<!DOCTYPE html><html lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<title>[2305.14325] Improving Factuality and Reasoning in Language Models through Multiagent Debate</title><meta property="og:description" content="Large language models (LLMs) have demonstrated remarkable capabilities in language generation, understanding, and few-shot learning in recent years. An extensive body of work has explored how their performance may be f…">
<meta name="viewport" content="width=device-width, initial-scale=1">
<meta name="twitter:card" content="summary">
<meta name="twitter:title" content="Improving Factuality and Reasoning in Language Models through Multiagent Debate">
<meta name="twitter:image:src" content="https://ar5iv.labs.arxiv.org/assets/ar5iv_card.png">
<meta name="twitter:image:alt" content="ar5iv logo">
<meta property="og:title" content="Improving Factuality and Reasoning in Language Models through Multiagent Debate">
<meta property="og:site_name" content="ar5iv">
<meta property="og:image" content="https://ar5iv.labs.arxiv.org/assets/ar5iv_card.png">
<meta property="og:type" content="article">
<meta property="og:url" content="https://ar5iv.labs.arxiv.org/html/2305.14325">

<!--Generated on Thu Feb 29 06:02:31 2024 by LaTeXML (version 0.8.8) http://dlmf.nist.gov/LaTeXML/.-->
<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">

<script>
  function detectColorScheme(){
    var theme="light";
    var current_theme = localStorage.getItem("ar5iv_theme");
    if(current_theme){
      if(current_theme == "dark"){
        theme = "dark";
      } }
    else if(!window.matchMedia) { return false; }
    else if(window.matchMedia("(prefers-color-scheme: dark)").matches) {
      theme = "dark"; }
    if (theme=="dark") {
      document.documentElement.setAttribute("data-theme", "dark");
    } else {
      document.documentElement.setAttribute("data-theme", "light"); } }

  detectColorScheme();

  function toggleColorScheme(){
    var current_theme = localStorage.getItem("ar5iv_theme");
    if (current_theme) {
      if (current_theme == "light") {
        localStorage.setItem("ar5iv_theme", "dark"); }
      else {
        localStorage.setItem("ar5iv_theme", "light"); } }
    else {
        localStorage.setItem("ar5iv_theme", "dark"); }
    detectColorScheme(); }
</script>
<link media="all" rel="stylesheet" href="/assets/ar5iv-fonts.0.7.9.min.css"><link media="all" rel="stylesheet" href="/assets/ar5iv.0.7.9.min.css"><link media="all" rel="stylesheet" href="/assets/ar5iv-site.0.2.2.css">
</head>
<body>
<div class="ltx_page_main">
<div class="ltx_page_content">
<article class="ltx_document ltx_authors_1line">
<h1 class="ltx_title ltx_title_document">Improving Factuality and Reasoning in Language Models through Multiagent Debate</h1>
<div class="ltx_authors">
<span class="ltx_creator ltx_role_author">
<span class="ltx_personname">Yilun Du 
<br class="ltx_break">MIT CSAIL
<br class="ltx_break">yilundu@mit.edu
<br class="ltx_break">&amp;Shuang Li 
<br class="ltx_break">MIT CSAIL
<br class="ltx_break">lishuang@mit.edu 
<br class="ltx_break">&amp;Antonio Torralba 
<br class="ltx_break">MIT CSAIL 
<br class="ltx_break">torralba@mit.edu 
<br class="ltx_break">&amp;Joshua B. Tenenbaum 
<br class="ltx_break">MIT CSAIL, BCS, CBMM
<br class="ltx_break">jbt@mit.edu 
<br class="ltx_break">&amp;Igor Mordatch 
<br class="ltx_break">Google Brain
<br class="ltx_break">imordatch@google.com
<br class="ltx_break">
</span></span>
</div>

<div class="ltx_abstract">
<h6 class="ltx_title ltx_title_abstract">Abstract</h6>
<p id="id1.id1" class="ltx_p">Large language models (LLMs) have demonstrated remarkable capabilities in language generation, understanding, and few-shot learning in recent years. An extensive body of work has explored how their performance may be further improved through the tools of prompting, ranging from verification, self-consistency, or intermediate scratchpads.
In this paper, we present a complementary approach to improve language responses
where multiple language model instances propose and debate their individual responses and reasoning processes over multiple rounds to arrive at a common final answer.
Our findings indicate that this approach significantly enhances mathematical and strategic reasoning across a number of tasks. We also demonstrate that our approach improves the factual validity of generated content, reducing fallacious answers and hallucinations that contemporary models are prone to. Our approach may be directly applied to existing black-box models and uses identical procedure and prompts for all tasks we investigate.
Overall, our findings suggest that such "society of minds" approach has the potential to significantly advance the capabilities of LLMs and pave the way for further breakthroughs in language generation and understanding. Project website at <a target="_blank" href="https://composable-models.github.io/llm_debate/" title="" class="ltx_ref ltx_url ltx_font_typewriter">https://composable-models.github.io/llm_debate/</a>.</p>
</div>
<section id="S1" class="ltx_section">
<h2 class="ltx_title ltx_title_section">
<span class="ltx_tag ltx_tag_section">1 </span>Introduction</h2>

<div id="S1.p1" class="ltx_para">
<p id="S1.p1.1" class="ltx_p">Large language models (LLMs) have demonstrated remarkable language generation, understanding, and few-shot learning capabilities in recent years. These methods are trained on a massive corpus of text on the internet, where the quality and accuracy of extracted natural language may not be ensured. Thus, current models may suffer from confidently hallucinating facts or making implausible jumps in chains of reasoning. An extensive body of recent work has focused on improving factual accuracy and reasoning in language models. These range from prompting models with few or zero-shot chain-of-thought demonstrations, use of verification, self-consistency, or intermediate scratchpads.</p>
</div>
<div id="S1.p2" class="ltx_para">
<p id="S1.p2.1" class="ltx_p">We note that these techniques are applied over a single model instance. Instead, we propose a complementary approach inspired by <em id="S1.p2.1.1" class="ltx_emph ltx_font_italic">The Society of Mind</em>  <cite class="ltx_cite ltx_citemacro_citep">[<a href="#bib.bib19" title="" class="ltx_ref">19</a>]</cite> and multi-agent settings, where multiple language model instances (or agents) individually propose and jointly debate their responses and reasoning processes to arrive at a single common answer. More specifically, given a query, multiple instances of a language model first generate individual candidate answers to a query. Then each individual model instance reads and critiques the responses of all other models and uses this content to update its own answer. This step is then repeated over several rounds. This process induces models to construct answers that are consistent with both their internal critic as well as sensible in light of the responses of other agents. The resulting quorum of models can hold and maintain multiple chains of reasoning and possible answers simultaneously before proposing the final answer.</p>
</div>
<div id="S1.p3" class="ltx_para">
<p id="S1.p3.1" class="ltx_p">We find that our debate approach outperforms single model baselines such as zero-shot chain of thought  <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib11" title="" class="ltx_ref">11</a>]</cite> and reflection  <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib26" title="" class="ltx_ref">26</a>, <a href="#bib.bib18" title="" class="ltx_ref">18</a>]</cite> on a variety of six reasoning, factuality, and question-answering tasks. Using both multiple model agents and multiple rounds of debate are important to achieve the best performance. Given an initial query, we find that individual model instances propose a diverse range of answers despite being the same model class (although we also investigate the case of mixing different model types, such as chatGPT  <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib21" title="" class="ltx_ref">21</a>]</cite> and Bard  <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib23" title="" class="ltx_ref">23</a>]</cite>). After debating and examining the responses of other model instances, we find that the population almost always converges on a single and more accurate common answer. Debate results are also less likely to include false facts that models are internally uncertain of. This is because as the debate progresses, individual model instances tend to disagree on uncertain facts and omit them from the answer (Figure <a href="#S3.F7" title="Figure 7 ‣ Tasks. ‣ 3.1 Improving Reasoning with Multiagent Debate ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">7</span></a>). Lastly, we find that debate does not just act to amplify one correct answer in a model quorum - we find many cases where all the models initially make incorrect predictions, but then arrive at the correct answer as debate progresses (Figure <a href="#S3.F4" title="Figure 4 ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">4</span></a>,<a href="#S3.F11" title="Figure 11 ‣ Results. ‣ 3.2 Extracting Factual Information from Multiagent Debate ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">11</span></a>).</p>
</div>
<div id="S1.p4" class="ltx_para">
<p id="S1.p4.1" class="ltx_p">We use the same methodology and prompt templates for all our tasks and require only black-box access to language model generations – no model-internal information such as likelihoods or gradients is needed. This allows our method to be used with common public models serving interfaces. The method is also orthogonal to other model generation improvements such as retrieval or prompt engineering (in fact, we combine our debate method with zero-shot chain of thought). While the debate process is more costly, requiring multiple model instances and rounds, it arrives at significantly improved answers and may be used to generate additional model training data, effectively creating a model self-improvement loop.</p>
</div>
<div id="S1.p5" class="ltx_para">
<p id="S1.p5.1" class="ltx_p">To help evaluate the effect of our approach on factual accuracy, we introduce a new benchmark and dataset evaluating factual accuracy of famous computer scientist biographies. We find that contemporary language models have an especially high tendency to hallucinate factually incorrect biographies, often misrepresenting the relevant institutions and dates. Moreover, these facts often inconsistent across different language model instances. By asking models to come to a consensus across their answers, such inconsistent facts may be either removed or corrected.</p>
</div>
<div id="S1.p6" class="ltx_para">
<p id="S1.p6.1" class="ltx_p">In summary, our work contributes the following. First, we present a novel approach to improving factual correctness and reasoning accuracy in contemporary language models, leveraging a multi-agent debate process between models. Second, we introduce a new benchmark of factual correctness which contemporary language models struggle with. Finally, we evaluate the performance of our debate procedure in language generation, both in terms of the number of agents, the underlying rounds of debate, and the prompts that elicit such behavior across a set of six different reasoning and factual accuracy tasks.</p>
</div>
<figure id="S1.F1" class="ltx_figure"><img src="/html/2305.14325/assets/x1.png" id="S1.F1.g1" class="ltx_graphics ltx_centering ltx_img_landscape" width="461" height="163" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="S1.F1.3.1.1" class="ltx_text" style="font-size:90%;">Figure 1</span>: </span><span id="S1.F1.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Multiagent Debate Improves Reasoning and Factual Accuracy.<span id="S1.F1.4.2.1" class="ltx_text ltx_font_medium"> Accuracy of traditional inference and our multi-agent debate over six benchmarks (chess move optimality reported as a normalized score)</span></span></figcaption>
</figure>
</section>
<section id="S2" class="ltx_section">
<h2 class="ltx_title ltx_title_section">
<span class="ltx_tag ltx_tag_section">2 </span>Language Generation through Multiagent Debate</h2>

<div id="S2.p1" class="ltx_para">
<p id="S2.p1.1" class="ltx_p">We present an approach to generate language responses through multiagent debate. We provide an overview of our approach in Section <a href="#S2.SS1" title="2.1 Multiagent Language Generation ‣ 2 Language Generation through Multiagent Debate ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">2.1</span></a>. We further discuss convergence to consensus in the debate process in Section <a href="#S2.SS2" title="2.2 Consensus in Debates ‣ 2 Language Generation through Multiagent Debate ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">2.2</span></a>. The overall overview of our approach is shown in Figure <a href="#S2.F2" title="Figure 2 ‣ 2 Language Generation through Multiagent Debate ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">2</span></a>.</p>
</div>
<figure id="S2.F2" class="ltx_figure"><img src="/html/2305.14325/assets/x2.png" id="S2.F2.g1" class="ltx_graphics ltx_centering ltx_img_square" width="461" height="501" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="S2.F2.3.1.1" class="ltx_text" style="font-size:90%;">Figure 2</span>: </span><span id="S2.F2.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Illustration of Debate.<span id="S2.F2.4.2.1" class="ltx_text ltx_font_medium"> Illustration of the debate procedure.</span></span></figcaption>
</figure>
<section id="S2.SS1" class="ltx_subsection">
<h3 class="ltx_title ltx_title_subsection">
<span class="ltx_tag ltx_tag_subsection">2.1 </span>Multiagent Language Generation</h3>

