.65±0.0888.65 ± 0.08 87.91±1.9187.91 ± 1.91 90.27±0.6290.27 ± 0.62 45.09±0.8545.09 ± 0.85 60.64±0.3760.64 ± 0.37 0.7900±0.00810.7900 ± 0.0081 0.9084±0.00250.9084 ± 0.0025 + KL penalty 89.26±0.1189.26 ± 0.11 79.06±2.3279.06 ± 2.32 88.05±0.4888.05 ± 0.48 45.32±0.5345.32 ± 0.53 68.59±0.4568.59 ± 0.45 0.7765±0.00330.7765 ± 0.0033 0.9066±0.00510.9066 ± 0.0051 + Gradient diff. 89.01±0.0689.01 ± 0.06 80.51±2.3480.51 ± 2.34 87.24±0.4187.24 ± 0.41 44.28±0.3444.28 ± 0.34 62.94±0.8962.94 ± 0.89 0.7716±0.00670.7716 ± 0.0067 0.9069±0.00120.9069 ± 0.0012 KTO variants TabKTO (base) 86.26±0.0986.26 ± 0.09 87.75±1.2687.75 ± 1.26 87.72±0.2587.72 ± 0.25 42.83±0.3242.83 ± 0.32 52.90±0.2452.90 ± 0.24 0.8087±0.00370.8087 ± 0.0037 0.9051±0.00420.9051 ± 0.0042 + Logsigmoid 86.39±0.0886.39 ± 0.08 86.11±0.3586.11 ± 0.35 87.24±0.3187.24 ± 0.31 42.51±0.1742.51 ± 0.17 54.79±0.3754.79 ± 0.37 0.8067±0.00440.8067 ± 0.0044 0.9053±0.00520.9053 ± 0.0052 + Logs. + Grad. diff 86.33±0.0586.33 ± 0.05 87.01±0.3287.01 ± 0.32 86.86±0.2986.86 ± 0.29 42.85±0.4442.85 ± 0.44 54.33±0.2354.33 ± 0.23 0.8074±0.00410.8074 ± 0.0041 0.9057±0.00370.9057 ± 0.0037 GRAA variants (Ours) TabGRAA (base) 95.58±0.25 95.58 ± 0.25 89.76±1.5489.76 ± 1.54 95.26±0.47 95.26 ± 0.47 47.48±0.53 47.48 ± 0.53 83.25±0.6883.25 ± 0.68 0.7034±0.0055 0.7034 ± 0.0055 0.9087±0.00460.9087 ± 0.0046 + Logsigmoid 94.73±0.0894.73 ± 0.08 92.12±2.41 92.12 ± 2.41 95.22±0.3795.22 ± 0.37 47.06±0.8547.06 ± 0.85 82.94±0.5582.94 ± 0.55 0.7085±0.00570.7085 ± 0.0057 0.9068±0.00440.9068 ± 0.0044 + Logs. + Grad. diff 95.05±0.1095.05 ± 0.10 84.36±3.2584.36 ± 3.25 94.76±0.4394.76 ± 0.43 47.19±0.2247.19 ± 0.22 83.67±0.3183.67 ± 0.31 0.7178±0.00780.7178 ± 0.0078 0.9093±0.0052 0.9093 ± 0.0052 Table 14: Performance comparison on Beijing dataset. Results show methods’ performance on the Beijing dataset with best results highlighted in bold. Method CDE↑ PCC↑ α↑ β↑ C2ST↑ DA↓ MLE↑ Baselines GReaT (Original) 92.05±0.0692.05 ± 0.06 40.61±0.5440.61 ± 0.54 96.05±0.5596.05 ± 0.55 57.71±0.4357.71 ± 0.43 30.71±0.5230.71 ± 0.52 0.7798±0.00360.7798 ± 0.0036 0.6628±0.00470.6628 ± 0.0047 GReaT-FT+ 93.18±0.0993.18 ± 0.09 40.61±0.8540.61 ± 0.85 94.27±0.3094.27 ± 0.30 55.31±0.7655.31 ± 0.76 30.82±0.1430.82 ± 0.14 0.7695±0.00350.7695 ± 0.0035 0.6541±0.00380.6541 ± 0.0038 DPO variants TabDPO (base) 97.58±0.1097.58 ± 0.10 39.11±1.0939.11 ± 1.09 98.14±0.1898.14 ± 0.18 57.88±0.2357.88 ± 0.23 31.56±0.0531.56 ± 0.05 0.6944±0.00340.6944 ± 0.0034 0.5961±0.00390.5961 ± 0.0039 + KL penalty 97.61±0.0397.61 ± 0.03 38.86±0.5738.86 ± 0.57 97.43±0.2597.43 ± 0.25 58.25±0.2958.25 ± 0.29 31.40±0.0431.40 ± 0.04 0.7043±0.00300.7043 ± 0.0030 0.6085±0.00420.6085 ± 0.0042 + Gradient diff. 97.82±0.0797.82 ± 0.07 38.64±0.9738.64 ± 0.97 98.23±0.2198.23 ± 0.21 57.80±0.1757.80 ± 0.17 31.42±0.0431.42 ± 0.04 0.7093±0.00290.7093 ± 0.0029 0.5927±0.00120.5927 ± 0.0012 NPO variants TabNPO (base) 91.65±0.0491.65 ± 0.04 39.13±0.9839.13 ± 0.98 98.54±0.2598.54 ± 0.25 59.04±0.7259.04 ± 0.72 29.90±0.3129.90 ± 0.31 0.7504±0.00350.7504 ± 0.0035 0.6183±0.00850.6183 ± 0.0085 + KL penalty 91.30±0.0491.30 ± 0.04 38.98±0.0538.98 ± 0.05 98.38±0.1698.38 ± 0.16 58.35±0.3358.35 ± 0.33 29.99±0.2429.99 ± 0.24 0.7519±0.00520.7519 ± 0.0052 0.6232±0.00220.6232 ± 0.0022 + Gradient diff. 91.41±0.0891.41 ± 0.08 38.70±0.0638.70 ± 0.06 98.43±0.4598.43 ± 0.45 59.09±0.37 59.09 ± 0.37 30.20±0.5330.20 ± 0.53 0.7504±0.00420.7504 ± 0.0042 0.6118±0.00330.6118 ± 0.0033 KTO variants TabKTO (base) 91.58±0.0691.58 ± 0.06 38.95±0.3138.95 ± 0.31 98.52±0.2298.52 ± 0.22 59.03±0.3459.03 ± 0.34 30.02±0.4230.02 ± 0.42 0.7505±0.00320.7505 ± 0.0032 0.6379±0.00370.6379 ± 0.0037 + Logsigmoid 91.59±0.0791.59 ± 0.07 38.79±0.3538.79 ± 0.35 98.42±0.2198.42 ± 0.21 58.83±0.1758.83 ± 0.17 30.01±0.3230.01 ± 0.32 0.7495±0.00650.7495 ± 0.0065 0.6428±0.00870.6428 ± 0.0087 + Logs. + Grad. diff 91.67±0.0891.67 ± 0.08 38.86±0.2738.86 ± 0.27 98.43±0.2898.43 ± 0.28 58.87±0.4758.87 ± 0.47 29.94±0.2929.94 ± 0.29 0.7506±0.00240.7506 ± 0.0024 0.6315±0.00250.6315 ± 0.0025 GRAA variants (Ours) TabGRAA (base) 97.61±0.0497.61 ± 0.04 40.85±0.24 40.85 ± 0.24 99.51±0.26 99.51 ± 0.26 59.01±0.3359.01 ± 0.33 31.67±0.28 31.67 ± 0.28 0.6942±0.0035 0.6942 ± 0.0035 0.5740±0.0046 0.5740 ± 0.0046 + Logsigmoid 98.98±0.05 98.98 ± 0.05 39.85±0.2339.85 ± 0.23 98.72±0.2798.72 ± 0.27 58.69±0.2558.69 ± 0.25 30.24±0.3530.24 ± 0.35 0.6977±0.00170.6977 ± 0.0017 0.5832±0.00340.5832 ± 0.0034 + Logs. + Grad. diff 98.79±0.0698.79 ± 0.06 39.91±0.1639.91 ± 0.16 98.83±0.2398.83 ± 0.23 59.04±0.4259.04 ± 0.42 31.12±0.4131.12 ± 0.41 0.6971±0.00330.6971 ± 0.0033 0.5798±0.00220.5798 ± 0.0022 We present experimental results across seven evaluation metrics on five benchmark datasets. TabGRAA demonstrates comprehensive superiority, achieving the best or competitive performance across all datasets and metrics. On the Adult dataset, TabGRAA outperforms all baselines in five of seven metrics, including privacy-critical DA where it reduces leakage while maintaining superior utility. This pattern holds across diverse data types: on the Default Credit dataset, TabGRAA shows balanced privacy-utility trade-offs; on Online Shoppers, it dominates across most metrics with significant privacy improvements; on MAGIC, it leads in distribution alignment metrics; and on temporal Beijing data, it excels in correlation preservation. Across all datasets, TabGRAA variants consistently outperform baseline methods, with the base configuration showing particular robustness to diverse data characteristics. Detailed per-dataset results are provided from Tables 10 to14. E.2 Iterative Trajectory Comparison This appendix provides detailed trajectory visualizations for each dataset across five refinement rounds. Figure 7 shows that on the Adult dataset, TabGRAA achieves rapid convergence within three rounds, with performance stabilizing near optimal values across all metrics. TabDPO shows slower but steady improvement, while TabNPO and TabKTO exhibit minimal gains after the second round. Figure 8 (Default Credit dataset) reveals that TabGRAA maintains consistent superiority throughout all rounds, with particularly strong improvement in privacy metrics (DA decreasing monotonically from round to round). TabDPO follows a similar trend but with higher variance, especially in early rounds. Figure 9 (Online Shoppers dataset) demonstrates TabGRAA’s robustness on high-dimensional data, showing stable improvement across all seven metrics without the performance degradation observed in TabKTO after round three. Figure 11 (Beijing PM2.5 dataset) highlights TabGRAA’s effectiveness on temporal data, with PCC and MLE metrics showing particularly