Multi-Agent Causal Discovery Using Large Language Models

## Abstract

Abstract Large Language Models (LLMs) have demonstrated significant potential in causal discovery tasks by utilizing their vast expert knowledge from extensive text corpora. However, the multi-agent capabilities of LLMs in causal discovery remain underexplored. This paper introduces a general framework to investigate this potential. The first is the Meta Agents Model, which relies exclusively on reasoning and discussions among LLM agents to conduct causal discovery. The second is the Coding Agents Model, which leverages the agents’ ability to plan, write, and execute code, utilizing advanced statistical libraries for causal discovery. The third is the Hybrid Model, which integrates both the Meta Agents Model and Coding Agents Model approaches, combining the statistical analysis and reasoning skills of multiple agents. Our proposed framework shows promising results by effectively utilizing LLMs’ expert knowledge, reasoning capabilities, multi-agent cooperation, and statistical causal methods. By exploring the multi-agent potential of LLMs, we aim to establish a foundation for further research in utilizing LLMs multi-agent for solving causal-related problems.

## 1 Introduction

Understanding causal relationships is crucial across scientific fields. While statistical causal inference is widely used, it heavily relies on assumed causal graphs. To address this limitation, data-driven methods have evolved, leading to statistical causal discovery (SCD) approaches and the creation of datasets for evaluation. Despite advancements in SCD algorithms, data-driven causal graphs without domain knowledge can be inaccurate. This inaccuracy is often due to a mismatch between SCD algorithm assumptions and real-world phenomena (Reisach et al. ()). Incorporating expert knowledge can mitigate this issue, but it is costly.

The advent of Large Language Models (LLMs), trained on vast amounts of data, has enabled them to acquire extensive knowledge, from common sense to specific domains such as math and science. Recent studies suggest that complex behaviors, such as writing code, generating long stories, and even reasoning capabilities, can emerge from large-scale training (Wei et al. (); Rozière et al. (); Zhao et al. (); Yao et al. ()). LLMs present a promising alternative for obtaining expert knowledge more accessible and affordable. Recent research (Kıcıman et al. ();Choi et al. (); Long et al. (); Chen et al. ()) has attempted to leverage these capabilities for causal discovery based on metadata and knowledge-based reasoning, akin to human domain experts.

However, most methods have not yet fully utilized the full capacity of LLMs, i.e., LLMs’ multi-agent approaches. An LLM agent can be seen as an entity with memory, reasoning, and the ability to access external tools or APIs such as a calculator, web search, and code compiler. Agent-based systems have demonstrated significant problem-solving abilities. However, a single-agent-based system sometimes still suffers from hallucinations despite having self-reflection capabilities (Li et al. (); Shinn et al. (), Madaan et al. ()). Inspired by the Society of Mind concept (Minsky ()), LLM multi-agent system discussion frameworks like MAD Liang et al. (), ReConcile (Chen et al. (), and CMD Wang et al. () have been proposed to address these issues. These LLM multi-agent systems not only achieve impressive results but also enable less capable models to perform on par with superior ones.

Despite the potential benefits, few studies have explored leveraging LLM multi-agent system capabilities in causal discovery. To address this gap, we propose a novel framework called Multi-Agent for Causality (MAC), which comprises three different models.

**Table 1: Comparison of Approaches for Using LLMs in Causal Discovery**
| Method / Approach | LLMs for metadata | Statistical Approach for structured data | Agentic Ability | Multi-Agent Workflow | Introduced By |
| --- | --- | --- | --- | --- | --- |
| Pairwise Causal Discovery | ✓ | × | × | × | Kıcıman et al. (); Zečević et al. () |
| Various of prompt-engineering strategies | ✓ | × | × | × | Chen et al. () |
| Efficiently asking question for Causal Graph Discovery Using LLMs | ✓ | ✓ | × | × | Jiralerspong et al. () |
| Combining LLMs with traditional causal methods. | ✓ | ✓ | × | × | Vashishtha et al. (); Takayama et al. () |
| Multi-Agent Causal Discover (MAC) | ✓ | ✓ | ✓ | ✓ | Our approach |

The first is called Meta Agents Model, which includes a *Meta-Debate Module* with two debater agents and one judge agent. These agents are designed for causal discovery problems and utilize the nature of debating to find causal relationships among variables through multiple rounds of discussion. The second is called Coding Agents Model, which includes a *Debate-Coding Module* with four agents operating in two phases. This group leverages both the debating abilities of the agents and statistical causal algorithms. The third one is Hybrid Model, which hybridizes the statistical causal discovery algorithms with the reasoning skills of multiple agents to construct the causal graph.

In this research, we experiment with various LLM models across small, medium, and large scales, paired with different MAC models. We conduct an in-depth analysis of performance for each MAC model and LLM, token consumption, and identify their usage patterns and limitations. Additionally, we propose alternative solutions to address the computational costs associated with LLMs.

Our proposed framework shows promising results by effectively utilizing LLMs’ expert knowledge, reasoning capabilities, multi-agent cooperation, and statistical causal methods. As far as we know, this paper is first work to explore LLMs’ multi-agent abilities in a causal context. We hope that our work will lay the foundation for further research in utilizing LLM multi-agent systems for solving causal-related problems.

## 2 Related Works

### 2.1 LLMs’ Agentic Workflow

A general LLM agent framework consists of core components: user request, agent/brain, planning, memory, and tools. The agent/brain acts as the main coordinator, activated by a prompt template. It can be profiled with specific details to define its role, using handcrafted, LLM-generated, or data-driven strategies. Planning employs techniques like Chain of Thought and Tree of Thoughts, and for complex tasks, feedback mechanisms like ReAct Yao et al. () and Reflexion Shinn et al. () refine plans based on past actions and observations. Memory stores the agent’s logs, with short-term memory for the current context and long-term memory for past behaviors. Hybrid memory combines both to enhance reasoning and experience accumulation. Tools enable interaction with external environments, such as APIs and code interpreters. Frameworks like MRKL Karpas et al. (), Toolformer Schick et al. (), Function Calling OpenAI (), and HuggingGPT Shen et al. () integrate tools to solve tasks effectively.

However, for more complex problems where a single LLM agent may struggle, LLM-MA (multi-agent) systems excel. Current LLM-MA systems primarily employ three communication paradigms: Cooperative, Competitive, and Debating. In the Cooperative paradigm, agents collaborate towards a shared goal, typically exchanging information to enhance a collective solution Qian et al. (); Chen et al. (). In the Competitive paradigm, agents work towards their own goals, which might conflict with those of other agents Zhao et al. (). The Debating paradigm involves agents engaging in argumentative interactions, where they present and defend their viewpoints or solutions while critiquing those of others. This approach is ideal for reaching a consensus or a more refined solution (Li et al. (); Liang et al. (); Xiong et al. ()). In this work, the debating paradigm will be implemented, as the nature of causal discovery problems requires diverse and potentially conflicting opinions to approach the truth.