<div id="S2.SS1.p1" class="ltx_para">
<p id="S2.SS1.p1.3" class="ltx_p">Consider your work process when solving the following math question on an exam: <span id="S2.SS1.p1.3.1" class="ltx_text ltx_font_italic">“What is the area of a triangle with side lengths of 3, 4, 5?"</span>. In one thread of work, you may recognize that the triangle side-lengths directly correspond to a right triangle, and thus directly compute the area as <math id="S2.SS1.p1.1.m1.1" class="ltx_Math" alttext="0.5\times 3\times 4=64" display="inline"><semantics id="S2.SS1.p1.1.m1.1a"><mrow id="S2.SS1.p1.1.m1.1.1" xref="S2.SS1.p1.1.m1.1.1.cmml"><mrow id="S2.SS1.p1.1.m1.1.1.2" xref="S2.SS1.p1.1.m1.1.1.2.cmml"><mn id="S2.SS1.p1.1.m1.1.1.2.2" xref="S2.SS1.p1.1.m1.1.1.2.2.cmml">0.5</mn><mo lspace="0.222em" rspace="0.222em" id="S2.SS1.p1.1.m1.1.1.2.1" xref="S2.SS1.p1.1.m1.1.1.2.1.cmml">×</mo><mn id="S2.SS1.p1.1.m1.1.1.2.3" xref="S2.SS1.p1.1.m1.1.1.2.3.cmml">3</mn><mo lspace="0.222em" rspace="0.222em" id="S2.SS1.p1.1.m1.1.1.2.1a" xref="S2.SS1.p1.1.m1.1.1.2.1.cmml">×</mo><mn id="S2.SS1.p1.1.m1.1.1.2.4" xref="S2.SS1.p1.1.m1.1.1.2.4.cmml">4</mn></mrow><mo id="S2.SS1.p1.1.m1.1.1.1" xref="S2.SS1.p1.1.m1.1.1.1.cmml">=</mo><mn id="S2.SS1.p1.1.m1.1.1.3" xref="S2.SS1.p1.1.m1.1.1.3.cmml">64</mn></mrow><annotation-xml encoding="MathML-Content" id="S2.SS1.p1.1.m1.1b"><apply id="S2.SS1.p1.1.m1.1.1.cmml" xref="S2.SS1.p1.1.m1.1.1"><eq id="S2.SS1.p1.1.m1.1.1.1.cmml" xref="S2.SS1.p1.1.m1.1.1.1"></eq><apply id="S2.SS1.p1.1.m1.1.1.2.cmml" xref="S2.SS1.p1.1.m1.1.1.2"><times id="S2.SS1.p1.1.m1.1.1.2.1.cmml" xref="S2.SS1.p1.1.m1.1.1.2.1"></times><cn type="float" id="S2.SS1.p1.1.m1.1.1.2.2.cmml" xref="S2.SS1.p1.1.m1.1.1.2.2">0.5</cn><cn type="integer" id="S2.SS1.p1.1.m1.1.1.2.3.cmml" xref="S2.SS1.p1.1.m1.1.1.2.3">3</cn><cn type="integer" id="S2.SS1.p1.1.m1.1.1.2.4.cmml" xref="S2.SS1.p1.1.m1.1.1.2.4">4</cn></apply><cn type="integer" id="S2.SS1.p1.1.m1.1.1.3.cmml" xref="S2.SS1.p1.1.m1.1.1.3">64</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p1.1.m1.1c">0.5\times 3\times 4=64</annotation></semantics></math>. To make sure that you have the right answer, you may then try to solve the problem differently by estimating an angle <math id="S2.SS1.p1.2.m2.1" class="ltx_Math" alttext="\theta" display="inline"><semantics id="S2.SS1.p1.2.m2.1a"><mi id="S2.SS1.p1.2.m2.1.1" xref="S2.SS1.p1.2.m2.1.1.cmml">θ</mi><annotation-xml encoding="MathML-Content" id="S2.SS1.p1.2.m2.1b"><ci id="S2.SS1.p1.2.m2.1.1.cmml" xref="S2.SS1.p1.2.m2.1.1">𝜃</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p1.2.m2.1c">\theta</annotation></semantics></math> in the triangle using the Law of Cosines, and then obtain the area by using the formula <math id="S2.SS1.p1.3.m3.2" class="ltx_Math" alttext="0.5\times 3\times 4\times\sin(\theta)" display="inline"><semantics id="S2.SS1.p1.3.m3.2a"><mrow id="S2.SS1.p1.3.m3.2.3" xref="S2.SS1.p1.3.m3.2.3.cmml"><mn id="S2.SS1.p1.3.m3.2.3.2" xref="S2.SS1.p1.3.m3.2.3.2.cmml">0.5</mn><mo lspace="0.222em" rspace="0.222em" id="S2.SS1.p1.3.m3.2.3.1" xref="S2.SS1.p1.3.m3.2.3.1.cmml">×</mo><mn id="S2.SS1.p1.3.m3.2.3.3" xref="S2.SS1.p1.3.m3.2.3.3.cmml">3</mn><mo lspace="0.222em" rspace="0.222em" id="S2.SS1.p1.3.m3.2.3.1a" xref="S2.SS1.p1.3.m3.2.3.1.cmml">×</mo><mn id="S2.SS1.p1.3.m3.2.3.4" xref="S2.SS1.p1.3.m3.2.3.4.cmml">4</mn><mo lspace="0.222em" rspace="0.222em" id="S2.SS1.p1.3.m3.2.3.1b" xref="S2.SS1.p1.3.m3.2.3.1.cmml">×</mo><mrow id="S2.SS1.p1.3.m3.2.3.5.2" xref="S2.SS1.p1.3.m3.2.3.5.1.cmml"><mi id="S2.SS1.p1.3.m3.1.1" xref="S2.SS1.p1.3.m3.1.1.cmml">sin</mi><mo id="S2.SS1.p1.3.m3.2.3.5.2a" xref="S2.SS1.p1.3.m3.2.3.5.1.cmml">⁡</mo><mrow id="S2.SS1.p1.3.m3.2.3.5.2.1" xref="S2.SS1.p1.3.m3.2.3.5.1.cmml"><mo stretchy="false" id="S2.SS1.p1.3.m3.2.3.5.2.1.1" xref="S2.SS1.p1.3.m3.2.3.5.1.cmml">(</mo><mi id="S2.SS1.p1.3.m3.2.2" xref="S2.SS1.p1.3.m3.2.2.cmml">θ</mi><mo stretchy="false" id="S2.SS1.p1.3.m3.2.3.5.2.1.2" xref="S2.SS1.p1.3.m3.2.3.5.1.cmml">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content" id="S2.SS1.p1.3.m3.2b"><apply id="S2.SS1.p1.3.m3.2.3.cmml" xref="S2.SS1.p1.3.m3.2.3"><times id="S2.SS1.p1.3.m3.2.3.1.cmml" xref="S2.SS1.p1.3.m3.2.3.1"></times><cn type="float" id="S2.SS1.p1.3.m3.2.3.2.cmml" xref="S2.SS1.p1.3.m3.2.3.2">0.5</cn><cn type="integer" id="S2.SS1.p1.3.m3.2.3.3.cmml" xref="S2.SS1.p1.3.m3.2.3.3">3</cn><cn type="integer" id="S2.SS1.p1.3.m3.2.3.4.cmml" xref="S2.SS1.p1.3.m3.2.3.4">4</cn><apply id="S2.SS1.p1.3.m3.2.3.5.1.cmml" xref="S2.SS1.p1.3.m3.2.3.5.2"><sin id="S2.SS1.p1.3.m3.1.1.cmml" xref="S2.SS1.p1.3.m3.1.1"></sin><ci id="S2.SS1.p1.3.m3.2.2.cmml" xref="S2.SS1.p1.3.m3.2.2">𝜃</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p1.3.m3.2c">0.5\times 3\times 4\times\sin(\theta)</annotation></semantics></math>, arriving at another answer to the given exam problem.</p>
</div>
<div id="S2.SS1.p2" class="ltx_para">
<p id="S2.SS1.p2.1" class="ltx_p">When these lines of work give the same answer, your confidence about the answer increases. In contrast, when these answers are different, individual lines of work may engage in a mental “debate" procedure, where you closely cross-examine the reasoning and assumptions of each line of work and refine solutions until a consistent answer.</p>
</div>
<div id="S2.SS1.p3" class="ltx_para">
<p id="S2.SS1.p3.1" class="ltx_p">Similarly, consider writing a biography of a historical figure. To ensure the factuality of the biography, you may consult multiple different sources on each fact. Facts that are consistent in each source increase your confidence about the fact. In contrast, facts that are inconsistent require careful cross-examination between sources to determine the final consistent data.</p>
</div>
<div id="S2.SS1.p4" class="ltx_para">
<p id="S2.SS1.p4.1" class="ltx_p">To mimic the above multi-threaded
reasoning process and multi-source factuality checking processes, we propose to generate answers subject to a multi-agent debate procedure between multiple instances of large language models. Given a question, multiple agents represented as copies of a large language model, generate answers to the question. Each response serves as a possible thought process or source of information which agents may re-examine to find consistent final answers.</p>
</div>
<div id="S2.SS1.p5" class="ltx_para">
<p id="S2.SS1.p5.1" class="ltx_p">After initial responses are generated from different agents, we initiate a round of debate between agents. Individual responses from other agents are concatenated and given as context to each agent, with each agent instructed to construct a new response based on such responses. Each language agent is thus responsible for both verifying the collection of responses given by other agents, and refining its own response based on other agents’ responses. We iteratively repeat this debate procedure over multiple rounds for improved performance.</p>
</div>
<div id="S2.SS1.p6" class="ltx_para">
<p id="S2.SS1.p6.1" class="ltx_p">Concretely, we first prompt each agent to independently solve the given problem or task. After each agent generates a response, we feed each agent a consensus prompt, illustrated in Figure <a href="#S2.F3" title="Figure 3 ‣ 2.1 Multiagent Language Generation ‣ 2 Language Generation through Multiagent Debate ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">3</span></a>, where each agent is instructed to update their responses based on the responses of other agents. This resultant consensus prompt may then be repeatedly given, using the updated responses of each agent.
We illustrate an overview of this multiagent debate procedure in Figure <a href="#S2.F2" title="Figure 2 ‣ 2 Language Generation through Multiagent Debate ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">2</span></a>.</p>
</div>
<div id="S2.SS1.p7" class="ltx_para">
<p id="S2.SS1.p7.1" class="ltx_p">Note that our proposed approach operates in an orthogonal manner to existing approaches to prompt language models. Given a question, we may apply additional techniques for prompting language models to further improve our debate procedure by eliciting additional more detailed responses from language models. We illustrate the synergy of our approach with existing approaches to prompting language models in Figure <a href="#S3.F6" title="Figure 6 ‣ Tasks. ‣ 3.1 Improving Reasoning with Multiagent Debate ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">6</span></a> and directly apply zero-shot chain-of-thought reasoning in our evaluations.</p>
</div>
<figure id="S2.SS1.2" class="ltx_table">
<div class="ltx_flex_figure ltx_flex_table">
<div class="ltx_flex_cell ltx_flex_size_2">
<div id="S2.SS1.2.2" class="ltx_inline-block ltx_figure_panel ltx_transformed_outer" style="width:406.2pt;height:81.9pt;vertical-align:-0.9pt;"><span class="ltx_transformed_inner" style="transform:translate(-22.6pt,4.5pt) scale(0.9,0.9) ;">
<table id="S2.SS1.2.2.2" class="ltx_tabular ltx_guessed_headers ltx_align_middle">
<thead class="ltx_thead">
<tr id="S2.SS1.2.2.2.3.1" class="ltx_tr">
<th id="S2.SS1.2.2.2.3.1.1" class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_th_row ltx_border_r" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S2.SS1.2.2.2.3.1.1.1" class="ltx_text ltx_font_bold" style="font-size:90%;">Debate Length</span></th>
<th id="S2.SS1.2.2.2.3.1.2" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S2.SS1.2.2.2.3.1.2.1" class="ltx_text ltx_font_bold" style="font-size:90%;">Prompt</span></th>
</tr>
</thead>
<tbody class="ltx_tbody">
<tr id="S2.SS1.2.2.2.4.1" class="ltx_tr">
<th id="S2.SS1.2.2.2.4.1.1" class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;" rowspan="2"><span id="S2.SS1.2.2.2.4.1.1.1" class="ltx_text" style="font-size:90%;">Short</span></th>
<td id="S2.SS1.2.2.2.4.1.2" class="ltx_td ltx_align_center ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="S2.SS1.2.2.2.4.1.2.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">" These are the solutions to the problem from other agents: [other answers]</em></td>
</tr>
<tr id="S2.SS1.1.1.1.1" class="ltx_tr">
<td id="S2.SS1.1.1.1.1.1" class="ltx_td ltx_align_center" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="S2.SS1.1.1.1.1.1.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">Based off the opinion of other agents, can you give an updated response <math id="S2.SS1.1.1.1.1.1.1.m1.1" class="ltx_Math" alttext="\ldots" display="inline"><semantics id="S2.SS1.1.1.1.1.1.1.m1.1a"><mi mathvariant="normal" id="S2.SS1.1.1.1.1.1.1.m1.1.1" xref="S2.SS1.1.1.1.1.1.1.m1.1.1.cmml">…</mi><annotation-xml encoding="MathML-Content" id="S2.SS1.1.1.1.1.1.1.m1.1b"><ci id="S2.SS1.1.1.1.1.1.1.m1.1.1.cmml" xref="S2.SS1.1.1.1.1.1.1.m1.1.1">…</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.1.1.1.1.1.1.m1.1c">\ldots</annotation></semantics></math>"</em></td>
</tr>
<tr id="S2.SS1.2.2.2.5.2" class="ltx_tr">
<th id="S2.SS1.2.2.2.5.2.1" class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_bb ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;" rowspan="2"><span id="S2.SS1.2.2.2.5.2.1.1" class="ltx_text" style="font-size:90%;">Long</span></th>
<td id="S2.SS1.2.2.2.5.2.2" class="ltx_td ltx_align_center ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="S2.SS1.2.2.2.5.2.2.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">" These are the solutions to the problem from other agents: [other answers]</em></td>
</tr>
<tr id="S2.SS1.2.2.2.2" class="ltx_tr">
<td id="S2.SS1.2.2.2.2.1" class="ltx_td ltx_align_center ltx_border_bb" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="S2.SS1.2.2.2.2.1.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">Using the opinion of other agents as additional advice, can you give an updated response <math id="S2.SS1.2.2.2.2.1.1.m1.1" class="ltx_Math" alttext="\ldots" display="inline"><semantics id="S2.SS1.2.2.2.2.1.1.m1.1a"><mi mathvariant="normal" id="S2.SS1.2.2.2.2.1.1.m1.1.1" xref="S2.SS1.2.2.2.2.1.1.m1.1.1.cmml">…</mi><annotation-xml encoding="MathML-Content" id="S2.SS1.2.2.2.2.1.1.m1.1b"><ci id="S2.SS1.2.2.2.2.1.1.m1.1.1.cmml" xref="S2.SS1.2.2.2.2.1.1.m1.1.1">…</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.2.2.2.2.1.1.m1.1c">\ldots</annotation></semantics></math>"</em></td>
</tr>
</tbody>
</table>
</span></div>
</div>
<div class="ltx_flex_cell ltx_flex_size_2">
<figure id="S2.F3" class="ltx_figure ltx_figure_panel ltx_align_center">
<figcaption class="ltx_caption" style="font-size:90%;"><span class="ltx_tag ltx_tag_figure">Figure 3: </span><span id="S2.F3.7.1" class="ltx_text ltx_font_bold">Prompts to induce long and short form debate.</span> Responses of other agents to questions are are inserted in the middle of the prompt (indicated with <em id="S2.F3.8.2" class="ltx_emph ltx_font_italic">[other answers]</em>)</figcaption>
</figure>
</div>
</div>
</figure>
</section>
<section id="S2.SS2" class="ltx_subsection">
<h3 class="ltx_title ltx_title_subsection">
<span class="ltx_tag ltx_tag_subsection">2.2 </span>Consensus in Debates</h3>