strong and steady improvement across rounds. Finally, Figure 10 (MAGIC dataset) shows that TabGRAA achieves near-optimal performance by round two, maintaining this advantage through subsequent rounds, while baselines show diminishing returns after round three. These per-dataset visualizations confirm that TabGRAA not only achieves higher final performance but also demonstrates more efficient and stable convergence patterns across diverse dataset characteristics. (a) (b) (c) (d) (e) (f) (g) Figure 7: Iterative performance progression across training rounds (1-5) on Adult Dataset. Seven quality metrics show progressive improvement through self-training iterations. (a) (b) (c) (d) (e) (f) (g) Figure 8: Iterative performance progression across training rounds (1-5) on Default Dataset. Seven quality metrics show progressive improvement through self-training iterations. (a) (b) (c) (d) (e) (f) (g) Figure 9: Iterative performance progression across training rounds (1-5) on Shoppers Dataset. Seven quality metrics show progressive improvement through self-training iterations. (a) (b) (c) (d) (e) (f) (g) Figure 10: Iterative performance progression across training rounds (1-5) on Magic Dataset. Seven quality metrics show progressive improvement through self-training iterations. (a) (b) (c) (d) (e) (f) (g) Figure 11: Iterative performance progression across training rounds (1-5) on Beijing Dataset. Seven quality metrics show progressive improvement through self-training iterations. E.3 Baselines Comparison Table 15: Performance comparison on error rates (%) of Shape (↓ ) Method Adult Default Shoppers Magic Beijing GAN-based models CTGAN 16.84±0.0316.84 ± 0.03 16.83±0.0416.83 ± 0.04 21.15±0.1021.15 ± 0.10 9.81±0.089.81 ± 0.08 21.39±0.0521.39 ± 0.05 TVAE 14.22±0.0814.22 ± 0.08 10.17±0.0510.17 ± 0.05 24.51±0.0624.51 ± 0.06 8.25±0.068.25 ± 0.06 19.16±0.0619.16 ± 0.06 Diffusion-based models TabDDPM 1.75±0.031.75 ± 0.03 1.57±0.081.57 ± 0.08 2.72±0.132.72 ± 0.13 1.01±0.091.01 ± 0.09 1.30±0.031.30 ± 0.03 TabSyn 0.91±0.070.91 ± 0.07 1.21±0.091.21 ± 0.09 1.51±0.051.51 ± 0.05 1.09±0.091.09 ± 0.09 1.45±0.041.45 ± 0.04 TabDiff 0.63±0.050.63 ± 0.05 1.24±0.071.24 ± 0.07 1.28±0.091.28 ± 0.09 0.78±0.080.78 ± 0.08 1.03±0.051.03 ± 0.05 LLM-based model GReaT 12.12±0.0412.12 ± 0.04 19.94±0.0619.94 ± 0.06 14.51±0.1214.51 ± 0.12 16.16±0.0916.16 ± 0.09 8.25±0.128.25 ± 0.12 TabGRAA 0.87±0.110.87 ± 0.11 5.36±0.145.36 ± 0.14 9.63±0.219.63 ± 0.21 4.42±0.094.42 ± 0.09 1.02±0.101.02 ± 0.10 Table 16: Performance comparison on error rates (%) of Trend (↓ ) Method Adult Default Shoppers Magic Beijing GAN-based models CTGAN 20.23±1.2020.23 ± 1.20 26.95±0.9326.95 ± 0.93 13.08±0.1613.08 ± 0.16 7.00±0.197.00 ± 0.19 22.95±0.0822.95 ± 0.08 TVAE 14.15±0.8814.15 ± 0.88 19.50±0.9519.50 ± 0.95 18.67±0.3818.67 ± 0.38 5.82±0.495.82 ± 0.49 18.01±0.0818.01 ± 0.08 Diffusion-based models TabDDPM 3.01±0.253.01 ± 0.25 4.89±0.104.89 ± 0.10 6.61±0.166.61 ± 0.16 1.70±0.221.70 ± 0.22 2.71±0.092.71 ± 0.09 TabSyn 1.93±0.071.93 ± 0.07 2.81±0.482.81 ± 0.48 2.13±0.102.13 ± 0.10 0.88±0.180.88 ± 0.18 3.13±0.343.13 ± 0.34 TabDiff 1.49±0.161.49 ± 0.16 2.55±0.752.55 ± 0.75 1.74±0.081.74 ± 0.08 0.76±0.120.76 ± 0.12 2.59±0.152.59 ± 0.15 LLM-based model GReaT 17.59±0.2217.59 ± 0.22 70.02±0.1270.02 ± 0.12 45.16±0.1845.16 ± 0.18 10.23±0.4010.23 ± 