### 2.2 Statistical and LLM-based Causal Methods

Traditional methods of statistical causal inference often depend heavily on assumed causal graphs to identify and measure causal impacts. To overcome this limitation, data-driven algorithmic approaches have been developed into statistical causal discovery (SCD) methods, encompassing both non-parametric (e.g., Spirtes et al. (); ;
; Yuan & Malone (); Huang et al. (); Xie et al. ()) and semi-parametric (e.g., Shimizu et al. (); Hoyer et al. (); Shimizu et al. ()) techniques. Many SCD algorithms can be systematically augmented with background knowledge and have accessible software packages. For example, the non-parametric and constraint-based Peter-Clerk (PC) algorithm (Spirtes et al. ()) in “causal-learn” integrates background knowledge of mandatory or forbidden directed edges. “Causal-learn” also includes the Exact Search algorithm (Shimizu et al. (); Yuan & Malone () ), a non-parametric and score-based SCD method that can incorporate background knowledge in the form of a super structure matrix of forbidden directed edges. Furthermore, the semi-parametric DirectLiNGAM (Shimizu et al. ()) algorithm can use prior knowledge of causal order (Inazumi et al. ()) in the “LiNGAM” project (Ikeuchi et al. ()).

In the context of knowledge-driven approaches using large language models (LLMs), applying LLMs for causal inference is relatively new. There have been a few significant efforts to use LLMs for causal inference among variables by merely prompting with the variable names, without going through the traditional SCD process with benchmark datasets (Kıcıman et al. (); Zečević et al. ()). Jiralerspong et al. () even uses a breadth-first search (BFS) approach which allows it to use only a linear number of queries to have a higher efficiency. Additionally, Chen et al. () proposes 9 prompting techniques comprise ICL, 0-shot CoT (e.g. ”let’s think step by step”), adversarial prompt, manual CoT, and explicit function (e.g using encouraging language in prompts). Moreover, the works of Ban et al. () and Vashishtha et al. () introduce interesting approach by integrate LLMs into traditional data-driven approaches. However, most of above-mentioned works have not investigate the LLM-agentic work-flows for causal graph discovery 1, which indeed requires heavy investigation on various models and graphs’ scales.

## 3 MAC: Multi-Agent Causality Framework

### 3.1 Multi-Agent Causality Modules

#### 3.1.1 Meta-Debate Module

Figure: Figure 1: Meta-Debate Module
Refer to caption: x1.png

The Meta-Debate Module is an advanced system comprising three intelligent agents: two causal debaters (an affirmative one and a negative one) and one causal judge. This structure emulates the dynamic and rigorous nature of human debate, specifically within the realm of causal discovery. The design of this debating module is meticulously crafted to ensure a thorough examination of critical elements in causal discovery, such as understanding the temporal order necessary to establish cause-and-effect relationships and identifying potential confounding variables that could distort perceived relationships between primary variables. Each side engages in active disagreement by presenting different opinions and viewpoints, fostering a comprehensive and robust debate. Additionally, each agent within Meta-Debate Module utilizes the ReAct prompting technique. This technique integrates the ability to dynamically formulate, modify, and refine action plans based on new information or insights gained during the debate. This integration allows the agents to engage in more sophisticated and adaptive reasoning processes, closely mimicking human-like debate and decision-making (Figure 2).

Figure: Figure 2: Prompting design of each agent in MAC, details in the Appendix A.3
Refer to caption: x2.png

The debating process begins with a meta-question. Initially, the causal affirmative side presents its answer along with the supporting rationale. Subsequently, the causal negative side offers diverse or conflicting perspectives by providing alternative viewpoints on the same question. The causal judge then evaluates the responses from both sides, determining either a winner or identifying the need for additional clarification. If further information is required, the causal judge poses specific follow-up questions, prompting the debaters to clarify and elaborate on their initial propositions. The causal judge reaches a final verdict once all relevant information has been thoroughly examined.

For meta-questions, questions might address aspects such as the appropriate algorithm for a particular problem, the causal relationship between two variables, or a step-by-step approach for solving a causal problem, as illustrated in Figure 1. The affirmative side initiates the debating process based on the constructed input. The final output is derived from the causal judge’s decision, reflecting a comprehensive evaluation of the arguments presented by both sides. This rigorous process ensures that the outcome is well-informed and considers multiple perspectives, thereby enhancing the robustness of causal discovery. A detailed visualization of this module can be found in Appendix A.2.1.

Figure: Figure 3: Debate-Coding Module
Refer to caption: x3.png

#### 3.1.2 Debate-Coding Module

The Debate-Coding Module leverages statistical algorithms to achieve precise causal discovery through a structured two-phase process. This group consists of four agents, divided into two phases: debating the algorithm and executing the algorithm.

In the initial phase, three agents engage in a debate format, similar to the workflow of Meta-Debate module at Section 3.1.1. However, the difference is that the affirmative and negative agent are pre-prompts the information with 3-5 statistical causal algorithms. Additionally, the meta-question posed to these agents is specifically curated to determine which algorithm should be used given the metadata, which includes the description and structure of the data. After the debate, the output is the most suitable algorithm for the particular dataset and question. Compared to the Meta-Debate Module, an additional step in this process is that the agent participating in the debate (whether affirmative or negative) will provide a step-by-step plan for implementing the selected algorithm.

In the second phase, the causal coding executor receives the plan from the previous phase along with the observational data. The causal coding executor is responsible for writing, executing, and debugging the code. It pre-prompts the functions and provides parameters within a specific Python library(^1^11More functions can be found at [https://causal-learn.readthedocs.io/en/latest/index.html](https://causal-learn.readthedocs.io/en/latest/index.html)) based on the algorithm selected by the debaters in the initial stage. This pre-prompting is crucial because LLMs can call functions from their training dataset, which may be outdated or incorrect, leading to errors and excessive debugging (details of prompting design can be found in the Appendix A.3). After executing the code, the causal coding executor outputs a matrix representation of the causal graph. A detailed visualization of this module can be found in the Appendix A.2.2.

### 3.2 Implementations of MAC

In this section, we will elaborate on the detailed implementation of the three models regarding their input and basic workflow.

