MALLM-GAN: Multi-Agent Large Language Model as Generative Adversarial Network for Synthesizing Tabular Data

We sincerely thank Reviewer hkAL for reviewing our paper and recognizing the novelty of our proposed method. Below, we address the two concerns you raised:

• Human effort for initial prompt. We respectfully disagree with the reviewer in that the proposed model requires substantial effort (e.g., empirical knowledge) for initialization. Our model requires three inputs: 1) brief one-sentence data description, 2) variable name, and 3) initial causal structure (Eq (1)). Specifically, the causal structure is automatically initialized using a Bayesian Network algorithm, and other contextual information is automatically extracted from table column headings and cells. The only component requiring manual input is a brief one-sentence data description, which provides background context for the dataset. We don't see the one-sentence data description (which serves as a seed input for LLM to grow) as a substantial effort compared to the typical data-driven approach.

• Same LLM Thank you for raising this concern. As noted in Lines 296–297,

"We used HIPPA-compliant Azure OpenAI GPT-3.5(7) as our generator and GPT-4 (25)(gpt-4-32k-0613) as our optimizer,"

we used GPT-3.5 as the data generator for our experiments, as the reviewer suggested. If the reviewer actually intended to suggest GPT-4 for the data generator, we cannot use GPT-4 for the data generator due to ethical concerns. We use privacy-sensitive patient data to avoid data leakage in evaluation. Only Azure OpenAI GPT-3.5 was a HIPAA-compliant LLM. It is our expectation that if we use GPT-4 for the data generator not GPT-3.5, our model's performance will only increase.

For the question:

This is a valid point, and the ablated comparison results that the reviewer suggested are already in Table 3. Let us clarify.

• First column (Few-shot): the results with human-written instruction and manually selected few-shot examples (Line 398)
• Second column (Few-shot+Causal): the results with the naive, heuristic causal structure without discriminator and optimizer.
• Third column (Few-shot+Causal+Opt): Full results

The results demonstrate that when using GPT-3.5 solely as the generator, the quality of the synthetic data, as evaluated through downstream task performance, is notably poorer than the data generated with causal structure guidance and optimization in our model. These findings highlight the added value of our proposed method in enhancing data quality.

We appreciate the reviewer for highlighting this point and welcome any further questions or suggestions for clarification.

We sincerely thank Reviewer hkAL for their thoughtful feedback and for recognizing the contributions and novelty of our study. Below, we address your concerns in detail:

• Models with longer context windows: We appreciate the reviewer’s suggestion to explore models with longer context windows that can process all data at once. However, due to data privacy concerns and the risk of data leakage, we cannot benchmark closed-source models like Gemini on our private dataset. Additionally, as demonstrated in our ablation study (Supplementary Figure 5 and Table 7, Lines 391–395),

Number n of example in in-context few shot learning. Due to the LLM’s limited context length, we implemented a“batches in a batch” method to leverage all training data within these constraints (Section 3.2.1). We varied the number n of examples and found $n = 1$ to be optimal, achieving high DCR without compromising MLE (Supplement Section 2.5).

simply increasing the number of in-context samples does not necessarily improve the quality of the generated synthetic data. These findings highlight the nuanced limitations of relying solely on longer context windows for quality enhancement.

• Convergence. Thank you for your careful review and for acknowledging our discussion of convergence in the manuscript. We acknowledge that a theoretical convergence guarantee is difficult to obtain as no numerical gradient is available. Instead, we have shown empirical convergence using the optimized parameters such as task instruction (Table 4, Table 10), change of causal structure (Figure 3, Figure 6), and discriminator's accuracy decrease (Table 4, Table 10). In all, we were able to see that the learning process has actually converged at the prompt level (Figure 3, Figure 6, Table 4, Table 10).

• Ability to deal with high dimensional data.: We agree with the reviewer that the proposed in-context learning method is constrained by the context length of LLM, limiting its applicability to high-dimensional datasets (e.g., datasets with 100+ columns). However, we believe this limitation can be addressed by switching to LLM with a longer context length, which we can do without substantial technical challenges to cope with. Nevertheless, we agree this is an exciting direction for future investigation and appreciate the reviewer’s perspective.

• Contribution: We appreciate the reviewer’s efforts in exploring related studies. While prompt optimization is not a novel concept and has been applied across various fields, as noted in our manuscript, our contribution is not from just simply utilizing existing prompt optimization. Rather, our contribution is making synthetic data generative models with very low data size. Our novelty is from optimizing causal structure via LLMs and seamlessly linking it to tabular data generative model.

• Other language models: We agree that evaluating the generalizability of the framework across different language models would be of great interest. We will enhance our experiments by including other local LLMs or HIPAA-compliant LLM.

Thank you for your detailed feedback. I would like to address some of your concerns as list below:

• Optimizing DAG: You are absolutely correct that the core of the proposed model is based on the assumption that by introducing "correct" causal relationships into the prompt can improve the generated data quality. You pointed out that line 398-400 is contradictory. Let us clarify the misunderstanding. In lines 398-400, we claimed that incorporating DAG initialized with a traditional approach (e.g., Hill Climbing heuristic) does not improve the MLE a lot because the data size is too small to learn correct causal relationships. However, in our proposed method, we learned DAG by prior knowledge in LLM, which does improve the MLE. In other words, having incorrect DAG was not helpful, but having correct DAG was helpful.

• Prompt optimization: The concept of transforming a parameter optimization problem into a prompt optimization problem originates from the ICLR 2023 paper [1], “Large Language Models as Optimizers,” as cited in our manuscript (Lines 140–141). We adopted the prompt optimization structure outlined in that paper, which has been demonstrated to be effective across various tasks where an LLM serves as an optimizer given a target score. The focus of our approach is not merely to optimize a score function but to leverage the pre-trained knowledge of the LLM to enrich the context and effectively guide the data generation process.