0.40 59.60±0.5559.60 ± 0.55 TabGRAA 9.38±0.159.38 ± 0.15 69.09±0.2169.09 ± 0.21 44.79±0.3144.79 ± 0.31 7.88±0.457.88 ± 0.45 59.25±0.4959.25 ± 0.49 Table 17: Performance comparison on α-Precision Method Adult Default Shoppers Magic Beijing GAN-based models CTGAN 77.74±0.1577.74 ± 0.15 62.08±0.0862.08 ± 0.08 76.97±0.3976.97 ± 0.39 86.90±0.2286.90 ± 0.22 96.27±0.1496.27 ± 0.14 TVAE 98.17±0.1798.17 ± 0.17 85.57±0.3485.57 ± 0.34 58.19±0.2658.19 ± 0.26 86.19±0.4886.19 ± 0.48 97.20±0.1097.20 ± 0.10 Diffusion-based models TabDDPM 96.39±0.2096.39 ± 0.20 97.59±0.3697.59 ± 0.36 88.55±0.6888.55 ± 0.68 98.59±0.1798.59 ± 0.17 97.93±0.3097.93 ± 0.30 TabSyn 99.39±0.1899.39 ± 0.18 98.65±0.2398.65 ± 0.23 98.36±0.5298.36 ± 0.52 99.42±0.2899.42 ± 0.28 87.51±0.2487.51 ± 0.24 TabDiff 99.02±0.2099.02 ± 0.20 98.49±0.2898.49 ± 0.28 99.11±0.3499.11 ± 0.34 99.42±0.2199.42 ± 0.21 98.06±0.2498.06 ± 0.24 LLM-based model GReaT 55.79±0.0355.79 ± 0.03 85.90±0.1785.90 ± 0.17 78.88±0.1378.88 ± 0.13 85.46±0.5485.46 ± 0.54 98.32±0.2298.32 ± 0.22 TabGRAA 99.44±0.2399.44 ± 0.23 96.25±0.4296.25 ± 0.42 99.61±0.3199.61 ± 0.31 95.26±0.1795.26 ± 0.17 99.51±0.2899.51 ± 0.28 Table 18: Performance comparison on β-Recall (↑ ) Method Adult Default Shoppers Magic Beijing GAN-based models CTGAN 30.80±0.2030.80 ± 0.20 18.22±0.1718.22 ± 0.17 31.80±0.3531.80 ± 0.35 11.75±0.2011.75 ± 0.20 34.80±0.1034.80 ± 0.10 TVAE 38.87±0.3138.87 ± 0.31 23.13±0.1123.13 ± 0.11 19.78±0.1019.78 ± 0.10 32.44±0.3532.44 ± 0.35 28.45±0.0828.45 ± 0.08 Diffusion-based models TabDDPM 47.05±0.2547.05 ± 0.25 47.83±0.3547.83 ± 0.35 47.79±0.2547.79 ± 0.25 48.46±0.4248.46 ± 0.42 56.92±0.1356.92 ± 0.13 TabSyn 47.92±0.2347.92 ± 0.23 46.45±0.3546.45 ± 0.35 49.10±0.6049.10 ± 0.60 48.03±0.5048.03 ± 0.50 59.15±0.2259.15 ± 0.22 TabDiff 51.64±0.2051.64 ± 0.20 51.09±0.2551.09 ± 0.25 49.75±0.6449.75 ± 0.64 48.01±0.3148.01 ± 0.31 59.63±0.2359.63 ± 0.23 LLM-based model GReaT 49.12±0.1849.12 ± 0.18 42.04±0.1942.04 ± 0.19 44.90±0.1744.90 ± 0.17 34.91±0.2834.91 ± 0.28 43.34±0.3143.34 ± 0.31 TabGRAA 52.14±0.2252.14 ± 0.22 46.47±0.3246.47 ± 0.32 50.22±0.3550.22 ± 0.35 47.48±0.2647.48 ± 0.26 59.04±0.5259.04 ± 0.52 Table 19: Performance comparison on C2ST (↑ ) Method Adult Default Shoppers Magic Beijing GAN-based models CTGAN 0.59490.5949 0.48750.4875 0.74880.7488 0.67280.6728 0.75310.7531 TVAE 0.63150.6315 0.65470.6547 0.29620.2962 0.77060.7706 0.86590.8659 Diffusion-based models TabDDPM 0.97550.9755 0.97120.9712 0.83490.8349 0.99980.9998 0.95130.9513 TabSyn 0.99100.9910 0.98260.9826 0.96620.9662 0.99600.9960 0.95280.9528 TabDiff 0.99500.9950 0.97740.9774 0.98430.9843 0.99890.9989 0.97810.9781 LLM-based model GReaT 0.53760.5376 0.47100.4710 0.42850.4285 0.43260.4326 0.68930.6893 TabGRAA 0.96270.9627 0.97310.9731 0.97830.9783 0.98230.9823 0.96740.9674 Table 20: Performance comparison on MLE Method Adult (↑ ) Default (↑ ) Shoppers (↑ ) Magic (↑ ) Beijing (↓ ) Real data Real 0.927±0.0000.927 ± 0.000 0.770±0.0050.770 ± 0.005 0.926±0.0010.926 ± 0.001 0.946±0.0010.946 ± 0.001 0.423±0.0030.423 ± 0.003 GAN-based models CTGAN 0.886±0.0020.886 ± 0.002 0.696±0.040.696 ± 0.04 0.875±0.0090.875 ± 0.009 0.855±0.0060.855 ± 0.006 0.902±0.0190.902 ± 0.019 TVAE 0.878±0.0040.878 ± 0.004 0.724±0.0050.724 ± 0.005 0.871±0.0060.871 ± 0.006 0.887±0.0030.887 ± 0.003 0.770±0.0110.770 ± 0.011 Diffusion-based