#### 3.2.1 Meta Agents Model

Figure: Algorithm 1 Algorithm for Meta Agents Model

The algorithm for the Meta Agents Model aims to identify direct causal relationships between variables in a dataset. It starts with the input data $X=[x_{1},...,x_{n}]$. The output of the algorithm is a graph $\mathcal{G}$, with its edges $G_{ij}$, where $i$ and $j$ are indices in the set of variables $n$

The algorithm proceeds by iterating through each variable $i$ from 1 to the number of variables in $X$. For each $i$, it checks all $j$ values less than $i$ (i.e., $j$ ranges from 1 to $i-1$). It queries the Meta-Debate Module to check if there is a direct causal relationship from $X[i]$ to $X[j]$ and stores the result in $G_{ij}$. Then, it checks all $j$ values greater than $i$ (i.e., $j$ ranges from $i+1$ to the number of labels in $X$). Those queries are meta-questions that use the Meta-Debate Module function to check if there is a direct causal relationship from $X[i]$ to $X[j]$ and store the result in $G_{ij}$. The algorithm concludes by returning the constructed graph $G_{ij}$. A detail of the function Meta-Debate Module has been described in section 3.1.1

#### 3.2.2 Coding Agents Model

Figure: Algorithm 2 Algorithm for Coding Agents Model

The inputs to the algorithm are a meta-question $Q_{X}$ and observational data $O_{X}$, and the output is the construction of a causal graph $G_{ij}$. The algorithm for the Coding Agents Model aims to determine causal relationships by first generating a causal analysis plan using a debate format. After yielding the plan, it will then be executed with the observational data using a causal code executor. The detailed implementation of the function causal code executor can also refer to the section 4.4.1

#### 3.2.3 Hybrid Model

Figure: Algorithm 3 Algorithm for Hybrid Group

There are two combinations of Hybrid Group: Coding-Debating Hybrid and Debating-Coding Hybrid. They are fundamentally identical to the Meta Agents Model and Coding Agents Model in terms of their internal architectures, algorithms, and outputs. The difference lies in their inputs.

For Coding-Debating Hybrid, the initial result will be obtained from the Coding Agents Model of Algorithm 2 given the input of a meta-question and observational data. The graph and the proposed algorithm for achieving the final graph will also be extracted and fed into the Meta Agents Model 1. For example, the proposed algorithm in the Coding Agents Model is PC, and the initial graph $\hat{G}$, when both of them were input to the Meta Agents Model, the query would change slightly at line $8$ and $11$ in the algorithm 1 which is illustrated by the box below. The final return output is a matrix representation of a causal graph.

For the Debating-Coding Hybrid, the initial graph comes from the Meta Agents Model of algorithm 1. This output is then considered as prior knowledge or background knowledge. It is aggregated with the meta-question, and input to the Coding Agent Model of algorithm 2. It will select a suitable statistical causal discovery algorithm and plan. This plan is then given to the code executor to implement, resulting in a matrix representation of a causal graph.

## 4 Experiment and Results

### 4.1 Experimental Setup and Metrics

We use OpenAI API including GPT-3.5, GPT-4o, and GPT-4o mini for our experiment, Groq API for Llama-8.1-70b, Llama-8.1-8b, and Gemini-9B for most of our experiments with the temperature set at 0. We experiment on three different datasets that adopted from the work of Takayama et al. () including Auto MPG data (Quinlan ()), DWD climate data (Mooij et al. ()), and Sachs protein data (Sachs et al. ()). For the evaluation metrics, we assess the adjacency matrix obtained from LLMs or a code executor using structural hamming distance (SHD) and Normalized Hamming Distance (NHD) as described by Takayama et al. () and Kıcıman et al. () respectively.

### 4.2 Performance of MAC

The results of our experiments indicate that the performance is highly dependent on the complexity of the dataset. We rank and summarize the performance of each model based on the empirical results: (1) Coding Agent, this model exhibits strong performance, particularly when larger models. (2) Coding-Debating Hybrid / Debating-Coding Hybrid, these models provide balanced performance but do not excel in handling highly complex datasets. They are particularly effective in moderate complexity settings. (3) Causal Agent Debate, this model performs well for simpler datasets but faces challenges with more complex ones.

Auto MPG Dataset: In the Auto MPG dataset, which has a 5x5 matrix graph’s structure, the Causal Agent Debate method performed strongly, particularly with GPT-4o mini, achieving the lowest SHD of 4 and a NHD of 0.16. The Coding Agent method also showed good results, with GPT-3.5 achieving a similarly low SHD of 4 but a higher NHD of 0.48. The Coding-Debating Hybrid method demonstrated balanced performance, with both GPT-4o mini and Llama 3.1 8b achieving an SHD of 5, while Llama 3.1 8b had the lowest NHD of 0.2. The traditional methods and other advanced methods show higher SHD values, indicating lower structural accuracy. For example, PC, DirectLiNGAM, and Single-agent zero-shot prompting (GPT-4o) all have SHD values of 8, demonstrating less accurate structural learning compared to the Coding agents

DWD Climate Dataset: In the DWD climate dataset, which comprises a 6x6 matrix graph, the Causal Agent Debate method again showed strong performance, with GPT-3.5 achieving the lowest SHD of 5 and NHD of 0.194. The Coding Agent method performed well with GPT-4o mini, achieving an SHD of 6 and NHD of 0.194. The Coding-Debating Hybrid method stood out, with Llama-3.1-8b achieving the lowest SHD (5) and NHD (0.138). Similarly, the Hybrid-Debating-Coding Hybrid method also performed well, with GPT-4o achieving an SHD of 5 and NHD of 0.138. The traditional methods such as PC and DirectLiNGAM have higher SHD values (9 and 10, respectively) and lower overall performance in other metrics. The Single-agent zero-shot prompting methods, including GPT-4o, show higher SHD values (10 and 11, respectively) and less competitive performance across the other metrics.

Sachs’ Protein Dataset : In the Sachs’ protein dataset, the Causal Agent Debate method displayed mixed results, with GPT-4o achieving an SHD of 21 and an NHD of 0.231. The Coding Agent method outperformed others, with Llama-3.1-70b achieving the lowest SHD of 18 and an NHD of 0.157. The Coding-Debating Hybrid method demonstrated consistent performance, with GPT-4o mini reaching an SHD of 21 and GPT-3.5 achieving the lowest NHD of 0.198. The Debating-Coding Hybrid method also performed well, with GPT-4o mini achieving an SHD of 22 and NHD of 0.190.