<div id="S2.SS2.p1" class="ltx_para">
<p id="S2.SS2.p1.1" class="ltx_p">Given multiple rounds of debate, how can we ensure that a set of language model agents will converge to a final consensus answer? In general, debate can be seen as a multi-agent game, where convergence is not guaranteed. Empirically, however, we find that language models are able to converge on a single shared answer after multiple rounds of debate (Figure <a href="#S3.F4" title="Figure 4 ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">4</span></a>).</p>
</div>
<div id="S2.SS2.p2" class="ltx_para">
<p id="S2.SS2.p2.1" class="ltx_p">We found that we could control the duration of debates by how changing how much a language model trusts its own outputs over those generated by other models through different prompts. We illustrate two prompts below in Figure <a href="#S2.F3" title="Figure 3 ‣ 2.1 Multiagent Language Generation ‣ 2 Language Generation through Multiagent Debate ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">3</span></a>, which we use to induce different debate durations between language models, and illustrate the effect of such prompts in Figure <a href="#S3.F12" title="Figure 12 ‣ Rounds of Debate ‣ 3.3 Analysis: Understanding Multiagent Debate ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">12</span></a>. In general, we found that prompts that encouraged models to be more “stubborn’ based on their own solutions led to longer debates and better final solutions. Overall, we observed that language model agents were relatively "agreeable", perhaps as a result of instruction tuning or reinforcement learning based on human feedback  <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib22" title="" class="ltx_ref">22</a>]</cite>.</p>
</div>
</section>
</section>
<section id="S3" class="ltx_section">
<h2 class="ltx_title ltx_title_section">
<span class="ltx_tag ltx_tag_section">3 </span>Experiments</h2>