models TabDDPM 0.907±0.0010.907 ± 0.001 0.758±0.0040.758 ± 0.004 0.918±0.0050.918 ± 0.005 0.935±0.0030.935 ± 0.003 0.580±0.0090.580 ± 0.009 TabSyn 0.909±0.0010.909 ± 0.001 0.763±0.0050.763 ± 0.005 0.914±0.0040.914 ± 0.004 0.937±0.0020.937 ± 0.002 0.580±0.0090.580 ± 0.009 TabDiff 0.912±0.0020.912 ± 0.002 0.763±0.0050.763 ± 0.005 0.921±0.0040.921 ± 0.004 0.936±0.0030.936 ± 0.003 0.555±0.0130.555 ± 0.013 LLM-based model GReaT 0.913±0.0030.913 ± 0.003 0.755±0.0060.755 ± 0.006 0.902±0.0050.902 ± 0.005 0.888±0.0080.888 ± 0.008 0.653±0.0130.653 ± 0.013 TabGRAA 0.921±0.0030.921 ± 0.003 0.784±0.0050.784 ± 0.005 0.911±0.0070.911 ± 0.007 0.903±0.0010.903 ± 0.001 0.574±0.0030.574 ± 0.003 Table 21: Performance comparison on DA(AUC) (↓ ) Method Adult Default Shoppers Magic Beijing GAN-based models CTGAN 1.000±0.0001.000 ± 0.000 0.999±0.0000.999 ± 0.000 1.000±0.0001.000 ± 0.000 1.000±0.0001.000 ± 0.000 1.000±0.0001.000 ± 0.000 TVAE 0.998±0.0000.998 ± 0.000 1.000±0.0001.000 ± 0.000 1.000±0.0001.000 ± 0.000 0.998±0.0000.998 ± 0.000 0.999±0.0000.999 ± 0.000 Diffusion-based models TabDDPM 0.428±0.0040.428 ± 0.004 0.696±0.0030.696 ± 0.003 0.684±0.4830.684 ± 0.483 0.412±0.090.412 ± 0.09 0.466±0.0060.466 ± 0.006 TabSyn 0.543±0.0050.543 ± 0.005 0.736±0.0080.736 ± 0.008 0.583±0.0040.583 ± 0.004 0.562±0.0060.562 ± 0.006 0.715±0.0050.715 ± 0.005 TabDiff 0.481±0.0030.481 ± 0.003 0.644±0.0060.644 ± 0.006 0.545±0.0050.545 ± 0.005 0.512±0.0010.512 ± 0.001 0.658±0.0030.658 ± 0.003 LLM-based model GReaT 0.720±0.0010.720 ± 0.001 0.863±0.0040.863 ± 0.004 0.832±0.0030.832 ± 0.003 0.859±0.0050.859 ± 0.005 0.748±0.0020.748 ± 0.002 TabGRAA 0.499±0.0030.499 ± 0.003 0.760±0.0040.760 ± 0.004 0.727±0.0060.727 ± 0.006 0.7034±0.0080.7034 ± 0.008 0.6942±0.030.6942 ± 0.03 This appendix provides a comprehensive comparison between TabGRAA and state-of-the-art tabular generation methods across seven evaluation metrics. Tables 15–21 present results for Shape error, Trend error, α-Precision, β-Recall, C2ST, MLE, and DA metrics across five datasets. Overall, TabGRAA demonstrates substantial improvements over the original GReaT baseline across all metrics and datasets, particularly excelling in α-Precision where it achieves state-of-the-art performance on three of five datasets. While diffusion-based methods maintain advantages in some trend and diversity metrics, TabGRAA achieves competitive or superior performance in fidelity (α-Precision, C2ST) and privacy (DA) metrics. Notably, TabGRAA transforms GReaT from a lagging approach into a competitive alternative that preserves the flexible conditioning capabilities of LLM-based generation while approaching diffusion method performance on key tabular data quality measures. E.4 TabGRAA: Top-K Retention Rate Trajectory Analysis In this appendix, we provide detailed analysis of TabGRAA’s iterative optimization trajectories when varying the Top-K retention rate during feature selection. We compare two configurations: 50% Top-K (where only the top 50% most important features are retained in each iteration) and 100% Top-K (where all features are retained). For each configuration, we track the following metrics across 10 optimization rounds. Results for individual datasets (Adult, Beijing, Default, Shoppers, and Magic) are shown in Figure 12 through Figure 16. We observe that