**Table 2: Combined results across Auto MPG, Climate, and Sachs Datasets**
| Model | Auto MPG | Climate | Sachs |  |  |  |
| --- | --- | --- | --- | --- | --- | --- |
| SHD | NHD | SHD | NHD | SHD | NHD |  |
| Other methods |  |  |  |  |  |  |
| PC | 8 | 0.48 | 9 | 0.305 | 24 | 0.206 |
| Exact Search | 7 | 0.44 | 6 | 0.194 | 31 | 0.33 |
| LINGAM | 8 | 0.48 | 10 | 0.388 | 29 | 0.289 |
| PC LLM-KBCI | 7 | 0.44 | 7 | 0.222 | 30 | 0.314 |
| ES LLM-KBCI | 7 | 0.44 | 7 | 0.222 | 31 | 0.33 |
| DirectLiGam LLM-KBCI | 7 | 0.4 | 9 | 0.305 | 29 | 0.289 |
| Single-agent (GPT-4o) | 8 | 0.36 | 11 | 0.388 | 18 | 0.214 |
| Single-agent (GPT-3.5) | 7 | 0.28 | 10 | 0.361 | 31 | 0.363 |
| Causal Agent Debate |  |  |  |  |  |  |
| GPT-4o | 5 | 0.2 | 9 | 0.333 | 35 | 0.371 |
| GPT-4o mini | 4 | 0.16 | 11 | 0.416 | 35 | 0.338 |
| GPT-3.5 | 5 | 0.2 | 5 | 0.194 | 21 | 0.231 |
| Llama 3.1 70b | 10 | 0.44 | 8 | 0.222 | 35 | 0.380 |
| Llama 3.1 8b | 7 | 0.28 | 9 | 0.277 | 35 | 0.338 |
| Gemini 2 9b | 5 | 0.2 | 7 | 0.222 | 25 | 0.223 |
| Coding Agents |  |  |  |  |  |  |
| GPT-4o | 8 | 0.48 | 9 | 0.388 | 30 | 0.322 |
| GPT-4o mini | 6 | 0.6 | 6 | 0.194 | 30 | 0.322 |
| GPT-3.5 | 4 | 0.48 | 9 | 0.305 | 29 | 0.28 |
| Llama 3.1 70b | 6 | 0.6 | 6 | 0.194 | 18 | 0.157 |
| Llama 3.1 8b | 6 | 0.6 | 9 | 0.388 | 36 | 0.396 |
| Gemini 2 9b (GPT-4o-mini’s plan) | 7 | 0.36 | - | - | - | - |
| Hybrid-Coding-Debating |  |  |  |  |  |  |
| GPT-4o | 6 | 0.28 | 10 | 0.305 | 23 | 0.247 |
| GPT-4o mini | 5 | 0.24 | 9 | 0.25 | 21 | 0.190 |
| GPT-3.5 | 6 | 0.32 | 7 | 0.25 | 23 | 0.198 |
| Llama 3.1 70b | 6 | 0.36 | 6 | 0.166 | 33 | 0.314 |
| Llama 3.1 8b | 5 | 0.2 | 5 | 0.138 | 33 | 0.305 |
| Gemini 2 9b | - | - | - | - | - | - |
| Hybrid-Debating-Coding |  |  |  |  |  |  |
| GPT-4o | 5 | 0.24 | 5 | 0.138 | 29 | 0.297 |
| GPT-4o mini | 8 | 0.48 | 7 | 0.25 | 22 | 0.190 |
| GPT-3.5 | 8 | 0.48 | 7 | 0.277 | 28 | 0.272 |
| Llama 3.1 70b | 5 | 0.24 | 6 | 0.194 | 29 | 0.289 |
| Llama 3.1 8b | 6 | 0.4 | 9 | 0.388 | - | - |
| Gemini 2 9b | - | - | - | - | - | - |

### 4.3 Performance among LLMs

Small size LLMs: Llama 3.1 8b is a strong small model, consistently achieving solid results in hybrid models and competing with larger models in simpler datasets like Auto MPG and Climate. It excels in Hybrid Coding-Debating settings. Gemini 2 9b, while capable, tends to lag behind Llama 3.1 8b, especially since the MAC models require coding, particularly when the prompting token count exceeds 8,000 to 9,000 tokens, which leads to random code generation and prolonged debugging loops. Therefore, we do not include the result of this model in our research.

Medium size LLM: Llama 3.1 70b is a versatile medium-sized model, excelling particularly in coding tasks and holding its own in hybrid models. It tends to perform better in more complex datasets like Sachs, where it even surpasses some larger models. This model strikes a balance between computational efficiency and strong performance.

Large size LLMs: GPT-4o mini (^2^22If GPT-4o mini were considered a small size model, it would be considered as the best model in this setting) is an outstanding performer across hybrid and debate models, particularly in simpler datasets like Auto MPG and Climate, where it achieves some of the lowest SHD and NHD scores. GPT-4o is similarly strong in hybrid tasks and coding tasks, making it a top-tier choice for flexible, multi-agent collaboration. GPT-3.5, while effective, tends to be outperformed by the GPT-4 models in hybrid tasks but remains strong in causal debates and coding tasks for simpler datasets.

### 4.4 Token Usages and LLMs insights on MAC

Figure: Figure 4: Tokens Usage Prompting-Completion Tokens Ratio
Refer to caption: extracted/5915102/Figures/output.png

#### 4.4.1 Debate-Coding Module

Based on overall token consumption (Figure 4), (1) Coding-Debating Hybrid and Debating-Coding Hybrid models consumed the highest number of tokens. (2) The Agents-only model used a moderate number of tokens. The Coding Agents model consistently required the fewest tokens, even for more complex datasets and larger language models.

For smaller datasets like 5x5 and 6x6 matrices, the Agents-only and Coding-Debating Hybrid models used 50,000 to 60,000 tokens. However, with larger datasets, such as the 11x11 matrix, token usage increased significantly to about 230,000 to 300,000 tokens. To reduce this, future implementations can limit debating rounds to one or two, as models occasionally initiated five or six rounds, leading to excessive token use. Conversely, the Coding Agents and Debating-Coding Hybrid models showed more stable token consumption, ranging from 40,000 to 100,000 tokens, with performance influenced by their ability to generate and debug code. While GPT-series models and Llama-3.1 series performed reliably, smaller models like Gemini 2-9b struggled with prompts exceeding 8,000 to 9,000 tokens, leading to random code generation. Surprisingly, Llama-3.1-8b outperformed others in Gemini 2-9b generation, except the last dataset, despite requiring more tokens for debugging. This suggests it can effectively utilize plans from larger models, which typically require fewer tokens. Further experiments will be detailed in the next Ablation Studies 4.5 section.

The prompt-to-completion token ratio varied across models (see Figure 4): the Agents-only and Coding-Debating Hybrid models had a 2:1 ratio (2,000 prompting tokens to 1,000 completion tokens), while the Coding Agents and Debating-Coding Hybrid models had a 10:1 ratio (10,000 prompting tokens to 1,000 completion tokens). This significant gap in the Coding Agents and Debating-Coding Hybrid models arises from the intensive debugging process, where even small codebases can generate large outputs as the system traces the source code, leading to increased token consumption, especially during debugging

### 4.5 Ablation Study

Single-agent vs Causal Agent Debate: Causal debating agents outperform single-agent models in handling complexity by leveraging multiple viewpoints, making them better suited for more intricate problems. For example, in the Auto MPG dataset, Causal Agent Debate GPT-4o achieves an SHD of 5, outperforming the Single-agent GPT-4o with an SHD of 8. In the Climate dataset, for example, Causal Agent Debate GPT-4o achieves an SHD of 9, while Single-agent GPT-4o achieves 11. However, in complex datasets, such as Sachs, single-agent GPT-3.5 has an SHD of 31 and an NHD of 0.363, while Causal Agent Debate GPT-4o performs worse (SHD = 35), but the debate framework at least provides a structured method to tackle the challenge, despite not being fully optimized here.

