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arxiv: 2503.02161 · v3 · pith:K3SVAHKYnew · submitted 2025-03-04 · 💻 cs.LG

LLM-TabLogic: Preserving Inter-Column Logical Relationships in Synthetic Tabular Data via Prompt-Guided Latent Diffusion

Yunbo Long , Liming Xu , Alexandra Brintrup This is my paper

Pith reviewed 2026-05-23 01:01 UTC · model grok-4.3

classification 💻 cs.LG
keywords synthetic data generationtabular datalogical consistencylarge language modelsdiffusion modelsinter-column relationshipsprivacy
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The pith

LLM-TabLogic preserves inter-column logical relationships in synthetic tabular data by integrating LLM reasoning into latent diffusion.

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

The paper presents LLM-TabLogic to create synthetic tabular data that maintains logical consistency between columns, important for applications like supply chains where dates, locations, and categories must align. It employs large language models to identify and compress these relationships, then incorporates them as constraints in a score-based diffusion model running in latent space. This addresses gaps in prior generative methods that ignore inter-column logic, leading to unusable synthetic data. Tests on industrial datasets demonstrate over 90% accuracy on new tables and superior performance over baselines in balancing fidelity, utility, and privacy.

Core claim

LLM-TabLogic is the first method to preserve inter-column logical relationships in synthetic tabular data generation without domain knowledge. It leverages large language model reasoning to capture complex logical constraints among columns and passes these as conditional inputs to a score-based diffusion model for generation in latent space. Extensive experiments on real-world industrial datasets show it achieves over 90% accuracy on unseen tables while outperforming five baselines, including SMOTE and state-of-the-art generative models, in data generation quality.

What carries the argument

The integration of LLM-extracted conditional constraints on inter-column logical relationships into a score-based diffusion model operating in latent space.

If this is right

  • Synthetic tabular data retains domain-specific logical consistency for real-world use cases.
  • No domain knowledge is required to enforce inter-column relationships.
  • Outperforms baselines in fidelity, utility, and privacy metrics.
  • Generalizes with over 90% accuracy to unseen tables.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Could allow safer data sharing in industries with strict consistency requirements.
  • The technique might apply to other data types with cross-field dependencies.
  • It may lower the effort needed to validate synthetic data for logical errors.

Load-bearing premise

Large language models can reliably capture complex domain-specific logical relationships from tabular data or prompts without domain knowledge or additional training.

What would settle it

Testing on a dataset with logical rules not deducible from prompts or column names, checking if accuracy drops below 90% or if generated data violates rules more than baselines.

Figures

Figures reproduced from arXiv: 2503.02161 by Alexandra Brintrup, Liming Xu, Yunbo Long.

Figure 1
Figure 1. Figure 1: Overview of the workflow of the LLM-TabLogic approach. [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of compressed data generation via score-based diffusion in the latent space. [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Real-world synthetic tabular data evaluation framework. [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Performance comparison of GPT-4 and DeepSeek-Chat on tabular reasoning tasks. (a) shows F1 scores of [PITH_FULL_IMAGE:figures/full_fig_p021_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Radar Charts illustrating the performance of all methods on the two datasets across the six dimensions: [PITH_FULL_IMAGE:figures/full_fig_p022_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Density plots for the three continuous columns (item profit ratio, product price, and latitude), comparing the distribution of real data and their synthetic counterparts generated by different methods. Curves that more closely align with the real data indicate better performance. Both LLM-TabLogic and TabSyn exhibit distributions that closely match the real data, outperforming other methods. accurate when … view at source ↗
Figure 7
Figure 7. Figure 7: Distribution plots for the three categorical columns (shipping mode, payment type, and order status), comparing synthetic data to real data. Distributions that closely match the real data indicate superior performance. Both LLM-TabLogic and TabSyn exhibit distributions that are significantly closer to the real data compared to other methods. (a) SMOTE (b) CTGAN (c) TabDDPM (d) GReaT (e) TabSyn (f) Ours (LL… view at source ↗
Figure 8
Figure 8. Figure 8: Heatmap illustrating the absolute divergence in pairwise column correlations between the synthetic and [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Visualization of the coverage score for both categorical and numerical columns using Radar charts. Labels [PITH_FULL_IMAGE:figures/full_fig_p026_9.png] view at source ↗
read the original abstract

Synthetic tabular data are increasingly being used to replace real data, serving as an effective solution that simultaneously protects privacy and addresses data scarcity. However, in addition to preserving global statistical properties, synthetic datasets must also maintain domain-specific logical consistency**-**especially in complex systems like supply chains, where fields such as shipment dates, locations, and product categories must remain logically consistent for real-world usability. Existing generative models often overlook these inter-column relationships, leading to unreliable synthetic tabular data in real-world applications. To address these challenges, we propose LLM-TabLogic, a novel approach that leverages Large Language Model reasoning to capture and compress the complex logical relationships among tabular columns, while these conditional constraints are passed into a Score-based Diffusion model for data generation in latent space. Through extensive experiments on real-world industrial datasets, we evaluate LLM-TabLogic for column reasoning and data generation, comparing it with five baselines including SMOTE and state-of-the-art generative models. Our results show that LLM-TabLogic demonstrates strong generalization in logical inference, achieving over 90% accuracy on unseen tables. Furthermore, our method outperforms all baselines in data generation by fully preserving inter-column relationships while maintaining the best balance between data fidelity, utility, and privacy. This study presents the first method to effectively preserve inter-column relationships in synthetic tabular data generation without requiring domain knowledge, offering new insights for creating logically consistent real-world tabular data. The code is available at https://github.com/Yunbo-max/TabKG.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes LLM-TabLogic, which uses an LLM to infer and compress inter-column logical relationships from tabular data via prompts, then injects these constraints into a score-based latent diffusion model to generate synthetic tabular data. It reports >90% accuracy on logical inference for unseen tables and claims to outperform five baselines (including SMOTE and SOTA generative models) on industrial datasets by fully preserving relationships while balancing fidelity, utility, and privacy, all without domain knowledge. Code is released at the provided GitHub link.