<div id="S3.p1" class="ltx_para">
<p id="S3.p1.1" class="ltx_p">In our experiments, we evaluate our multiagent debate procedure and answer the following questions: <span id="S3.p1.1.1" class="ltx_text ltx_font_bold">(1)</span> To what extent does multiagent debate improve reasoning? <span id="S3.p1.1.2" class="ltx_text ltx_font_bold">(2)</span> To what extent does multiagent debate improve factual validity? <span id="S3.p1.1.3" class="ltx_text ltx_font_bold">(3)</span> What design choices enable multiagent debate to improve language generation performance?</p>
</div>
<figure id="S3.F4" class="ltx_figure"><img src="/html/2305.14325/assets/x3.png" id="S3.F4.g1" class="ltx_graphics ltx_centering ltx_img_landscape" width="461" height="121" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="S3.F4.3.1.1" class="ltx_text" style="font-size:90%;">Figure 4</span>: </span><span id="S3.F4.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Illustration of Solving Math.<span id="S3.F4.4.2.1" class="ltx_text ltx_font_medium"> Reasoning between agents is omitted.</span></span></figcaption>
</figure>
<figure id="S3.F5" class="ltx_figure"><img src="/html/2305.14325/assets/x4.png" id="S3.F5.g1" class="ltx_graphics ltx_centering ltx_img_landscape" width="415" height="86" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="S3.F5.3.1.1" class="ltx_text" style="font-size:90%;">Figure 5</span>: </span><span id="S3.F5.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Illustration of Solving Grade School Math.<span id="S3.F5.4.2.1" class="ltx_text ltx_font_medium"> Reasoning between agents omitted.</span></span></figcaption>
</figure>
<figure id="S3.T1" class="ltx_table">
<table id="S3.T1.16" class="ltx_tabular ltx_centering ltx_guessed_headers ltx_align_middle">
<thead class="ltx_thead">
<tr id="S3.T1.4.4" class="ltx_tr">
<th id="S3.T1.4.4.5" class="ltx_td ltx_align_left ltx_th ltx_th_column ltx_th_row" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T1.4.4.5.1" class="ltx_text ltx_font_bold" style="font-size:90%;">Model</span></th>
<th id="S3.T1.1.1.1" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T1.1.1.1.1" class="ltx_text ltx_font_bold" style="font-size:90%;">Arithmetic (%) <math id="S3.T1.1.1.1.1.m1.1" class="ltx_Math" alttext="\uparrow" display="inline"><semantics id="S3.T1.1.1.1.1.m1.1a"><mo stretchy="false" id="S3.T1.1.1.1.1.m1.1.1" xref="S3.T1.1.1.1.1.m1.1.1.cmml">↑</mo><annotation-xml encoding="MathML-Content" id="S3.T1.1.1.1.1.m1.1b"><ci id="S3.T1.1.1.1.1.m1.1.1.cmml" xref="S3.T1.1.1.1.1.m1.1.1">↑</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.T1.1.1.1.1.m1.1c">\uparrow</annotation></semantics></math></span></th>
<th id="S3.T1.2.2.2" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T1.2.2.2.1" class="ltx_text ltx_font_bold" style="font-size:90%;">Grade School Math (%) <math id="S3.T1.2.2.2.1.m1.1" class="ltx_Math" alttext="\uparrow" display="inline"><semantics id="S3.T1.2.2.2.1.m1.1a"><mo stretchy="false" id="S3.T1.2.2.2.1.m1.1.1" xref="S3.T1.2.2.2.1.m1.1.1.cmml">↑</mo><annotation-xml encoding="MathML-Content" id="S3.T1.2.2.2.1.m1.1b"><ci id="S3.T1.2.2.2.1.m1.1.1.cmml" xref="S3.T1.2.2.2.1.m1.1.1">↑</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.T1.2.2.2.1.m1.1c">\uparrow</annotation></semantics></math></span></th>
<th id="S3.T1.4.4.4" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T1.4.4.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Chess (<math id="S3.T1.3.3.3.1.m1.1" class="ltx_Math" alttext="\Delta" display="inline"><semantics id="S3.T1.3.3.3.1.m1.1a"><mi mathvariant="normal" id="S3.T1.3.3.3.1.m1.1.1" xref="S3.T1.3.3.3.1.m1.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="S3.T1.3.3.3.1.m1.1b"><ci id="S3.T1.3.3.3.1.m1.1.1.cmml" xref="S3.T1.3.3.3.1.m1.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.T1.3.3.3.1.m1.1c">\Delta</annotation></semantics></math>PS) <math id="S3.T1.4.4.4.2.m2.1" class="ltx_Math" alttext="\uparrow" display="inline"><semantics id="S3.T1.4.4.4.2.m2.1a"><mo stretchy="false" id="S3.T1.4.4.4.2.m2.1.1" xref="S3.T1.4.4.4.2.m2.1.1.cmml">↑</mo><annotation-xml encoding="MathML-Content" id="S3.T1.4.4.4.2.m2.1b"><ci id="S3.T1.4.4.4.2.m2.1.1.cmml" xref="S3.T1.4.4.4.2.m2.1.1">↑</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.T1.4.4.4.2.m2.1c">\uparrow</annotation></semantics></math></span></th>
</tr>
</thead>
<tbody class="ltx_tbody">
<tr id="S3.T1.7.7" class="ltx_tr">
<th id="S3.T1.7.7.4" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T1.7.7.4.1" class="ltx_text" style="font-size:90%;">Single Agent</span></th>
<td id="S3.T1.5.5.1" class="ltx_td ltx_align_center ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;">
<span id="S3.T1.5.5.1.1" class="ltx_text" style="font-size:90%;">67.0 </span><math id="S3.T1.5.5.1.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T1.5.5.1.m1.1a"><mo mathsize="90%" id="S3.T1.5.5.1.m1.1.1" xref="S3.T1.5.5.1.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T1.5.5.1.m1.1b"><csymbol cd="latexml" id="S3.T1.5.5.1.m1.1.1.cmml" xref="S3.T1.5.5.1.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T1.5.5.1.m1.1c">\pm</annotation></semantics></math><span id="S3.T1.5.5.1.2" class="ltx_text" style="font-size:90%;"> 4.7</span>
</td>
<td id="S3.T1.6.6.2" class="ltx_td ltx_align_center ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;">
<span id="S3.T1.6.6.2.1" class="ltx_text" style="font-size:90%;">77.0 </span><math id="S3.T1.6.6.2.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T1.6.6.2.m1.1a"><mo mathsize="90%" id="S3.T1.6.6.2.m1.1.1" xref="S3.T1.6.6.2.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T1.6.6.2.m1.1b"><csymbol cd="latexml" id="S3.T1.6.6.2.m1.1.1.cmml" xref="S3.T1.6.6.2.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T1.6.6.2.m1.1c">\pm</annotation></semantics></math><span id="S3.T1.6.6.2.2" class="ltx_text" style="font-size:90%;"> 4.2</span>
</td>
<td id="S3.T1.7.7.3" class="ltx_td ltx_align_center ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;">
<span id="S3.T1.7.7.3.1" class="ltx_text" style="font-size:90%;">91.4 </span><math id="S3.T1.7.7.3.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T1.7.7.3.m1.1a"><mo mathsize="90%" id="S3.T1.7.7.3.m1.1.1" xref="S3.T1.7.7.3.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T1.7.7.3.m1.1b"><csymbol cd="latexml" id="S3.T1.7.7.3.m1.1.1.cmml" xref="S3.T1.7.7.3.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T1.7.7.3.m1.1c">\pm</annotation></semantics></math><span id="S3.T1.7.7.3.2" class="ltx_text" style="font-size:90%;"> 10.6</span>
</td>
</tr>
<tr id="S3.T1.10.10" class="ltx_tr">
<th id="S3.T1.10.10.4" class="ltx_td ltx_align_left ltx_th ltx_th_row" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T1.10.10.4.1" class="ltx_text" style="font-size:90%;">Single Agent (Reflection)</span></th>
<td id="S3.T1.8.8.1" class="ltx_td ltx_align_center" style="padding-left:5.5pt;padding-right:5.5pt;">
<span id="S3.T1.8.8.1.1" class="ltx_text" style="font-size:90%;">72.1 </span><math id="S3.T1.8.8.1.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T1.8.8.1.m1.1a"><mo mathsize="90%" id="S3.T1.8.8.1.m1.1.1" xref="S3.T1.8.8.1.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T1.8.8.1.m1.1b"><csymbol cd="latexml" id="S3.T1.8.8.1.m1.1.1.cmml" xref="S3.T1.8.8.1.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T1.8.8.1.m1.1c">\pm</annotation></semantics></math><span id="S3.T1.8.8.1.2" class="ltx_text" style="font-size:90%;"> 4.5</span>
</td>
<td id="S3.T1.9.9.2" class="ltx_td ltx_align_center" style="padding-left:5.5pt;padding-right:5.5pt;">
<span id="S3.T1.9.9.2.1" class="ltx_text" style="font-size:90%;">75.0 </span><math id="S3.T1.9.9.2.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T1.9.9.2.m1.1a"><mo mathsize="90%" id="S3.T1.9.9.2.m1.1.1" xref="S3.T1.9.9.2.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T1.9.9.2.m1.1b"><csymbol cd="latexml" id="S3.T1.9.9.2.m1.1.1.cmml" xref="S3.T1.9.9.2.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T1.9.9.2.m1.1c">\pm</annotation></semantics></math><span id="S3.T1.9.9.2.2" class="ltx_text" style="font-size:90%;"> 4.3</span>
</td>
<td id="S3.T1.10.10.3" class="ltx_td ltx_align_center" style="padding-left:5.5pt;padding-right:5.5pt;">
<span id="S3.T1.10.10.3.1" class="ltx_text" style="font-size:90%;">102.1 </span><math id="S3.T1.10.10.3.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T1.10.10.3.m1.1a"><mo mathsize="90%" id="S3.T1.10.10.3.m1.1.1" xref="S3.T1.10.10.3.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T1.10.10.3.m1.1b"><csymbol cd="latexml" id="S3.T1.10.10.3.m1.1.1.cmml" xref="S3.T1.10.10.3.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T1.10.10.3.m1.1c">\pm</annotation></semantics></math><span id="S3.T1.10.10.3.2" class="ltx_text" style="font-size:90%;"> 11.9</span>
</td>
</tr>
<tr id="S3.T1.13.13" class="ltx_tr">
<th id="S3.T1.13.13.4" class="ltx_td ltx_align_left ltx_th ltx_th_row" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T1.13.13.4.1" class="ltx_text" style="font-size:90%;">Multi-Agent (Majority)</span></th>
<td id="S3.T1.11.11.1" class="ltx_td ltx_align_center" style="padding-left:5.5pt;padding-right:5.5pt;">
<span id="S3.T1.11.11.1.1" class="ltx_text" style="font-size:90%;">69.0 </span><math id="S3.T1.11.11.1.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T1.11.11.1.m1.1a"><mo mathsize="90%" id="S3.T1.11.11.1.m1.1.1" xref="S3.T1.11.11.1.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T1.11.11.1.m1.1b"><csymbol cd="latexml" id="S3.T1.11.11.1.m1.1.1.cmml" xref="S3.T1.11.11.1.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T1.11.11.1.m1.1c">\pm</annotation></semantics></math><span id="S3.T1.11.11.1.2" class="ltx_text" style="font-size:90%;"> 4.6</span>
</td>
<td id="S3.T1.12.12.2" class="ltx_td ltx_align_center" style="padding-left:5.5pt;padding-right:5.5pt;">
<span id="S3.T1.12.12.2.1" class="ltx_text" style="font-size:90%;">81.0 </span><math id="S3.T1.12.12.2.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T1.12.12.2.m1.1a"><mo mathsize="90%" id="S3.T1.12.12.2.m1.1.1" xref="S3.T1.12.12.2.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T1.12.12.2.m1.1b"><csymbol cd="latexml" id="S3.T1.12.12.2.m1.1.1.cmml" xref="S3.T1.12.12.2.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T1.12.12.2.m1.1c">\pm</annotation></semantics></math><span id="S3.T1.12.12.2.2" class="ltx_text" style="font-size:90%;"> 3.9</span>
</td>
<td id="S3.T1.13.13.3" class="ltx_td ltx_align_center" style="padding-left:5.5pt;padding-right:5.5pt;">
<span id="S3.T1.13.13.3.1" class="ltx_text" style="font-size:90%;">102.2 </span><math id="S3.T1.13.13.3.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T1.13.13.3.m1.1a"><mo mathsize="90%" id="S3.T1.13.13.3.m1.1.1" xref="S3.T1.13.13.3.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T1.13.13.3.m1.1b"><csymbol cd="latexml" id="S3.T1.13.13.3.m1.1.1.cmml" xref="S3.T1.13.13.3.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T1.13.13.3.m1.1c">\pm</annotation></semantics></math><span id="S3.T1.13.13.3.2" class="ltx_text" style="font-size:90%;"> 6.2</span>
</td>
</tr>
<tr id="S3.T1.16.16" class="ltx_tr">
<th id="S3.T1.16.16.4" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_bb" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T1.16.16.4.1" class="ltx_text" style="font-size:90%;">Multi-Agent (Debate)</span></th>
<td id="S3.T1.14.14.1" class="ltx_td ltx_align_center ltx_border_bb" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T1.14.14.1.1" class="ltx_text ltx_font_bold" style="font-size:90%;">81.8 <math id="S3.T1.14.14.1.1.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T1.14.14.1.1.m1.1a"><mo id="S3.T1.14.14.1.1.m1.1.1" xref="S3.T1.14.14.1.1.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T1.14.14.1.1.m1.1b"><csymbol cd="latexml" id="S3.T1.14.14.1.1.m1.1.1.cmml" xref="S3.T1.14.14.1.1.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T1.14.14.1.1.m1.1c">\pm</annotation></semantics></math> 2.3</span></td>
<td id="S3.T1.15.15.2" class="ltx_td ltx_align_center ltx_border_bb" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T1.15.15.2.1" class="ltx_text ltx_font_bold" style="font-size:90%;">85.0 <math id="S3.T1.15.15.2.1.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T1.15.15.2.1.m1.1a"><mo id="S3.T1.15.15.2.1.m1.1.1" xref="S3.T1.15.15.2.1.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T1.15.15.2.1.m1.1b"><csymbol cd="latexml" id="S3.T1.15.15.2.1.m1.1.1.cmml" xref="S3.T1.15.15.2.1.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T1.15.15.2.1.m1.1c">\pm</annotation></semantics></math> 3.5</span></td>
<td id="S3.T1.16.16.3" class="ltx_td ltx_align_center ltx_border_bb" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T1.16.16.3.1" class="ltx_text ltx_font_bold" style="font-size:90%;">122.9 <math id="S3.T1.16.16.3.1.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T1.16.16.3.1.m1.1a"><mo id="S3.T1.16.16.3.1.m1.1.1" xref="S3.T1.16.16.3.1.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T1.16.16.3.1.m1.1b"><csymbol cd="latexml" id="S3.T1.16.16.3.1.m1.1.1.cmml" xref="S3.T1.16.16.3.1.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T1.16.16.3.1.m1.1c">\pm</annotation></semantics></math> 7.6</span></td>
</tr>
</tbody>
</table>
<figcaption class="ltx_caption ltx_centering" style="font-size:90%;"><span class="ltx_tag ltx_tag_table">Table 1: </span><span id="S3.T1.21.1" class="ltx_text ltx_font_bold">Multiagent Debate Improves Reasoning</span> Multi-agent debate improves the reasoning abilities of language models. Multi-agent results in the table are run with 3 agents and two rounds of debate.</figcaption>
</figure>
<section id="S3.SS1" class="ltx_subsection">
<h3 class="ltx_title ltx_title_subsection">
<span class="ltx_tag ltx_tag_subsection">3.1 </span>Improving Reasoning with Multiagent Debate</h3>

<div id="S3.SS1.p1" class="ltx_para">
<p id="S3.SS1.p1.1" class="ltx_p">We first evaluate the extent to which multiagent debate improves the underlying reasoning process in language models.</p>
</div>
<section id="S3.SS1.SSS0.Px1" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Tasks.</h4>

<div id="S3.SS1.SSS0.Px1.p1" class="ltx_para">
<p id="S3.SS1.SSS0.Px1.p1.1" class="ltx_p">We evaluate our approach on three reasoning tasks of increasing difficulty:</p>
<ul id="S3.I1" class="ltx_itemize">
<li id="S3.I1.i1" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_item">•</span> 
<div id="S3.I1.i1.p1" class="ltx_para">
<p id="S3.I1.i1.p1.1" class="ltx_p"><span id="S3.I1.i1.p1.1.1" class="ltx_text ltx_font_typewriter">Arithmetic.</span> We first evaluate the ability of models to correctly evaluate an arithmetic expression (containing addition, multiplication, and subtraction) consisting of six different two-digit numbers. For example: <span id="S3.I1.i1.p1.1.2" class="ltx_text ltx_font_italic">What is the result of 12+15*21+0-3*27?</span></p>
</div>
</li>
<li id="S3.I1.i2" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_item">•</span> 
<div id="S3.I1.i2.p1" class="ltx_para">
<p id="S3.I1.i2.p1.1" class="ltx_p"><span id="S3.I1.i2.p1.1.1" class="ltx_text ltx_font_typewriter">GSM8K.</span> Next, we consider harder mathematical reasoning tasks. Using the GSM8K dataset <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib3" title="" class="ltx_ref">3</a>]</cite>, the models must correctly solve grade school mathematical reasoning tasks.</p>
</div>
</li>
<li id="S3.I1.i3" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_item">•</span> 
<div id="S3.I1.i3.p1" class="ltx_para">
<p id="S3.I1.i3.p1.1" class="ltx_p"><span id="S3.I1.i3.p1.1.1" class="ltx_text ltx_font_typewriter">Chess Move Prediction.</span> Finally, we consider the strategic reasoning of the ability of models, and ask models to predict the best next move in a game of chess, given the first 14 moves of a chess game between two chess grand-masters described in PGN notation <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib6" title="" class="ltx_ref">6</a>]</cite>.</p>
</div>
</li>
</ul>
<p id="S3.SS1.SSS0.Px1.p1.2" class="ltx_p">We report the accuracy of final answers in arithmetic and GSM8K tasks and report the pawn score (advantage) of predicted moves, as estimated by Stockfish in the Chess move prediction tasks. Additional details may be found in the Appendix.</p>
</div>
<figure id="S3.F6" class="ltx_figure ltx_align_floatright"><img src="/html/2305.14325/assets/x5.png" id="S3.F6.g1" class="ltx_graphics ltx_centering ltx_img_landscape" width="461" height="303" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="S3.F6.3.1.1" class="ltx_text" style="font-size:90%;">Figure 6</span>: </span><span id="S3.F6.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Synergy with Other Methods.<span id="S3.F6.4.2.1" class="ltx_text ltx_font_medium"> Performance of debate increases with use of Chain of Thought prompting.</span></span></figcaption>
</figure>
<figure id="S3.F7" class="ltx_figure"><img src="/html/2305.14325/assets/x6.png" id="S3.F7.g1" class="ltx_graphics ltx_centering ltx_img_landscape" width="415" height="323" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="S3.F7.3.1.1" class="ltx_text" style="font-size:90%;">Figure 7</span>: </span><span id="S3.F7.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Illustration of Generating Biographies.<span id="S3.F7.4.2.1" class="ltx_text ltx_font_medium"> Illustration of generating bullet biographies of computer scientists. For brevity, only the first 3 generated bullets are shown.</span></span></figcaption>
</figure>
<figure id="S3.F8" class="ltx_figure"><img src="/html/2305.14325/assets/x7.png" id="S3.F8.g1" class="ltx_graphics ltx_centering ltx_img_landscape" width="461" height="111" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="S3.F8.3.1.1" class="ltx_text" style="font-size:90%;">Figure 8</span>: </span><span id="S3.F8.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Illustration of MMLU.<span id="S3.F8.4.2.1" class="ltx_text ltx_font_medium"> Illustration of debate when answering factual tasks. Reasoning omitted.</span></span></figcaption>
</figure>
</section>
<section id="S3.SS1.SSS0.Px2" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Baselines.</h4>