**Table 3: Comparision between various single-agent designs**
| Model | Auto Dataset | Climate Dataset | Sachs Dataset |  |  |  |
| --- | --- | --- | --- | --- | --- | --- |
| SHD | NHD | SHD | NHD | SHD | NHD |  |
| Single-agent (GPT 3.5) | 7 | 0.28 | 10 | 0.361 | 31 | 0.363 |
| Single-agent (GPT-4o) | 8 | 0.36 | 11 | 0.388 | 18 | 0.214 |
| Our single-agent (GPT-4o mini) | 6 | 0.28 | 9 | 0.361 | 24 | 0.289 |

Eliminating the Judge: We retained only one causal single agent (GPT-4o-mini) with our curated prompt, as shown in Figure 3. This causal-single-agent did not perform better than other MAC models, except the Agents-only Model in the Sachs dataset. However, compared with other agents such as GPT-3.5 and GPT-4o, which use 0-CoT and ICL techniques, our single-agent model achieved better performance but only stayed behind GPT-4o on the Sachs dataset given the complexity of the dataset.

**Table 4: Performance of Gemini 2 9b and Llama 3.1 8b combining superior models**
| Model | Dataset | SHD | NHD | Condition |
| --- | --- | --- | --- | --- |
| Gemini 2 9b | Auto MPG | 0 | 0 | Baseline |
| Gemini 2 9b | Auto MPG | 7 | 0.36 | With GPT-4o-mini’s plan |
| Llama 3.1 8b | Sachs | 36 | 0.396 | Baseline |
| Llama 3.1 8b | Sachs | 18 | 0.157 | With Llama 3.1 70b’s plan |

Combining small and large models: In the Coding Agents Model, we experimented with the combination of using the plan from GPT-4o and coding from Gemini 2-9b. With only an exception in the dataset Auto MPG, the model was able to complete and implement the plan successfully but was not able to precede the rest of the other datasets. However, as for the Llama-3.1-70b and Llama-3.1-8b, it exhibits promising performance. Specifically, after observing that Llama-3.1-70b achieved the best performance with its proposed plan in the Sachs dataset, we used that plan to prompt Llama-3.1-8b to implement it. Surprisingly, the smaller model yielded similar performance. Therefore, if computational resources are limited, it is advisable to use larger models for high-level tasks such as planning and smaller models (Coding Agents) for computationally intensive tasks like coding and debugging.

## 5 Conclusion

In this study, we introduce a novel framework, MAC, that integrates the agentic workflows of large language models (LLMs) with data-driven methods. To the best of our knowledge, this is the first investigation into the agentic workflows of LLMs within a causal context. Our framework enhances causal discovery by synergizing the capabilities of LLMs with empirical data analysis. We propose three distinct models that leverage the causal reasoning abilities of LLMs alongside observational data. Additionally, we conducted extensive experiments across various LLM sizes, analyzing token consumption and developing strategies to address related challenges. We recognize the necessity for further research to explore across domains such as healthcare, economics, and social sciences. We hope our work serves as a foundational stone for future research, inspiring advancements in the integration of LLMs with causal inference methodologies and contributing to more informed decision-making and policy development.

## Appendix A Appendix

### A.1 Additionally experiment results

#### A.1.1 Auto MPG data

Auto MPG data (Quinlan ()): This dataset consists of the variables around the fuel consumption of cars. With five variables: “Weight”, “Displacement”, “Horsepower”, “Acceleration” and “Mpg”(miles per gallon)

**Table 5: Results on Auto MPG Dataset**
| Model | SHD | NHD |
| --- | --- | --- |
| Other methods |  |  |
| PC | 8 | 0.48 |
| Exact Search | 7 | 0.44 |
| LINGAM | 8 | 0.48 |
| PC LLM-KBCI | 7 | 0.44 |
| ES LLM-KBCI | 7 | 0.44 |
| DirectLiGam LLM-KBCI | 7 | 0.4 |
| Single-agent (GPT-4o) | 8 | 0.36 |
| Single-agent (GPT-3.5) | 7 | 0.28 |
| Causal Agent Debate |  |  |
| GPT-4o | 5 | 0.2 |
| GPT-4o mini | 4 | 0.16 |
| GPT-3.5 | 5 | 0.2 |
| Llama 3.1 70b | 10 | 0.44 |
| Llama 3.1 8b | 7 | 0.28 |
| Gemini 2 9b | 5 | 0.2 |
| Coding Agents |  |  |
| GPT-4o | 8 | 0.48 |
| GPT-4o mini | 6 | 0.6 |
| GPT-3.5 | 4 | 0.48 |
| Llama 3.1 70b | 6 | 0.6 |
| Llama 3.1 8b | 6 | 0.6 |
| Gemini 2 9b (gpt-4o-mini’s plan) | 7 | 0.36 |
| Hybrid-Coding-Debating |  |  |
| GPT-4o | 6 | 0.28 |
| GPT-4o mini | 5 | 0.24 |
| GPT-3.5 | 6 | 0.32 |
| Llama 3.1 70b | 6 | 0.36 |
| Llama 3.1 8b | 5 | 0.2 |
| Gemini 2 9b | - | - |
| Hybrid-Debating-Coding |  |  |
| GPT-4o | 5 | 0.24 |
| GPT-4o mini | 8 | 0.48 |
| GPT-3.5 | 8 | 0.48 |
| Llama 3.1 70b | 5 | 0.24 |
| Llama 3.1 8b | 6 | 0.4 |
| Gemini 2 9b | - | - |

#### A.1.2 DWD climate data

DWD climate data (Mooij et al. ()): This dataset encompasses six continuous variables capturing climate observations such as altitude, temperature, precipitation levels, longitude, sunshine duration, and latitude. It is aimed at studying weather patterns, climate change impacts, and geographical correlations in climate variables.