the 100% Top-K configuration accelerates early-stage improvements on utility metrics (CDE, C2ST) but shows increased privacy risk (DA) in later rounds, while the 50% Top-K configuration provides more stable and consistent gains across all metrics. This trade-off highlights the importance of data selection strategy in iterative tabular data refinement. Figure 12: TabGRAA optimization trajectories under different Top-K retention rates: 50% vs. 100% on Adult dataset. Performance metrics tracked across 10 rounds with 95% CI. Figure 13: TabGRAA optimization trajectories under different Top-K retention rates: 50% vs. 100% on Beijing dataset. Performance metrics tracked across 10 rounds with 95% CI. Figure 14: TabGRAA optimization trajectories under different Top-K retention rates: 50% vs. 100% on Default dataset. Performance metrics tracked across 10 rounds with 95% CI. Figure 15: TabGRAA optimization trajectories under different Top-K retention rates: 50% vs. 100% on Magic dataset. Performance metrics tracked across 10 rounds with 95% CI. Figure 16: TabGRAA optimization trajectories under different Top-K retention rates: 50% vs. 100% on Shoppers dataset. Performance metrics tracked across 10 rounds with 95% CI. E.5 Classifier Variants Performance Analysis We provide a comprehensive comparison of two classifier variants across five datasets to evaluate their robustness and performance characteristics. Figure 17 shows that different classifier models exhibit varying performance across datasets, with each demonstrating distinct advantages depending on data characteristics. (a) Adult (b) Default (c) Shoppers (d) Magic (e) Beijing Figure 17: Performance comparison of two classifiers across five dataset. The values are scaled to show the difference apparently E.6 Impact of β Parameter The β parameter controls the fidelity-utility trade-off across methods. Figures 18–21 show consistent trends across four datasets: TabNPO and TabKTO exhibit high β-sensitivity, performing poorly with small β values and showing instability across the parameter range. TabDPO maintains reasonable performance across multiple β values but requires careful tuning to achieve optimal results. In contrast, TabGRAA demonstrates robust performance with β=1β=1 across all evaluation metrics and datasets, achieving the best overall balance without requiring extensive hyperparameter search. This characteristic of TabGRAA at β=1β=1 simplifies deployment while maintaining state-of-the-art performance compared to other methods that require dataset-specific β fine-tuning. Figure 18: Radar plot comparison of four tabular alignment methods across seven metrics with β0.1,1,10,100 on Beijing dataset. Filled areas show performance regions for each β (colored by β); markers distinguish methods. Arrows indicate optimization direction (↑: maximize, ↓: minimize). Figure 19: Radar plot comparison of four tabular alignment methods across seven metrics with β0.1,1,10,100 on Default dataset. Filled areas show performance regions for each β (colored by β); markers distinguish methods. Arrows indicate optimization direction (↑: maximize, ↓: minimize). Figure 20: Radar plot comparison of four tabular alignment methods across seven metrics with β0.1,1,10,100 on Magic dataset. Filled areas show performance regions for each β (colored by