<div id="S3.SS1.SSS0.Px2.p1" class="ltx_para">
<p id="S3.SS1.SSS0.Px2.p1.1" class="ltx_p">We compare our approach to three alternative approaches to generate responses for reasoning problems. First, we ask agents to directly generate responses (single agent). Next, we consider asking language models to generate and then "self-reflect" on the responses generated <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib26" title="" class="ltx_ref">26</a>, <a href="#bib.bib18" title="" class="ltx_ref">18</a>]</cite>. Finally, we consider generating responses using multiple agents and performing majority voting <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib15" title="" class="ltx_ref">15</a>, <a href="#bib.bib3" title="" class="ltx_ref">3</a>]</cite>. As the focus of our experiments is to verify the effectiveness of multiagent agent debate, we run both baselines and our approach, using the identical starting prompt and language model across all evaluations. We evaluate models in a zero-shot setting, with prompts found in the Appendix of the paper. We use chatGPT-based language model  <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib21" title="" class="ltx_ref">21</a>]</cite> in all our experiments except those in Figure <a href="#S3.F11" title="Figure 11 ‣ Results. ‣ 3.2 Extracting Factual Information from Multiagent Debate ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">11</span></a> where we compare multiple language models.</p>
</div>
<div id="S3.SS1.SSS0.Px2.p2" class="ltx_para">
<p id="S3.SS1.SSS0.Px2.p2.1" class="ltx_p">Due to computational expense, we evaluate our approach across benchmarks mainly using three agents with two rounds of debates, although we found further gains with both more agents and rounds of debate (Figure <a href="#S3.F10" title="Figure 10 ‣ Compatibility with other reasoning methods. ‣ 3.1 Improving Reasoning with Multiagent Debate ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">10</span></a>). Additional evaluation details are found in the Appendix.</p>
</div>
</section>
<section id="S3.SS1.SSS0.Px3" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Quantitative Results.</h4>

<div id="S3.SS1.SSS0.Px3.p1" class="ltx_para">
<p id="S3.SS1.SSS0.Px3.p1.1" class="ltx_p">In Table <a href="#S3.T1" title="Table 1 ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">1</span></a>, we report the results of each approach on arithmetic, grade school math, and chess reasoning task. In each task, we observe that utilizing multiple different agents to generate solutions improves performance over using a single language model agent to generate a solution. Simultaneously, we also see that reflection, where a language model is asked to critique its early generation, generally gives a modest boost in performance. Multiagent debate, which may be seen as a combination of both reflection and multiagent generation, gives a substantial boost in reasoning across each of the tasks.</p>
</div>
</section>
<section id="S3.SS1.SSS0.Px4" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Qualitative Results.</h4>

<div id="S3.SS1.SSS0.Px4.p1" class="ltx_para">
<p id="S3.SS1.SSS0.Px4.p1.1" class="ltx_p">In Figure  <a href="#S3.F4" title="Figure 4 ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">4</span></a>, <a href="#S3.F5" title="Figure 5 ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">5</span></a>, we provide qualitative illustrations of the debate procedure between models. Interestingly, we find cases in which all models initially give an incorrect response, yet the result of debate still obtains the correct answer as agents critique each others’ reasoning. Thus, the purpose of our debate isn’t just to amplify a correct answer – all models can initially be wrong but arrive at the correct answer through the debate process.</p>
</div>
</section>
<section id="S3.SS1.SSS0.Px5" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Compatibility with other reasoning methods.</h4>

<div id="S3.SS1.SSS0.Px5.p1" class="ltx_para">
<p id="S3.SS1.SSS0.Px5.p1.1" class="ltx_p">Our multiagent generation procedure operates orthogonally approach to other prompting methods which focus on single-agent generation. In Figure <a href="#S3.F6" title="Figure 6 ‣ Tasks. ‣ 3.1 Improving Reasoning with Multiagent Debate ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">6</span></a>, we illustrate the performance of multi-agent debate with and without zero-shot chain-of-thought prompting <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib11" title="" class="ltx_ref">11</a>]</cite> on GSM8K. In both settings, multiagent generation is beneficial.</p>
</div>
<figure id="S3.T2" class="ltx_table">
<table id="S3.T2.9" class="ltx_tabular ltx_centering ltx_guessed_headers ltx_align_middle">
<thead class="ltx_thead">
<tr id="S3.T2.9.10.1" class="ltx_tr">
<th id="S3.T2.9.10.1.1" class="ltx_td ltx_align_left ltx_th ltx_th_column ltx_th_row" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T2.9.10.1.1.1" class="ltx_text ltx_font_bold" style="font-size:90%;">Model</span></th>
<th id="S3.T2.9.10.1.2" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T2.9.10.1.2.1" class="ltx_text ltx_font_bold" style="font-size:90%;">Biographies</span></th>
<th id="S3.T2.9.10.1.3" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T2.9.10.1.3.1" class="ltx_text ltx_font_bold" style="font-size:90%;">MMLU</span></th>
<th id="S3.T2.9.10.1.4" class="ltx_td ltx_align_center ltx_th ltx_th_column" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T2.9.10.1.4.1" class="ltx_text ltx_font_bold" style="font-size:90%;">Chess Move Validity</span></th>
</tr>
</thead>
<tbody class="ltx_tbody">
<tr id="S3.T2.3.3" class="ltx_tr">
<th id="S3.T2.3.3.4" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T2.3.3.4.1" class="ltx_text" style="font-size:90%;">Single Agent</span></th>
<td id="S3.T2.1.1.1" class="ltx_td ltx_align_center ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;">
<span id="S3.T2.1.1.1.1" class="ltx_text" style="font-size:90%;">66.0 </span><math id="S3.T2.1.1.1.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T2.1.1.1.m1.1a"><mo mathsize="90%" id="S3.T2.1.1.1.m1.1.1" xref="S3.T2.1.1.1.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T2.1.1.1.m1.1b"><csymbol cd="latexml" id="S3.T2.1.1.1.m1.1.1.cmml" xref="S3.T2.1.1.1.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T2.1.1.1.m1.1c">\pm</annotation></semantics></math><span id="S3.T2.1.1.1.2" class="ltx_text" style="font-size:90%;"> 2.2</span>
</td>
<td id="S3.T2.2.2.2" class="ltx_td ltx_align_center ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;">
<span id="S3.T2.2.2.2.1" class="ltx_text" style="font-size:90%;">63.9 </span><math id="S3.T2.2.2.2.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T2.2.2.2.m1.1a"><mo mathsize="90%" id="S3.T2.2.2.2.m1.1.1" xref="S3.T2.2.2.2.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T2.2.2.2.m1.1b"><csymbol cd="latexml" id="S3.T2.2.2.2.m1.1.1.cmml" xref="S3.T2.2.2.2.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T2.2.2.2.m1.1c">\pm</annotation></semantics></math><span id="S3.T2.2.2.2.2" class="ltx_text" style="font-size:90%;"> 4.8</span>
</td>
<td id="S3.T2.3.3.3" class="ltx_td ltx_align_center ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;">
<span id="S3.T2.3.3.3.1" class="ltx_text" style="font-size:90%;">29.3 </span><math id="S3.T2.3.3.3.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T2.3.3.3.m1.1a"><mo mathsize="90%" id="S3.T2.3.3.3.m1.1.1" xref="S3.T2.3.3.3.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T2.3.3.3.m1.1b"><csymbol cd="latexml" id="S3.T2.3.3.3.m1.1.1.cmml" xref="S3.T2.3.3.3.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T2.3.3.3.m1.1c">\pm</annotation></semantics></math><span id="S3.T2.3.3.3.2" class="ltx_text" style="font-size:90%;"> 2.6</span>
</td>
</tr>
<tr id="S3.T2.6.6" class="ltx_tr">
<th id="S3.T2.6.6.4" class="ltx_td ltx_align_left ltx_th ltx_th_row" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T2.6.6.4.1" class="ltx_text" style="font-size:90%;">Single Agent (Reflection)</span></th>
<td id="S3.T2.4.4.1" class="ltx_td ltx_align_center" style="padding-left:5.5pt;padding-right:5.5pt;">
<span id="S3.T2.4.4.1.1" class="ltx_text" style="font-size:90%;">68.3 </span><math id="S3.T2.4.4.1.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T2.4.4.1.m1.1a"><mo mathsize="90%" id="S3.T2.4.4.1.m1.1.1" xref="S3.T2.4.4.1.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T2.4.4.1.m1.1b"><csymbol cd="latexml" id="S3.T2.4.4.1.m1.1.1.cmml" xref="S3.T2.4.4.1.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T2.4.4.1.m1.1c">\pm</annotation></semantics></math><span id="S3.T2.4.4.1.2" class="ltx_text" style="font-size:90%;"> 2.9</span>
</td>
<td id="S3.T2.5.5.2" class="ltx_td ltx_align_center" style="padding-left:5.5pt;padding-right:5.5pt;">
<span id="S3.T2.5.5.2.1" class="ltx_text" style="font-size:90%;">57.7 </span><math id="S3.T2.5.5.2.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T2.5.5.2.m1.1a"><mo mathsize="90%" id="S3.T2.5.5.2.m1.1.1" xref="S3.T2.5.5.2.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T2.5.5.2.m1.1b"><csymbol cd="latexml" id="S3.T2.5.5.2.m1.1.1.cmml" xref="S3.T2.5.5.2.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T2.5.5.2.m1.1c">\pm</annotation></semantics></math><span id="S3.T2.5.5.2.2" class="ltx_text" style="font-size:90%;"> 5.0</span>
</td>
<td id="S3.T2.6.6.3" class="ltx_td ltx_align_center" style="padding-left:5.5pt;padding-right:5.5pt;">
<span id="S3.T2.6.6.3.1" class="ltx_text" style="font-size:90%;">38.8 </span><math id="S3.T2.6.6.3.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T2.6.6.3.m1.1a"><mo mathsize="90%" id="S3.T2.6.6.3.m1.1.1" xref="S3.T2.6.6.3.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T2.6.6.3.m1.1b"><csymbol cd="latexml" id="S3.T2.6.6.3.m1.1.1.cmml" xref="S3.T2.6.6.3.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T2.6.6.3.m1.1c">\pm</annotation></semantics></math><span id="S3.T2.6.6.3.2" class="ltx_text" style="font-size:90%;"> 2.9</span>
</td>
</tr>
<tr id="S3.T2.9.9" class="ltx_tr">
<th id="S3.T2.9.9.4" class="ltx_td ltx_align_left ltx_th ltx_th_row ltx_border_bb" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T2.9.9.4.1" class="ltx_text" style="font-size:90%;">Multi-Agent (Debate)</span></th>
<td id="S3.T2.7.7.1" class="ltx_td ltx_align_center ltx_border_bb" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T2.7.7.1.1" class="ltx_text ltx_font_bold" style="font-size:90%;">73.8 <math id="S3.T2.7.7.1.1.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T2.7.7.1.1.m1.1a"><mo id="S3.T2.7.7.1.1.m1.1.1" xref="S3.T2.7.7.1.1.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T2.7.7.1.1.m1.1b"><csymbol cd="latexml" id="S3.T2.7.7.1.1.m1.1.1.cmml" xref="S3.T2.7.7.1.1.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T2.7.7.1.1.m1.1c">\pm</annotation></semantics></math> 2.3</span></td>
<td id="S3.T2.8.8.2" class="ltx_td ltx_align_center ltx_border_bb" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T2.8.8.2.1" class="ltx_text ltx_font_bold" style="font-size:90%;">71.1 <math id="S3.T2.8.8.2.1.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T2.8.8.2.1.m1.1a"><mo id="S3.T2.8.8.2.1.m1.1.1" xref="S3.T2.8.8.2.1.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T2.8.8.2.1.m1.1b"><csymbol cd="latexml" id="S3.T2.8.8.2.1.m1.1.1.cmml" xref="S3.T2.8.8.2.1.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T2.8.8.2.1.m1.1c">\pm</annotation></semantics></math> 4.6</span></td>
<td id="S3.T2.9.9.3" class="ltx_td ltx_align_center ltx_border_bb" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="S3.T2.9.9.3.1" class="ltx_text ltx_font_bold" style="font-size:90%;">45.2 <math id="S3.T2.9.9.3.1.m1.1" class="ltx_Math" alttext="\pm" display="inline"><semantics id="S3.T2.9.9.3.1.m1.1a"><mo id="S3.T2.9.9.3.1.m1.1.1" xref="S3.T2.9.9.3.1.m1.1.1.cmml">±</mo><annotation-xml encoding="MathML-Content" id="S3.T2.9.9.3.1.m1.1b"><csymbol cd="latexml" id="S3.T2.9.9.3.1.m1.1.1.cmml" xref="S3.T2.9.9.3.1.m1.1.1">plus-or-minus</csymbol></annotation-xml><annotation encoding="application/x-tex" id="S3.T2.9.9.3.1.m1.1c">\pm</annotation></semantics></math> 2.9</span></td>
</tr>
</tbody>
</table>
<figcaption class="ltx_caption ltx_centering" style="font-size:90%;"><span class="ltx_tag ltx_tag_table">Table 2: </span><span id="S3.T2.14.1" class="ltx_text ltx_font_bold">Multiagent Debate Improves Factual Accuracy</span> Multi-agent debate improves the factual accuracy.</figcaption>
</figure>
<figure id="S3.F9" class="ltx_figure"><img src="/html/2305.14325/assets/x8.png" id="S3.F9.g1" class="ltx_graphics ltx_centering ltx_img_landscape" width="461" height="95" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="S3.F9.3.1.1" class="ltx_text" style="font-size:90%;">Figure 9</span>: </span><span id="S3.F9.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Expressing Uncertainty with Multiple Answers.<span id="S3.F9.4.2.1" class="ltx_text ltx_font_medium"> For facts that a language model is uncertain about, different language agents generate different facts. Debate causes agents to converge to one fact that is more accurate, but not necessarily always factually correct.</span></span></figcaption>
</figure>
<figure id="S3.F10" class="ltx_figure"><img src="/html/2305.14325/assets/x9.png" id="S3.F10.g1" class="ltx_graphics ltx_centering ltx_img_landscape" width="461" height="147" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="S3.F10.4.1.1" class="ltx_text" style="font-size:90%;">Figure 10</span>: </span><span id="S3.F10.5.2" class="ltx_text ltx_font_bold" style="font-size:90%;">(a) Performance with Increased Agents.<span id="S3.F10.5.2.1" class="ltx_text ltx_font_medium"> Performance improves as the number of underlying agents involved in debate increases. </span>(b) Performance with Increased Rounds.<span id="S3.F10.5.2.2" class="ltx_text ltx_font_medium"> Performance rises as the number of rounds of underlying debate increases.</span></span></figcaption>
</figure>
</section>
</section>
<section id="S3.SS2" class="ltx_subsection">
<h3 class="ltx_title ltx_title_subsection">
<span class="ltx_tag ltx_tag_subsection">3.2 </span>Extracting Factual Information from Multiagent Debate</h3>