**Table 6: Results on Climate Dataset**
| Model | SHD | NHD |
| --- | --- | --- |
| Other methods |  |  |
| PC | 9 | 0.305 |
| Exact Search | 6 | 0.194 |
| LINGAM | 10 | 0.388 |
| PC LLM-KBCI | 7 | 0.222 |
| ES LLM-KBCI | 7 | 0.222 |
| DirectLiGam LLM-KBCI | 9 | 0.305 |
| Single-agent (GPT-4o) | 11 | 0.388 |
| Single-agent (GPT-3.5) | 10 | 0.361 |
| Causal Agent Debate |  |  |
| GPT-4o | 9 | 0.333 |
| GPT-4o mini | 11 | 0.416 |
| GPT-3.5 | 5 | 0.194 |
| Llama 3.1 70b | 8 | 0.222 |
| Llama 3.1 8b | 9 | 0.277 |
| Gemini 2 9b | 7 | 0.222 |
| Coding Agents |  |  |
| GPT-4o | 9 | 0.388 |
| GPT-4o mini | 6 | 0.194 |
| GPT-3.5 | 9 | 0.305 |
| Llama 3.1 70b | 6 | 0.194 |
| Llama 3.1 8b | 9 | 0.388 |
| Gemini 2 9b | - | - |
| Hybrid-Coding-Debating |  |  |
| GPT-4o | 10 | 0.305 |
| GPT-4o-mini | 9 | 0.25 |
| GPT-3.5 | 7 | 0.25 |
| Llama 3.1 70b | 6 | 0.166 |
| Llama 3.1 8b | 5 | 0.138 |
| Gemini 2 9b | - | - |
| Hybrid-Debating-Coding |  |  |
| GPT-3.5 | 7 | 0.277 |
| GPT-4o | 5 | 0.138 |
| GPT-4o mini | 7 | 0.25 |
| Llama 3.1 70b | 6 | 0.194 |
| Llama 3.1 8b | 9 | 0.388 |
| Gemini 2 9b | - | - |

#### A.1.3 Sachs protein data

Sachs protein data (Sachs et al. ()): The dataset comprises protein signaling measurements from multiparameter single-cell data, capturing the interactions among various proteins (raf, mek, plc, pip2, pip3, erk, akt, pka, pkc, p38, jnk). It’s aimed at understanding signal transduction pathways within cells, derived from an influential study published in Science.

**Table 7: Results on Sachs Dataset**
| Model | SHD | NHD |
| --- | --- | --- |
| Other methods |  |  |
| PC | 24 | 0.206 |
| Exact Search | 31 | 0.33 |
| LINGAM | 29 | 0.289 |
| PC LLM-KBCI | 30 | 0.314 |
| ES LLM-KBCI | 31 | 0.33 |
| DirectLiGam LLM-KBCI | 29 | 0.289 |
| Single-agent (GPT-4o) | 18 | 0.214 |
| Single-agent (GPT-3.5) | 31 | 0.363 |
| Causal Agent Debate |  |  |
| GPT-4o | 35 | 0.371 |
| GPT-4o mini | 35 | 0.338 |
| GPT-3.5 | 21 | 0.231 |
| Llama 3.1 70b | 35 | 0.380 |
| Llama 3.1 8b | 35 | 0.338 |
| Gemini 2 9b | 25 | 0.223 |
| Coding Agents |  |  |
| GPT-4o | 30 | 0.322 |
| GPT-4o mini | 30 | 0.322 |
| GPT-3.5 | 29 | 0.28 |
| Llama 3.1 70b | 18 | 0.157 |
| Llama 3.1 8b | 36 | 0.396 |
| Gemini 2 9b | - | - |
| Hybrid-Coding-Debating |  |  |
| GPT-4o | 23 | 0.247 |
| GPT-4o-mini | 21 | 0.190 |
| GPT-3.5 | 23 | 0.198 |
| Llama 3.1 70b | 33 | 0.314 |
| Llama 3.1 8b | 33 | 0.305 |
| Gemini 2 9b | - | - |
| Hybrid-Debating-Coding |  |  |
| GPT-4o | 29 | 0.297 |
| GPT-4o mini | 22 | 0.190 |
| GPT-3.5 | 28 | 0.272 |
| Llama 3.1 70b | 29 | 0.289 |
| Llama 3.1 8b | - | - |
| Gemini 2 9b | - | - |

### A.2 Visualization of MAC modules

#### A.2.1 Meta-Debate Module Visualization

Step 1: Constructing a prompting question between two variables with the description of the data for extra information.

[Uncaptioned image]: x4.png

Step 2: Prompting the affirmative agent for giving its opinion.

[Uncaptioned image]: x5.png

Step 3: The negative agent then gives its opinion of the question.

[Uncaptioned image]: x6.png

Step 4: The Judge will give verdict of who wins the debate or continue asking follow-up question for each or both side if further clarifications are needed

[Uncaptioned image]: x7.png

Step 5: The final result will be obtained from the debate process of knowing whether there is a causal relationship between two variables

[Uncaptioned image]: x8.png

#### A.2.2 Debate-Coding Module Visualization

Phase 1: Plan Debating

Step 1: Constructing input that comprises: The description of the dataset, Sample of the structured data, planning debating question

[Uncaptioned image]: x9.png

Step 2: The affirmative agent will propose a plan and algorithm for the given input

[Uncaptioned image]: x10.png

Step 3: The negative agent rebuttals with another plan and algorithm

[Uncaptioned image]: x11.png

Step 4: The Judge evaluates which plan and algorithm are superior.

[Uncaptioned image]: x12.png

Step 5: The final plan for coding agent is extracted from the debate process

[Uncaptioned image]: x13.png

Phase 2: Code Executing

Step 1: The step-by-step plan is given to the coding executor

[Uncaptioned image]: x14.png

Step 2: The coding executor implements the plan by writing Python script and debugging code.

[Uncaptioned image]: x15.png

Step 3: The final result of a causal graph is obtained

[Uncaptioned image]: x16.png

### A.3 Details prompting design of each agent in MAC

We use AutoGen (Wu et al. ()) framework to implement our methods

#### A.3.1 Meta-Debate Module

Debaters’ Prompt
\UseRawInputEncoding

Figure: Listing 1: Debaters’ prompt

Judge Prompt

Figure: Listing 2: Judge’s Prompt

#### A.3.2 Debate-Coding Module

Plan Debaters Prompt

Figure: Listing 3: Plan Debaters’ prompt

Judge Prompt

Figure: Listing 4: Judge Prompt

Code Executor Prompt

Figure: Listing 5: Code Executor Prompt

## Appendix B Sample Answers from Experiments

#### B.0.1 Meta Agents Model

Figure: Listing 6: Agents-only responses

#### B.0.2 Coding Agents Model

Phase 1: Plan Debating

Figure: Listing 7: Plan Debating responses

Phase 2: Code Executing

Figure: Listing 8: Code executing responses

## Peer Reviews

confidence: 3
contribution: 2
initial_rating: 1
presentation: 1
questions: 1. Why the Gemini 2 9b rows are empty in Table 2?