• Convergence: The training trajectory is a well-known challenge in the GAN field. During training, we observed that the discriminator’s accuracy score initially decreased over the first few updates and then stabilized, fluctuating around 0.5. However, simply monitoring the discriminator’s accuracy is insufficient to confirm convergence, as the model may still suffer from issues like mode collapse. In the original submission, we addressed this by including additional training trajectory details in Supplementary Table 4 and Table 10, which provide insights into the training progress from both a scoring and prompt perspective. Additionally, we acknowledged in the limitations section that the proposed method incurs high computational costs due to iterating over the entire dataset. To mitigate these challenges, we implemented several strategies. These include using smaller batches during “gradient” descent to allow for more frequent updates, thereby improving convergence speed compared to processing the entire dataset at once. Furthermore, we employed a simpler model with incremental updates, which helps stabilize the discriminator during training. These measures collectively enhance the robustness and practicality of our method.

• Lack of important baseline: We agree with the reviewer that CLLM is an important baseline to consider, as it also utilizes the in-context learning method to address low-data regimes. In fact, we have already included results of CLLM in the original submission. The prompt style we used is similar to that of CLLM, and we did not perform any additional data curation for the downstream task, as suggested.

Lines 398–399: We compared the full model, which includes both components, to a version without them, similar to CLLM (31) without post-processing data selection (Table 3).

• Missing evaluation metric We sincerely thank the reviewer for their thoughtful suggestions regarding evaluation metrics. We fully acknowledge the importance of robust metrics in assessing the quality of synthetic data. The discriminator's accuracy you mentioned is in Table 6 due to limited space. We followed the evaluation framework in [6]. We will include all those important metrics in the revised version. We appreciate your suggestions.

[6] "Language models are realistic tabular data generators. In The Eleventh International Conference on Learning Representations 2023."

Sorry for my late response. I appreciate the authors' effort in addressing my concerns. While some of my initial questions have been clarified, some issues remain:

1. I still found the effect of incorporating DAG into the prompt unclear, and I still doubt whether LLM can find the correct DAG.

In lines 398-400, we claimed that incorporating DAG initialized with a traditional approach (e.g., Hill Climbing heuristic) does not improve the MLE a lot because the data size is too small to learn correct causal relationships.

I acknowledge that this paper studies the low data resource setting. However, I believe it is necessary to examine if the LLM prompt optimization procedure can actually find the correct DAG. To do this, we can use the full training set and apply traditional methods [1] to estimate the DAG from data. Then we can compare the DAG produced by traditional methods and the one optimized by the LLM. Does the LLM optimize the DAG to converge to the correct one?

2. About convergence.

However, simply monitoring the discriminator’s accuracy is insufficient to confirm convergence, as the model may still suffer from issues like mode collapse.

The rebuttal acknowledges that discriminator accuracy alone is insufficient for confirming convergence due to potential issues like mode collapse. However, this raises a critical question: what are the specific criteria used to determine when training should stop? This needs to be clearly defined and justified.

3. About evaluation metrics.

The discriminator's accuracy you mentioned is in Table 6 due to limited space.

Table 6 only contains results for one dataset, and it lacks comparison with other deep generative model baselines. Also, this table is not referred to in the main context, and I cannot find any text describing the details of it.

In summary, I think this paper needs significant revision to improve its clarity, motivation, and convinceness, thus I will keep my score.

Reference: [1] Ankan, Ankur, Abinash, Panda. "pgmpy: Probabilistic Graphical Models using Python." Proceedings of the Python in Science Conference. SciPy, 2015.

We sincerely thank Reviewer iZoG for thoroughly reading our paper and providing thoughtful feedback. Below, we address your three key concerns:

• Performance concern. We appreciate the reviewer’s careful examination of our results. While we agree that our proposed model does not consistently achieve state-of-the-art (SOTA) performance across all scenarios, the primary goal of our work is to address data scarcity in low-data regimes (e.g., N=100, 200). Our intention is not to claim that our model outperforms all other data-driven methods in general settings. The results for moderate (N=400) and larger datasets (N=800) are included to demonstrate that our model remains competitive, achieving 1st or 2nd place across all datasets, as shown in Table 2. This indicates that our method performs robustly even when sufficient training data is available.

• Highlight of contribution. We thank the reviewer for acknowledging the technical contribution of our proposed method. Actually, the technical challenge we addressed in our work was generating synthetic data when the data size was very small. Integrating ICL-LLM and GAN was our solution. We do believe that lines 084-087 have highlighted the novelty of our proposed solution. Regarding technical challenges when integrating LLM and GAN, we encountered and addressed several technical challenges, such as limited context length (lines 193-197), intractability of discriminator over iterations (lines 302-305), and degrading discriminator's performance for convergence (line 245-249).

• Standard benchmark. We appreciate the suggestion to incorporate standard benchmarks. To the best of our knowledge, this is the first paper to benchmark synthetic data generation across datasets of varying sizes. While incorporating standard benchmarks could make this paper more solid, it also introduces potential biases, such as data leakage from LLM training data. To address this, we included evaluations on two private datasets, Lines 306–310:

"Data. Our benchmarks include several datasets from various domains: three public datasets (Adult(4), Medical Insurance(1), Asia(30)), and two private medical datasets (ATACH2, ERICH) (22). To ensure fair comparison without memorization concerns of LLM (e.g., public datasets are in the training corpus of LLM), private datasets were included. Details are in Supplement Table 5."

To alleviate concerns, we will make all subsampled public datasets available for future benchmarking, ensuring transparency and reproducibility.