<div id="S3.SS2.p1" class="ltx_para">
<p id="S3.SS2.p1.1" class="ltx_p">We next evaluate the extent to which multiagent debate improves the underlying factuality in language models.</p>
</div>
<section id="S3.SS2.SSS0.Px1" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Tasks.</h4>

<div id="S3.SS2.SSS0.Px1.p1" class="ltx_para">
<p id="S3.SS2.SSS0.Px1.p1.1" class="ltx_p">We evaluate the factuality of language models in three different settings:</p>
</div>
<div id="S3.SS2.SSS0.Px1.p2" class="ltx_para">
<ul id="S3.I2" class="ltx_itemize">
<li id="S3.I2.i1" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_item">•</span> 
<div id="S3.I2.i1.p1" class="ltx_para">
<p id="S3.I2.i1.p1.1" class="ltx_p"><span id="S3.I2.i1.p1.1.1" class="ltx_text ltx_font_typewriter">Biographies.</span> To evaluate the factuality of language models, we introduce a novel task of accurately generating historical biographies of people. In preliminary testing, we found that existing language models had a tendency to hallucinate many facts on this task. We constructed ground truth bullet point biographies of 524 well-known computer scientists. We then asked language models to generate bullet point biographies for each person, and evaluated the accuracy at which each ground truth bullet point agreed with generated bullets. We report additional evaluation details in the Appendix.</p>
</div>
</li>
<li id="S3.I2.i2" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_item">•</span> 
<div id="S3.I2.i2.p1" class="ltx_para">
<p id="S3.I2.i2.p1.1" class="ltx_p"><span id="S3.I2.i2.p1.1.1" class="ltx_text ltx_font_typewriter">MMLU.</span> Next, we assess the factuality of language models in responding to different factual knowledge questions typically learned and assessed in different exams. We utilize the existing MMLU dataset <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib8" title="" class="ltx_ref">8</a>]</cite> to benchmark the accuracy of responses.</p>
</div>
</li>
<li id="S3.I2.i3" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_item">•</span> 
<div id="S3.I2.i3.p1" class="ltx_para">
<p id="S3.I2.i3.p1.1" class="ltx_p"><span id="S3.I2.i3.p1.1.1" class="ltx_text ltx_font_typewriter">Chess Move Validity.</span> Lastly, we study the hallucinations in language models when planning under to the given rules of an existing environment or game. Specifically, we measure the validity of possible moves in a game of Chess given by BIG-Bench Chess-State Tracking Benchmark  <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib27" title="" class="ltx_ref">27</a>]</cite> task of chess-move prediction. In this task, an agent is given a set of next moves, and must make a valid next move of a piece on a board.</p>
</div>
</li>
</ul>
</div>
</section>
<section id="S3.SS2.SSS0.Px2" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Baselines.</h4>

<div id="S3.SS2.SSS0.Px2.p1" class="ltx_para">
<p id="S3.SS2.SSS0.Px2.p1.1" class="ltx_p">We use the same baselines as in Section <a href="#S3.SS1" title="3.1 Improving Reasoning with Multiagent Debate ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">3.1</span></a>. The multiagent (majority) is not directly applicable in this setting as individual responses are not easily comparable, and so we omit baseline comparison with the majority voting in this setting.</p>
</div>
</section>
<section id="S3.SS2.SSS0.Px3" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Results.</h4>

<div id="S3.SS2.SSS0.Px3.p1" class="ltx_para">
<p id="S3.SS2.SSS0.Px3.p1.1" class="ltx_p">We analyze the performance of each method in Table <a href="#S3.T2" title="Table 2 ‣ Compatibility with other reasoning methods. ‣ 3.1 Improving Reasoning with Multiagent Debate ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">2</span></a>. We found that approaches based on reflection led to poor performance in the factuality setting. In contrast, debate gives the best performance in this setting also, and significantly outperforms each baseline. We illustrate a debate between agents on the biography task in Figure <a href="#S3.F7" title="Figure 7 ‣ Tasks. ‣ 3.1 Improving Reasoning with Multiagent Debate ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">7</span></a> and on MMLU in Figure <a href="#S3.F8" title="Figure 8 ‣ Tasks. ‣ 3.1 Improving Reasoning with Multiagent Debate ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">8</span></a>. We found that multiagent debate improved and settled on bullets that were more consistent across agents.</p>
</div>
<div id="S3.SS2.SSS0.Px3.p2" class="ltx_para">
<p id="S3.SS2.SSS0.Px3.p2.1" class="ltx_p">We found that different language agents tended to give different answers when the underlying language model was uncertain about the question. However, directly asking each agent about their confidence  <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib10" title="" class="ltx_ref">10</a>]</cite> of the answer led to high confidence assessments on each answer. However, when these different language agents were asked to communicate with each other, each agent would quickly change their opinion to a consensus answer which was more accurate. We illustrate this in Figure <a href="#S3.F9" title="Figure 9 ‣ Compatibility with other reasoning methods. ‣ 3.1 Improving Reasoning with Multiagent Debate ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">9</span></a>. Interestingly, we found that on facts that the language model was confident in (i.e. many instances of the same model all gave the same answer), it was very difficult to convince an agent to change their opinion, suggesting that “ease of persuasion” may be a method to assess factual confidence.</p>
</div>
<figure id="S3.F11" class="ltx_figure"><img src="/html/2305.14325/assets/x10.png" id="S3.F11.g1" class="ltx_graphics ltx_centering ltx_img_landscape" width="461" height="350" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="S3.F11.3.1.1" class="ltx_text" style="font-size:90%;">Figure 11</span>: </span><span id="S3.F11.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Debate Between chatGPT and Bard<span id="S3.F11.4.2.1" class="ltx_text ltx_font_medium"> Illustration of debate between different models.</span></span></figcaption>
</figure>
</section>
</section>
<section id="S3.SS3" class="ltx_subsection">
<h3 class="ltx_title ltx_title_subsection">
<span class="ltx_tag ltx_tag_subsection">3.3 </span>Analysis: Understanding Multiagent Debate</h3>

<div id="S3.SS3.p1" class="ltx_para">
<p id="S3.SS3.p1.1" class="ltx_p">Finally, we analyze how multiagent debate improves the underlying language generation procedure in language models.</p>
</div>
<section id="S3.SS3.SSS0.Px1" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Number of Agents.</h4>

<div id="S3.SS3.SSS0.Px1.p1" class="ltx_para">
<p id="S3.SS3.SSS0.Px1.p1.1" class="ltx_p">First, we analyze the impact of agents number in debate. In Figure <a href="#S3.F10" title="Figure 10 ‣ Compatibility with other reasoning methods. ‣ 3.1 Improving Reasoning with Multiagent Debate ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">10</span></a>(a), we increase the number of agents used in debate, while fixing the debate length to be two. On arithmetic, performance monotonically increases with the increased number of agents. For larger number of agents, we first summarize all agent responses with chatGPT instead of directly concatenating responses due to context length error.</p>
</div>
</section>
<section id="S3.SS3.SSS0.Px2" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Rounds of Debate</h4>

<div id="S3.SS3.SSS0.Px2.p1" class="ltx_para">
<p id="S3.SS3.SSS0.Px2.p1.1" class="ltx_p">Next, we analyze the impact of the number of rounds of debate in multiagent debate. In Figure <a href="#S3.F10" title="Figure 10 ‣ Compatibility with other reasoning methods. ‣ 3.1 Improving Reasoning with Multiagent Debate ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">10</span></a>(b), we increase the debate length between agents, while fixing the number of agents to three. We find that on the arithmetic task, the performance also monotonically increases with debate length. However, we found that additional debate rounds above four led to a similar final performance to 4 rounds of debate.</p>
</div>
<figure id="S3.F12" class="ltx_figure ltx_align_floatright"><img src="/html/2305.14325/assets/x11.png" id="S3.F12.g1" class="ltx_graphics ltx_centering ltx_img_landscape" width="461" height="307" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="S3.F12.3.1.1" class="ltx_text" style="font-size:90%;">Figure 12</span>: </span><span id="S3.F12.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Performance vs Debate Length.<span id="S3.F12.4.2.1" class="ltx_text ltx_font_medium"> Prompts which induce longer debate improve performance.</span></span></figcaption>
</figure>
</section>
<section id="S3.SS3.SSS0.Px3" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Effect of Debate Length on Accuracy</h4>