β); markers distinguish methods. Arrows indicate optimization direction (↑: maximize, ↓: minimize). Figure 21: Radar plot comparison of four tabular alignment methods across seven metrics with β0.1,1,10,100 on Shoppers dataset. Filled areas show performance regions for each β (colored by β); markers distinguish methods. Arrows indicate optimization direction (↑: maximize, ↓: minimize). Appendix F Additional Ablation Studies This appendix reports three additional ablation experiments that complement the main results: (D.1) the effect of the reward signal choice on multiple quality dimensions, (D.2) random within-half group selection vs. explicit top-vs-bottom matching, and (D.3) lightweight adaptation under three controlled distribution shifts on Adult. F.1 Reward Signal Choice We hold the GRAA pipeline fixed and vary only the per-sample quality signal used to stratify synthetic samples. Three reward variants are compared against the GReaT baseline: the distinguishability classifier ρcls _cls used in the main paper, a held-out-split variant of the classifier reward ρholdout _holdout (the classifier is trained on a disjoint half of the synthetic pool and applied to the other half), and Distance to Closest Record ρdcr _dcr (a pointwise distance-to-nearest-real-record reward). The full comparison on five datasets is reported in main-body Table 7. All three rewards improve statistical fidelity over the GReaT baseline and maintain privacy (MIA AUC close to 0.50.5); their effect on structural fidelity, evaluated via the train-on-synthetic, test-on-real protocol of (Jiang and others, 2025), varies by reward type. The near-equivalence of ρcls _cls and ρholdout _holdout is the empirical evidence against classifier–synthetic-sample leakage discussed in Section 3.2. F.2 Group Membership: Random vs. Top-vs-Bottom A natural concern is whether GRAA’s improvements stem from the explicit top-vs-bottom matching of high- and low-quality samples (as in DPO/NPO), or only from the underlying group-level contrast. We test this by replacing the matching (x~ihigh,x~N−i+1low)\( x_i^high, x_N-i+1^low)\ with uniform random sampling within the high-half and low-half (same batch size, 5 iterations, identical hyperparameters). The full comparison is reported in the main-body Table 6: the two strategies are statistically indistinguishable across all five datasets and all three distributional metrics, confirming that GRAA operates as a genuine group-level method—contrasting two populations rather than a ranked assignment between them. F.3 Necessity of the Quality Signal: Random Scoring and Random Pairing To isolate whether TabGRAA’s improvements come from having a meaningful quality signal or simply from having any stratified groups at all, we run two degenerate variants on Adult, keeping all other hyperparameters fixed: (i) Random scoring—assign uniform random scores s(x~)∼[0,1]s( x) [0,1] before stratification, so that the high/low groups carry no information; and (i) Random pairing—keep valid classifier scores but pair samples at random (no top-vs-bottom structure). The full comparison, including MIA AUC, is reported in main-body Table 5: both degenerate variants perform at or near the baseline across all four metrics, whereas full TabGRAA substantially improves Wasserstein, MMD, and JSD. This confirms that (a) a valid real-data-dependent quality signal is necessary—random signals cannot substitute for it—and (b) the quality-stratified group construction (either top-vs-bottom or random-within-halves, cf. Appendix F.2) is the mechanism through which the signal produces gains. F.4 Long-Horizon Iterative Improvement To probe whether the self-improving loop exhibits sustained improvement over many rounds rather than saturating after a few iterations, we extended TabGRAA on Adult to 20 rounds (batch size 4, classifier reward, otherwise identical setup). The Wasserstein distance to the real distribution decreases monotonically from 0.04980.0498 at round 1 to 0.00990.0099 at round 20—an 80.1%80.1\% reduction—with a Spearman rank correlation between iteration index and Wasserstein of ρ=−0.917ρ=-0.917 (p<0.001p<0.001), and a two-sided Welch’s t-test comparing rounds 1–5 vs. rounds 16–20 at p<0.001p<0.001. This provides empirical evidence of convergent improvement well beyond the 5 rounds reported in the main body; a formal monotonic-improvement theorem remains open (the landscape is non-stationary because the policy, classifier, and group assignments all update each round), which we discuss as a limitation. F.5 Lightweight Adaptation under Distribution Shift We further evaluate TabGRAA in a non-stationary setting on Adult: starting from a generator trained on a pre-shift slice of the data, we measure how cheaply alignment iterations can adapt the generator to a shifted real distribution. Three scenarios are considered: (i) mild covariate shift (age range [20,40]→[30,50][20,40]→[30,50]), (i) strong covariate shift (age [20,40]→[40,60][20,40]→[40,60]), and (i) concept shift via the income-rule change. For each scenario we compare the static pre-shift generator (no adaptation), one epoch of supervised fine-tuning on the shifted data without alignment, and 3 iterations of TabGRAA alignment with the classifier reward. As shown in Table 22, TabGRAA improves over both baselines across all three shift types on both Wasserstein and JSD. The complete training-loss trajectories and per-iteration sample sizes are stored in the experiment artifacts (experiments/drift_*/). Table 22: Dynamic adaptation under three shift types on Adult. Static: use the pre-shift generator without adaptation. Fine-tune: one epoch of supervised fine-tuning on the shifted data, without alignment. TabGRAA: self-improving alignment with classifier reward ρcls _cls, evaluated per iteration. GRAA improves consistently over both the static baseline and one-epoch fine-tuning across covariate and concept shifts. Lower is better for both metrics. Covariate (mild): age [20,40]→[30,50][20,40]\!→\![30,50] Covariate (strong): age [20,40]→[40,60][20,40]\!→\![40,60] Concept: income rule shift Strategy W↓ JSD↓ W↓ JSD↓ W↓ JSD↓ Static (no adaptation) 0.06520.0652 0.04420.0442 0.12000.1200 0.06330.0633 0.02100.0210 0.01280.0128 Fine-tune (1 epoch) 0.06310.0631 0.03950.0395 0.11530.1153 0.05930.0593 0.01870.0187 0.00780.0078 TabGRAA (ρcls _cls, iter 1) 0.05990.0599 0.03950.0395 0.11730.1173 0.05690.0569 0.01940.0194 0.00850.0085 TabGRAA (ρcls _cls, iter 2) 0.05960.0596 0.03810.0381 0.11270.1127 0.05770.0577 0.01740.0174 0.00750.0075 TabGRAA (ρcls _cls, iter 3) 0.05840.0584 0.03740.0374 0.11090.1109 0.05480.0548 0.01720.0172 0.00810.0081