2. The results in Table 2 look similar; are bold results significnatly better? 

3. How large are the dataset used?

4. What does it mean by "agentic ability" in table 1? What is "multi-agent" in table 1 refers to, does it simply means multiple components are used in MAC?
soundness: 1
strengths: The idea of using multi-agent systems to solve causal discovery problem is interesting.
summary: This paper proposed a meta-debator model for causal discovery using large language models called MAC and perform simulations on three datasets.
weaknesses: ### General

I found it a bit hard to assess the significance of this work, partly because the writing (especially on the experimental setup) is a bit opaque, and I did not find the result to be super exciting. The constant stylish and grammatical imperfections also seem to suggest this paper was written in a rush. I would also recommended the authors proofread the paper and make the writing clearer. Furthermore, mechanically, I do not see how using a multi-agent setup is fundemantally better. I acknowledge that the SHD/NHD metrics were better on some models in authors' experiments, but I am not sure if (1) those improvements were large enough to be significnat; and (2) the inference cost of having more LLMs in the pipeline. I am hoping to see more supporting eveidence that the proposed framework compares favorably to existing methods.




### Writing issues (excerpt)

1. Citation missing at line 150.
2. Empty citations at line 130.
3. Double quotes styld at line 146.
4. Missing period at line 371.
5. Missing figure reference at line 463.
6. Missing figure reference at line 479.
7. Missing period at line 484.
8. Missing period at footnote 2.

---

confidence: 4
contribution: 1
initial_rating: 3
presentation: 3
questions: 1. Generalizability Across Different Datasets: How would MAC’s performance vary on datasets with more complex causal structures or differing distributions? Would integrating domain-specific statistical models or causal priors into the MAC framework improve its adaptability?

2. Impact of Noise Reduction Techniques: Since causal discovery is sensitive to noise, could pre-processing techniques (e.g., noise reduction or causal regularization) improve MAC’s stability in identifying causal graphs? How would the SHD and NHD scores change under varying noise levels?

3. Effectiveness of Hybrid Model Configurations: Given that the Hybrid Model combines Meta-Debate and Coding Agents, what is the optimal sequencing or balance between these agents for tasks with different complexities? Would tasks benefit from a dynamic hybrid approach that adjusts the agent workflow based on intermediate inference outcomes?

4. Convergence Criteria and Agentic Redundancy: Does the MAC framework have a convergence criterion to stop debate or coding cycles, especially when agents are unlikely to yield new information? What role could redundancy elimination techniques play in enhancing efficiency, and are there scenarios where additional agents create diminishing returns?
soundness: 2
strengths: 1. Comprehensive Multi-Agent Approach: The paper introduces a well-structured framework that incorporates debate, planning, and coding agents to address causal inference, allowing MAC to explore causal discovery from multiple angles (e.g., reasoning and statistical analysis).

2. Thorough Evaluation Metrics: The study uses detailed metrics (SHD, NHD) across three datasets with varying complexities, providing an empirical basis for evaluating each model’s effectiveness. This comparison offers valuable insights into MAC’s strengths and areas of improvement in different causal discovery scenarios.

3. Resource Efficiency Analysis: The paper’s analysis of token consumption across models (e.g., Coding-Debating Hybrid and Meta Agents Model) offers practical insights into optimizing multi-agent frameworks, allowing future research to refine token efficiency in LLM-based causal discovery.
summary: This paper explores the use of multi-agent Large Language Models (LLMs) for causal discovery, introducing a new framework called Multi-Agent Causality (MAC). MAC includes three distinct models—Meta Agents Model, Coding Agents Model, and Hybrid Model—each designed to leverage multi-agent interactions to enhance causal inference. The framework addresses several key challenges in causal discovery, such as harnessing agents for debate (Meta Agents Model), employing coding agents for data-driven causal graph construction (Coding Agents Model), and combining both approaches to optimize performance (Hybrid Model). The study assesses the efficacy of MAC across three datasets (Auto MPG, DWD Climate, and Sachs Protein) using metrics like Structural Hamming Distance (SHD) and Normalized Hamming Distance (NHD). Results suggest that MAC’s multi-agent collaboration effectively improves LLM-based causal discovery by integrating structured debates and coding execution, with varying performance based on dataset complexity.
weaknesses: 1. Lack of Formal Framework for Agentic Workflow Convergence: Although MAC leverages multi-agent interactions for causal discovery, it lacks a formal mathematical model that defines or ensures convergence of the agents' outputs to a stable causal graph. In high-dimensional causal graphs, where causal inference is combinatorially complex, the absence of convergence guarantees can lead to oscillating or suboptimal solutions.

2. Inadequate Quantification of Noise Propagation in Causal Inference: While the study qualitatively discusses errors in causal relationships and agentic noise, it lacks a quantitative model of error propagation, particularly in the Coding Agents and Hybrid Models. In causal discovery, noise in initial data or agentic decision-making can propagate through the inference process, leading to accumulated inaccuracies.

3. Limited Theoretical Justification for Agent Roles and Workflow Sequencing: The paper introduces different agent roles (debate agents, coding agents) and workflows (Meta, Coding, and Hybrid Models) but lacks a theoretical basis for why certain roles or workflows are expected to perform better in specific causal inference tasks. For example, why should debates be prioritized in certain instances over coding, or vice versa? Without a rigorous framework, the choice of agent configurations appears ad hoc.

4. Scalability Constraints in Token and Computational Costs: The MAC framework requires significant token and computational resources, especially in complex datasets or with high-dimensional graphs. Although the paper provides empirical token usage data, it does not propose concrete solutions for reducing token or computational overhead, limiting MAC's practical applicability to smaller datasets or high-resource settings.

Summary: While MAC offers a novel multi-agent approach for LLM-based causal discovery, its theoretical framework and practical scalability are limited. The lack of formal convergence guarantees, quantification of noise propagation, and rigorous justification for agent workflows restrict its contribution to the field. Future work that addresses these theoretical gaps and practical constraints could make MAC a more impactful framework for causal discovery with LLMs.