<div id="S3.SS3.SSS0.Px3.p1" class="ltx_para">
<p id="S3.SS3.SSS0.Px3.p1.1" class="ltx_p">As discussed in Section <a href="#S2.SS2" title="2.2 Consensus in Debates ‣ 2 Language Generation through Multiagent Debate ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">2.2</span></a>, the underlying convergence time in the debate between agents can be controlled by the extent to which agents are encouraged to maintain their opinions.
In Figure <a href="#S3.F12" title="Figure 12 ‣ Rounds of Debate ‣ 3.3 Analysis: Understanding Multiagent Debate ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">12</span></a>, we consider the effect of short and long-form prompts discussed in Figure <a href="#S2.F3" title="Figure 3 ‣ 2.1 Multiagent Language Generation ‣ 2 Language Generation through Multiagent Debate ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">3</span></a>. We find that debates using longer prompts lead to slower convergence to correct answers, but also lead to a better final consensus on the correct answer. We provide an analysis of consensus between agents in Figure <a href="#A1.F14" title="Figure 14 ‣ A.1 Additional Results ‣ Appendix A Appendix ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">14</span></a>.</p>
</div>
</section>
<section id="S3.SS3.SSS0.Px4" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Using Different Initialization Prompts</h4>

<div id="S3.SS3.SSS0.Px4.p1" class="ltx_para">
<p id="S3.SS3.SSS0.Px4.p1.1" class="ltx_p">In our experiments we use the same prompts for all agents. We also consider the effect of using different questions, where we first instruct each language model to behave like a different persona (professor, doctor, mathematician) on the MMLU dataset. We found that improved performance on MMLU from 71.1 to 74.2 with different agents, suggesting further gains can be obtained with different initialization prompts.</p>
</div>
<figure id="S3.F13" class="ltx_figure ltx_align_floatright"><img src="/html/2305.14325/assets/x12.png" id="S3.F13.g1" class="ltx_graphics ltx_centering ltx_img_landscape" width="461" height="307" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="S3.F13.3.1.1" class="ltx_text" style="font-size:90%;">Figure 13</span>: </span><span id="S3.F13.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Effect of Summarization.<span id="S3.F13.4.2.1" class="ltx_text ltx_font_medium"> When there are many agents in a debate, responses from other agents may be first summarized and then given as context, reducing context length. This operation improves performance.</span></span></figcaption>
</figure>
</section>
<section id="S3.SS3.SSS0.Px5" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Summarization.</h4>

<div id="S3.SS3.SSS0.Px5.p1" class="ltx_para">
<p id="S3.SS3.SSS0.Px5.p1.1" class="ltx_p">While in the majority of experiments in the paper we directly concatenate the responses of other agents as context for an agent to generate a new response, this is expensive when the number of agents involved in debate gets large. We may alternatively first summarize the responses from all other agents into a single response that we provide to agent at each round for more efficient debate. We apply this strategy in Figure <a href="#S3.F10" title="Figure 10 ‣ Compatibility with other reasoning methods. ‣ 3.1 Improving Reasoning with Multiagent Debate ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">10</span></a> to enable the use of five or more agents in debate. In Figure <a href="#S3.F13" title="Figure 13 ‣ Using Different Initialization Prompts ‣ 3.3 Analysis: Understanding Multiagent Debate ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">13</span></a>, we analyze the effect compared to directly concatenating the responses of other agents. We find this improves the performance of debate, suggesting that summarization is another tool that can further improve multiagent debate.</p>
</div>
</section>
<section id="S3.SS3.SSS0.Px6" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Utilizing Different Language Models</h4>

<div id="S3.SS3.SSS0.Px6.p1" class="ltx_para">
<p id="S3.SS3.SSS0.Px6.p1.1" class="ltx_p">Our existing debate results are reported using multiple instances of a chatGPT language model. We further assess the impact of using two different language models, where we ask chatGPT and Bard  <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib23" title="" class="ltx_ref">23</a>]</cite> language models to debate with each other on a set of 20 GSM8K math problems. In this set, we find that multi-agent debate improves the performance of both agents, with Bard solving 11 problems, chatGPT solving 14 problems, and joint multi-agent debate solving 17 problems. We qualitatively illustrate a debate between agents in Figure <a href="#S3.F11" title="Figure 11 ‣ Results. ‣ 3.2 Extracting Factual Information from Multiagent Debate ‣ 3 Experiments ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">11</span></a>. While both agents initially provide incorrect answers to the problem, chatGPT is able to utilize the incorrect response given by Bard to generate the final correct answer.</p>
</div>
</section>
</section>
</section>
<section id="S4" class="ltx_section">
<h2 class="ltx_title ltx_title_section">
<span class="ltx_tag ltx_tag_section">4 </span>Related Work</h2>

<section id="S4.SS0.SSS0.Px1" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Reasoning and Factuality in Language Models.</h4>

<div id="S4.SS0.SSS0.Px1.p1" class="ltx_para">
<p id="S4.SS0.SSS0.Px1.p1.1" class="ltx_p">A wide range of work has explored how to enable reasoning and factuality in language models. To improve reasoning, approaches have relied on prompting techniques such as scratchpads  <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib20" title="" class="ltx_ref">20</a>]</cite>, verification  <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib3" title="" class="ltx_ref">3</a>]</cite>, chain-of-thought demonstrations  <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib30" title="" class="ltx_ref">30</a>, <a href="#bib.bib11" title="" class="ltx_ref">11</a>, <a href="#bib.bib25" title="" class="ltx_ref">25</a>]</cite>, and intermediate self-reflection  <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib26" title="" class="ltx_ref">26</a>, <a href="#bib.bib18" title="" class="ltx_ref">18</a>]</cite> and finetuning <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib13" title="" class="ltx_ref">13</a>, <a href="#bib.bib24" title="" class="ltx_ref">24</a>, <a href="#bib.bib31" title="" class="ltx_ref">31</a>]</cite>. To improve factuality, approaches have relied on training techniques such as RLHF  <cite class="ltx_cite ltx_citemacro_citep">[<a href="#bib.bib33" title="" class="ltx_ref">33</a>, <a href="#bib.bib16" title="" class="ltx_ref">16</a>, <a href="#bib.bib2" title="" class="ltx_ref">2</a>]</cite>, pruning truthful datasets <cite class="ltx_cite ltx_citemacro_citep">[<a href="#bib.bib12" title="" class="ltx_ref">12</a>]</cite>, external knowledge retrieval <cite class="ltx_cite ltx_citemacro_citep">[<a href="#bib.bib7" title="" class="ltx_ref">7</a>]</cite> and training-free methods based off likelihood estimation  <cite class="ltx_cite ltx_citemacro_citep">[<a href="#bib.bib10" title="" class="ltx_ref">10</a>]</cite>.</p>
</div>
<div id="S4.SS0.SSS0.Px1.p2" class="ltx_para">
<p id="S4.SS0.SSS0.Px1.p2.1" class="ltx_p">Our work provides an alternative way to obtain reasoning and factuality in language models using multiagent debates, which only requires black-box access to a language generator. Prior work also has explored how to take the majority vote across different models  <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib15" title="" class="ltx_ref">15</a>, <a href="#bib.bib3" title="" class="ltx_ref">3</a>, <a href="#bib.bib29" title="" class="ltx_ref">29</a>, <a href="#bib.bib28" title="" class="ltx_ref">28</a>]</cite> while in this work, we use the power of a language model to combine different answers. Most similar to our work, <cite class="ltx_cite ltx_citemacro_citet">Irving et al. [<a href="#bib.bib9" title="" class="ltx_ref">9</a>]</cite> also proposes a debate procedure to verify the accuracy and safety of powerful AI agents. In contrast to our approach, in their work, agents are asked to alternatively provide proof of a input, and humans are tasked with assessing these debates and determining safety.</p>
</div>
</section>
<section id="S4.SS0.SSS0.Px2" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Compositional Generation.</h4>

<div id="S4.SS0.SSS0.Px2.p1" class="ltx_para">
<p id="S4.SS0.SSS0.Px2.p1.1" class="ltx_p">Our work is also related to existing works that focus on text generation by combining different models  <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib4" title="" class="ltx_ref">4</a>, <a href="#bib.bib17" title="" class="ltx_ref">17</a>, <a href="#bib.bib32" title="" class="ltx_ref">32</a>, <a href="#bib.bib1" title="" class="ltx_ref">1</a>, <a href="#bib.bib5" title="" class="ltx_ref">5</a>]</cite>. Most similar to our work, <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib14" title="" class="ltx_ref">14</a>, <a href="#bib.bib32" title="" class="ltx_ref">32</a>]</cite> propose to combine multiple different large pretrained models together for multimodal reasoning. In contrast, in our work, we aim to use communication between different language models to enable more effective reasoning and factuality in language models.</p>
</div>
</section>
</section>
<section id="S5" class="ltx_section">
<h2 class="ltx_title ltx_title_section">
<span class="ltx_tag ltx_tag_section">5 </span>Limitations and Discussion</h2>

<div id="S5.p1" class="ltx_para">
<p id="S5.p1.1" class="ltx_p">In this paper, we present an orthogonal approach to improve the performance of language models using multi-agent debate. We find that the approach is simple and effective across a wide set of different reasoning and validity language modeling tasks.</p>
</div>
<section id="S5.SS0.SSS0.Px1" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Limitations.</h4>

<div id="S5.SS0.SSS0.Px1.p1" class="ltx_para">
<p id="S5.SS0.SSS0.Px1.p1.1" class="ltx_p">In comparison to other prompting techniques, our multiagent debate procedure is more computationally expensive, as it requires both multiple language generations, and an underlying debate procedure. However, we believe that this approach may be seen as a method to generate additional data that may be distilled back to self-improve the original base model.</p>
</div>
<div id="S5.SS0.SSS0.Px1.p2" class="ltx_para">
<p id="S5.SS0.SSS0.Px1.p2.1" class="ltx_p">Further, we observed that as debates became longer in duration, current language models sometimes struggled to fully process the entire debate input, and typically only focused on the most recent generations. We believe that this performance will be alleviated with longer-context and improved language models or by summarizing early portions of the debate.</p>
</div>
<div id="S5.SS0.SSS0.Px1.p3" class="ltx_para">
<p id="S5.SS0.SSS0.Px1.p3.1" class="ltx_p">Finally, we found that while debates typically converged into single final answers, these answers were not necessarily correct. Despite answers being incorrect, language models would confidently affirm that their answer is correct and consistent with all other agent responses. We believe this result is in part due to the fact that LMs do not correctly express their uncertainty when generating responses, and believe that other orthogonal approaches to improve this performance would improve the results of multiagent debate.</p>
</div>
</section>
</section>
<section id="bib" class="ltx_bibliography">
<h2 class="ltx_title ltx_title_bibliography">References</h2>

<ul class="ltx_biblist">
<li id="bib.bib1" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Alayrac et al. [2022]</span>
<span class="ltx_bibblock">
J.-B. Alayrac, J. Donahue, P. Luc, A. Miech, I. Barr, Y. Hasson, K. Lenc,
A. Mensch, K. Millican, M. Reynolds, et al.

</span>
<span class="ltx_bibblock">Flamingo: A visual language model for few-shot learning.

</span>
<span class="ltx_bibblock"><em id="bib.bib1.1.1" class="ltx_emph ltx_font_italic">NeurIPS</em>, 2022.

</span>
<span class="ltx_bibblock">URL <a target="_blank" href="https://arxiv.org/abs/2204.14198" title="" class="ltx_ref ltx_url ltx_font_typewriter">https://arxiv.org/abs/2204.14198</a>.

</span>
</li>
<li id="bib.bib2" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Christiano et al. [2017]</span>
<span class="ltx_bibblock">
P. F. Christiano, J. Leike, T. Brown, M. Martic, S. Legg, and D. Amodei.

</span>
<span class="ltx_bibblock">Deep reinforcement learning from human preferences.

</span>
<span class="ltx_bibblock">In <em id="bib.bib2.1.1" class="ltx_emph ltx_font_italic">Neural Information Processing Systems</em>, 2017.

</span>
</li>
<li id="bib.bib3" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Cobbe et al. [2021]</span>
<span class="ltx_bibblock">
K. Cobbe, V. Kosaraju, M. Bavarian, M. Chen, H. Jun, L. Kaiser, M. Plappert,
J. Tworek, J. Hilton, R. Nakano, et al.

</span>
<span class="ltx_bibblock">Training verifiers to solve math word problems.

</span>
<span class="ltx_bibblock"><em id="bib.bib3.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2110.14168</em>, 2021.

</span>
</li>
<li id="bib.bib4" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Du et al. [2020]</span>
<span class="ltx_bibblock">
Y. Du, S. Li, and I. Mordatch.

</span>
<span class="ltx_bibblock">Compositional visual generation with energy based models.