Significance. If the central claims are substantiated, the approach would offer a practical advance for synthetic data in domains like supply chains where logical consistency (e.g., date and category constraints) is required for usability. The combination of LLM reasoning with diffusion, if shown to reliably enforce constraints, could lower the barrier compared to methods needing explicit domain rules. Open code aids reproducibility.

major comments (2)
  1. [Abstract] Abstract: The claim of 'fully preserving inter-column relationships' and achieving '>90% accuracy on unseen tables' is load-bearing for the contribution, yet the abstract provides no mechanism for how LLM outputs are injected into the diffusion process (classifier-free guidance, latent conditioning, or post-hoc filtering). This leaves the enforcement step unexamined and prevents assessment of whether the three required steps (inference, compression, and constraint) hold for relations outside the LLM pre-training corpus.
  2. [Methods] Methods (inferred from abstract description): The premise that an off-the-shelf LLM can reliably extract complex domain-specific constraints (e.g., shipment-date > order-date) directly from generic prompts or examples without training or domain knowledge is central but unsupported by any reported validation of the LLM step alone; if this fails, the reported outperformance over SMOTE and other baselines would not follow.
minor comments (2)
  1. [Abstract] Abstract: Formatting artifact '**-**' appears in the sentence on logical consistency; this should be cleaned for readability.
  2. [Abstract] Abstract: The five baselines are mentioned but not named; listing them explicitly would improve clarity on the comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below with clarifications from the full manuscript and indicate where revisions will be made.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim of 'fully preserving inter-column relationships' and achieving '>90% accuracy on unseen tables' is load-bearing for the contribution, yet the abstract provides no mechanism for how LLM outputs are injected into the diffusion process (classifier-free guidance, latent conditioning, or post-hoc filtering). This leaves the enforcement step unexamined and prevents assessment of whether the three required steps (inference, compression, and constraint) hold for relations outside the LLM pre-training corpus.

    Authors: We agree the abstract is high-level. The full manuscript (Section 3) specifies that LLM-derived constraints are compressed into embeddings and injected via latent conditioning into the score-based diffusion model, using classifier-free guidance for enforcement during sampling. We will revise the abstract to briefly state this mechanism. revision: yes

  2. Referee: [Methods] Methods (inferred from abstract description): The premise that an off-the-shelf LLM can reliably extract complex domain-specific constraints (e.g., shipment-date > order-date) directly from generic prompts or examples without training or domain knowledge is central but unsupported by any reported validation of the LLM step alone; if this fails, the reported outperformance over SMOTE and other baselines would not follow.

    Authors: The reported >90% accuracy on logical inference for unseen tables (detailed in the experiments) directly validates the LLM extraction step on held-out data without domain knowledge or fine-tuning. This accuracy metric isolates the inference performance. We will add a dedicated paragraph in the methods/experiments to explicitly separate and highlight this LLM validation from the downstream generation results. revision: partial

Circularity Check

0 steps flagged

No circularity; method composes external LLM and diffusion components

full rationale

The paper describes a pipeline that invokes an off-the-shelf LLM to extract logical constraints from tabular examples or prompts and then conditions a separate score-based diffusion model on those constraints. No equations, fitted parameters, or uniqueness theorems are presented that reduce to the paper's own outputs by construction. No self-citations are invoked as load-bearing premises. The reported >90% accuracy and outperformance are empirical claims evaluated against external baselines (SMOTE, etc.), not internal redefinitions. This is a standard engineering composition of pre-existing models and therefore receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The paper introduces a hybrid architecture but relies on standard assumptions about LLM capabilities and diffusion model conditioning; no new entities postulated. Details on specific free parameters are absent from the abstract.

free parameters (2)
  • Diffusion model hyperparameters
    Parameters such as number of diffusion steps, noise schedules, and latent space dimensions are typically fitted or chosen to optimize generation quality.
  • LLM prompt templates
    The design of prompts to extract logical relationships is a key tunable element that affects the captured constraints.
axioms (2)
  • domain assumption Large language models possess sufficient reasoning capability to identify inter-column logical relationships in tabular data without domain expertise
    This underpins the claim of operating without domain knowledge.
  • domain assumption The logical constraints can be effectively encoded and enforced via conditioning in the latent diffusion model
    Central to the generation process described.

pith-pipeline@v0.9.0 · 5809 in / 1436 out tokens · 71496 ms · 2026-05-23T01:01:54.483373+00:00 · methodology

discussion (0)

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