---

confidence: 3
contribution: 2
initial_rating: 5
presentation: 3
questions: - In Figure 2, the prompt in the role section concludes with 'Today is <current date>.' Is this addition essential for performance?
- How does the debating phase in the coding agents model determine the appropriate algorithm? Model selection can be challenging, even for domain experts, as algorithms often rely on different assumptions about the data, which are difficult to verify. Does the proposed method account for this when recommending an algorithm?
- In the debate-coding module, the prompts enumerate all causal discovery methods under consideration, detailing their functions and parameters as sourced from a Python library. Will there be any potential scalability challenges, if more methods are to be included? Additionally, might the accuracy of method recommendations be impacted by the growing number of methods included in the prompts?
- In the debate-coding module visualization in Appendix A2.2, several additional steps are included in the final suggested plan beyond implementing a causal discovery algorithm, such as interpretation, model evaluation, .etc. How are these other steps executed?
- In the experimental results, the coding agent outperforms traditional causal discovery methods on the Sachs dataset. Could you explain the rationale behind this improvement? From my understanding, the key difference introduced by the coding agent, compared to traditional causal discovery algorithms, is the debating phase for method selection and planning. Intuitively, shouldn't the performance of the coding agent align with the direct implementation of the algorithm chosen during the debating phase?
- In the ablation analysis section, 'Single-Agent vs. Causal Agent Debate,' what prompt is used for the single agent? If we instruct a single LLM to handle both the debating and judging processes during reasoning, would its performance be comparable to that of the multi-agent framework?
- In the ablation analysis section, 'Eliminating the Judge,' why not include a comparison with GPT-4o mini?
soundness: 3
strengths: - It is the first to leverage an LLM multi-agent system for causal discovery.
- The paper proposes a multi-agent framework for causality, presenting three distinct models that demonstrate strong performance in experiments on real datasets.
- It provides an extensive comparison of diverse LLM models and includes an informative ablation analysis to illustrate the necessity of each key component in the proposed method.
summary: Driven by the potential of multi-agent large language models (LLMs) in complex problem-solving, the authors propose agent-based frameworks to enhance causal discovery. They introduce three multi-agent frameworks (models): (i) the Meta-Agent Model, featuring two debate agents and a judge agent who collaboratively perform causal discovery through reasoning and discussions; (ii) the Coding Agent Model, which operates in two phases: first, two debate agents and a judge agent determine the appropriate causal discovery method and devise an execution plan; in the second phase, they write and run the code using advanced statistical libraries; and (iii) the Hybrid Model, which integrates both the Meta-Agent and Coding Agent models. Experiments on three datasets demonstrate that these frameworks outperform baseline models, including traditional causal discovery algorithms and standard LLMs.
weaknesses: - The paper’s methodological novelty may be somewhat limited, as its primary contribution appears to be the use of a multi-agent debating mechanism to improve the precision of causal reasoning, with much of the effort focused on constructing prompts tailored to causal discovery-specific problems. It would be valuable if the authors could further elaborate on any additional innovative aspects of the design.
- Clarity could be improved throughout the paper. For example, i) the distinction between the debate-coding module and the coding agent is unclear; ii) some figure references are missing, iii) there is a lack of explanation of rationale behind the hybrid models, such as how information from the coding agent enhances the performance of the meta-agent and how prior knowledge from the meta-agent is utilized within the coding agent.
- The experimental results may not be sufficient to fully demonstrate the method’s robustness, as the performance comparison is limited to only three datasets, which might not provide a representative evaluation. Additionally, including a more detailed discussion on the stability of LLM responses could be helpful.

---

confidence: 4
contribution: 2
initial_rating: 3
presentation: 2
questions: See the weaknesses
soundness: 3
strengths: The use of cooperation and competition among multiple agents enhances the accuracy and comprehensiveness of causal discovery.

The framework combines the characteristics of different models for more efficient and flexible causal analysis.

The paper demonstrates the performance of different models on various datasets, using metrics such as SHD and NHD for comparison.

Exploration of LLM Potential in Causal Inference: This is the first in-depth study of LLMs’ multi-agent approaches in causal discovery, highlighting the potential for applying this method across diverse fields.
summary: This paper introduces a MAC for causal discovery using LLMs. The authors propose three distinct models: the Meta Agents Model, the Coding Agents Model, and the Hybrid Model. The Meta Agents Model uses multiple rounds of debate among different agents to discuss and identify causal relationships. The Coding Agents Model combines statistical causal algorithms, employing code writing and execution to identify causal links. Finally, the Hybrid Model merges the strengths of the previous two models, using both multi-agent statistical analysis and logical reasoning to construct causal graphs.
weaknesses: A hybrid model can balance statistical inference with the reasoning abilities of a language model, making it suitable for tasks with high complexity. However, the hybrid approach does not consistently outperform other methods significantly.

While multi-agent systems can enhance model performance, their effectiveness largely depends on the complexity and structure of the dataset. For example, Coding Agents perform well on moderately complex datasets, but their performance may fall short for simpler or highly complex cases. This suggests that models may require tuning or selection based on the dataset, which increases the usage barrier.

Due to the iterative debugging needed in Coding Agents models during code execution, handling longer or more complex code may lead to errors or debugging loops. Furthermore, coordinating multiple agents can, in some cases, produce unexpected outputs, requiring additional debugging and testing to ensure stability.

When processing larger datasets, multi-agent models—particularly the Coding-Debating Hybrid and Debating-Coding Hybrid models—consume a significant amount of tokens. Although the framework incorporates methods to reduce token consumption (such as limiting debate rounds), token usage remains a critical constraint for applications with limited resources.

The paper also has numerous issues in expression. For instance, the citation format in the introduction and related work sections needs improvement, and lines 463 and 478 lack references to specific images.

---

confidence: 3
contribution: 2
initial_rating: 5
presentation: 2
questions: Questions:
- Given that prompt-based approaches for LLMs can sometimes yield unstable results, would you consider including statistical significance results to enhance robustness?
- Conducting full graph discovery on three datasets may be insufficient to fully demonstrate the framework's validity. Would you consider including additional data sources and exploring more causal settings, such as causal event identification?
- Here are some relevant works that could strengthen the validity of your findings:

   [1] Improving factuality and reasoning in language models through multiagent debate. ICML 2024 

   [2] Causal Parrots: Large Language Models May Talk Causality But Are Not Causal. TMLR 2023

   [3] LLM4Causal: Democratized Causal Tools for Everyone via Large Language Model. COLM 2024

   [4] Causal evaluation of language models.

   [5] Is Knowledge All Large Language Models Needed for Causal Reasoning?
soundness: 3
strengths: Strengths:
- The authors aim to establish a multi-LLM agent framework for addressing causal discovery problems, leveraging advanced statistical algorithms and the internal knowledge of LLMs to achieve more accurate discovery results, as LLMs alone may not produce optimal outcomes in causal discovery.
- The authors conduct a full graph discovery experiment using the latest LLM models.
- The Meta-Debate module is designed to enhance the reasoning capabilities of LLMs.
summary: This paper proposes a multi-LLM agent framework for causal discovery. The framework, particularly the Hybrid Model, leverages cooperation and debate among different LLM agents, along with their function-calling capabilities to employ statistical algorithms for causal discovery. The designed experiments demonstrate promising results by integrating LLMs' internal knowledge, agent debate and cooperation, and statistical algorithms. This framework lays a foundation for future research on multi-agent LLMs in causal problems.
weaknesses: Weaknesses:
- There are some formatting errors, such as unresolved references like "Figure ?."
- Given that the causal discovery results provided by LLMs alone sometimes lack stability [Altering the order of variables in the prompts can impact the results], presenting statistical significance results and trying more data source could enhance the validity of the findings.
- The experiments might not fully capture the complexity of real-world datasets. The generalizability of the model to more diverse settings remains unclear.