</span>
<span class="ltx_bibblock">In <em id="bib.bib4.1.1" class="ltx_emph ltx_font_italic">Advances in Neural Information Processing Systems</em>, 2020.

</span>
</li>
<li id="bib.bib5" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Du et al. [2023]</span>
<span class="ltx_bibblock">
Y. Du, C. Durkan, R. Strudel, J. B. Tenenbaum, S. Dieleman, R. Fergus,
J. Sohl-Dickstein, A. Doucet, and W. Grathwohl.

</span>
<span class="ltx_bibblock">Reduce, reuse, recycle: Compositional generation with energy-based
diffusion models and mcmc.

</span>
<span class="ltx_bibblock"><em id="bib.bib5.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2302.11552</em>, 2023.

</span>
</li>
<li id="bib.bib6" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">[6]</span>
<span class="ltx_bibblock">
Fsmosca.

</span>
<span class="ltx_bibblock">Fsmosca/pgn-standard: Portable game notation specification and
implementation guide.

</span>
<span class="ltx_bibblock">URL <a target="_blank" href="https://github.com/fsmosca/PGN-Standard" title="" class="ltx_ref ltx_url ltx_font_typewriter">https://github.com/fsmosca/PGN-Standard</a>.

</span>
</li>
<li id="bib.bib7" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Guu et al. [2020]</span>
<span class="ltx_bibblock">
K. Guu, K. Lee, Z. Tung, P. Pasupat, and M.-W. Chang.

</span>
<span class="ltx_bibblock">REALM: Retrieval-augmented language model pre-training.

</span>
<span class="ltx_bibblock"><em id="bib.bib7.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2002.08909</em>, 2020.

</span>
</li>
<li id="bib.bib8" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Hendrycks et al. [2020]</span>
<span class="ltx_bibblock">
D. Hendrycks, C. Burns, S. Basart, A. Zou, M. Mazeika, D. Song, and
J. Steinhardt.

</span>
<span class="ltx_bibblock">Measuring massive multitask language understanding.

</span>
<span class="ltx_bibblock"><em id="bib.bib8.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2009.03300</em>, 2020.

</span>
</li>
<li id="bib.bib9" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Irving et al. [2018]</span>
<span class="ltx_bibblock">
G. Irving, P. Christiano, and D. Amodei.

</span>
<span class="ltx_bibblock">Ai safety via debate.

</span>
<span class="ltx_bibblock"><em id="bib.bib9.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:1805.00899</em>, 2018.

</span>
</li>
<li id="bib.bib10" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Kadavath et al. [2022]</span>
<span class="ltx_bibblock">
S. Kadavath, T. Conerly, A. Askell, T. Henighan, D. Drain, E. Perez,
N. Schiefer, Z. H. Dodds, N. DasSarma, E. Tran-Johnson, et al.

</span>
<span class="ltx_bibblock">Language models (mostly) know what they know.

</span>
<span class="ltx_bibblock"><em id="bib.bib10.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2207.05221</em>, 2022.

</span>
</li>
<li id="bib.bib11" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Kojima et al. [2022]</span>
<span class="ltx_bibblock">
T. Kojima, S. S. Gu, M. Reid, Y. Matsuo, and Y. Iwasawa.

</span>
<span class="ltx_bibblock">Large language models are zero-shot reasoners.

</span>
<span class="ltx_bibblock"><em id="bib.bib11.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2205.11916</em>, 2022.

</span>
</li>
<li id="bib.bib12" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Lee et al. [2022]</span>
<span class="ltx_bibblock">
N. Lee, W. Ping, P. Xu, M. Patwary, P. N. Fung, M. Shoeybi, and B. Catanzaro.

</span>
<span class="ltx_bibblock">Factuality enhanced language models for open-ended text generation.

</span>
<span class="ltx_bibblock"><em id="bib.bib12.1.1" class="ltx_emph ltx_font_italic">Advances in Neural Information Processing Systems</em>,
35:34586–34599, 2022.

</span>
</li>
<li id="bib.bib13" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Lewkowycz et al. [2022]</span>
<span class="ltx_bibblock">
A. Lewkowycz, A. Andreassen, D. Dohan, E. Dyer, H. Michalewski, V. Ramasesh,
A. Slone, C. Anil, I. Schlag, T. Gutman-Solo, et al.

</span>
<span class="ltx_bibblock">Solving quantitative reasoning problems with language models.

</span>
<span class="ltx_bibblock"><em id="bib.bib13.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2206.14858</em>, 2022.

</span>
</li>
<li id="bib.bib14" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Li et al. [2022a]</span>
<span class="ltx_bibblock">
S. Li, Y. Du, J. B. Tenenbaum, A. Torralba, and I. Mordatch.

</span>
<span class="ltx_bibblock">Composing ensembles of pre-trained models via iterative consensus.

</span>
<span class="ltx_bibblock"><em id="bib.bib14.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2210.11522</em>, 2022a.

</span>
</li>
<li id="bib.bib15" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Li et al. [2022b]</span>
<span class="ltx_bibblock">
Y. Li, D. Choi, J. Chung, N. Kushman, J. Schrittwieser, R. Leblond, T. Eccles,
J. Keeling, F. Gimeno, A. Dal Lago, et al.

</span>
<span class="ltx_bibblock">Competition-level code generation with alphacode.

</span>
<span class="ltx_bibblock"><em id="bib.bib15.1.1" class="ltx_emph ltx_font_italic">Science</em>, 378(6624):1092–1097,
2022b.

</span>
</li>
<li id="bib.bib16" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Liu et al. [2022a]</span>
<span class="ltx_bibblock">
H. Liu, L. Lee, K. Lee, and P. Abbeel.

</span>
<span class="ltx_bibblock">Instruction-following agents with jointly pre-trained vision-language
models.

</span>
<span class="ltx_bibblock"><em id="bib.bib16.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2210.13431</em>, 2022a.

</span>
</li>
<li id="bib.bib17" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Liu et al. [2022b]</span>
<span class="ltx_bibblock">
N. Liu, S. Li, Y. Du, A. Torralba, and J. B. Tenenbaum.

</span>
<span class="ltx_bibblock">Compositional visual generation with composable diffusion models.

</span>
<span class="ltx_bibblock"><em id="bib.bib17.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2206.01714</em>, 2022b.

</span>
</li>
<li id="bib.bib18" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Madaan et al. [2023]</span>
<span class="ltx_bibblock">
A. Madaan, N. Tandon, P. Gupta, S. Hallinan, L. Gao, S. Wiegreffe, U. Alon,
N. Dziri, S. Prabhumoye, Y. Yang, et al.

</span>
<span class="ltx_bibblock">Self-refine: Iterative refinement with self-feedback.

</span>
<span class="ltx_bibblock"><em id="bib.bib18.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2303.17651</em>, 2023.

</span>
</li>
<li id="bib.bib19" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Minsky [1988]</span>
<span class="ltx_bibblock">
M. Minsky.

</span>
<span class="ltx_bibblock"><em id="bib.bib19.1.1" class="ltx_emph ltx_font_italic">Society of mind</em>.

</span>
<span class="ltx_bibblock">Simon and Schuster, 1988.

</span>
</li>
<li id="bib.bib20" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Nye et al. [2021]</span>
<span class="ltx_bibblock">
M. Nye, A. J. Andreassen, G. Gur-Ari, H. Michalewski, J. Austin, D. Bieber,
D. Dohan, A. Lewkowycz, M. Bosma, D. Luan, et al.

</span>
<span class="ltx_bibblock">Show your work: Scratchpads for intermediate computation with
language models.

</span>
<span class="ltx_bibblock"><em id="bib.bib20.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2112.00114</em>, 2021.

</span>
</li>
<li id="bib.bib21" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">OpenAI [2022]</span>
<span class="ltx_bibblock">
OpenAI.

</span>
<span class="ltx_bibblock">Chatgpt: Optimizing language models for dialogue, Dec 2022.

</span>
<span class="ltx_bibblock">URL <a target="_blank" href="https://openai.com/blog/chatgpt/" title="" class="ltx_ref ltx_url ltx_font_typewriter">https://openai.com/blog/chatgpt/</a>.

</span>
</li>
<li id="bib.bib22" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Ouyang et al. [2022]</span>
<span class="ltx_bibblock">
L. Ouyang, J. Wu, X. Jiang, D. Almeida, C. L. Wainwright, P. Mishkin, C. Zhang,
S. Agarwal, K. Slama, A. Ray, et al.

</span>
<span class="ltx_bibblock">Training language models to follow instructions with human feedback.

</span>
<span class="ltx_bibblock"><em id="bib.bib22.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2203.02155</em>, 2022.

</span>
</li>
<li id="bib.bib23" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Pichai [2023]</span>
<span class="ltx_bibblock">
S. Pichai.

</span>
<span class="ltx_bibblock">An important next step on our ai journey, Feb 2023.

</span>
<span class="ltx_bibblock">URL
<a target="_blank" href="https://blog.google/technology/ai/bard-google-ai-search-updates/" title="" class="ltx_ref ltx_url ltx_font_typewriter">https://blog.google/technology/ai/bard-google-ai-search-updates/</a>.

</span>
</li>
<li id="bib.bib24" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Rajani et al. [2019]</span>
<span class="ltx_bibblock">
N. F. Rajani, B. McCann, C. Xiong, and R. Socher.

</span>
<span class="ltx_bibblock">Explain yourself! leveraging language models for commonsense
reasoning.

</span>
<span class="ltx_bibblock"><em id="bib.bib24.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:1906.02361</em>, 2019.

</span>
</li>
<li id="bib.bib25" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Reynolds and McDonell [2021]</span>
<span class="ltx_bibblock">
L. Reynolds and K. McDonell.

</span>
<span class="ltx_bibblock">Prompt programming for large language models: Beyond the few-shot
paradigm.

</span>
<span class="ltx_bibblock">In <em id="bib.bib25.1.1" class="ltx_emph ltx_font_italic">Extended Abstracts of the 2021 CHI Conference on Human
Factors in Computing Systems</em>, pages 1–7, 2021.

</span>
</li>
<li id="bib.bib26" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Shinn et al. [2023]</span>
<span class="ltx_bibblock">
N. Shinn, B. Labash, and A. Gopinath.

</span>
<span class="ltx_bibblock">Reflexion: an autonomous agent with dynamic memory and
self-reflection.

</span>
<span class="ltx_bibblock"><em id="bib.bib26.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2303.11366</em>, 2023.

</span>
</li>
<li id="bib.bib27" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Srivastava et al. [2022]</span>
<span class="ltx_bibblock">
A. Srivastava, A. Rastogi, A. Rao, A. A. M. Shoeb, A. Abid, A. Fisch, A. R.
Brown, A. Santoro, A. Gupta, A. Garriga-Alonso, et al.

</span>
<span class="ltx_bibblock">Beyond the imitation game: Quantifying and extrapolating the
capabilities of language models.

</span>
<span class="ltx_bibblock"><em id="bib.bib27.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2206.04615</em>, 2022.

</span>
</li>
<li id="bib.bib28" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Thoppilan et al. [2022]</span>
<span class="ltx_bibblock">
R. Thoppilan, D. De Freitas, J. Hall, N. Shazeer, A. Kulshreshtha, H.-T. Cheng,
A. Jin, T. Bos, L. Baker, Y. Du, et al.

</span>
<span class="ltx_bibblock">Lamda: Language models for dialog applications.

</span>
<span class="ltx_bibblock"><em id="bib.bib28.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2201.08239</em>, 2022.

</span>
</li>
<li id="bib.bib29" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Wang et al. [2022]</span>
<span class="ltx_bibblock">
X. Wang, J. Wei, D. Schuurmans, Q. Le, E. Chi, and D. Zhou.

</span>
<span class="ltx_bibblock">Self-consistency improves chain of thought reasoning in language
models.

</span>
<span class="ltx_bibblock"><em id="bib.bib29.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2203.11171</em>, 2022.

</span>
</li>
<li id="bib.bib30" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Wei et al. [2022]</span>
<span class="ltx_bibblock">
J. Wei, X. Wang, D. Schuurmans, M. Bosma, E. Chi, Q. Le, and D. Zhou.

</span>
<span class="ltx_bibblock">Chain of thought prompting elicits reasoning in large language
models.

</span>
<span class="ltx_bibblock"><em id="bib.bib30.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2201.11903</em>, 2022.

</span>
</li>
<li id="bib.bib31" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Zelikman et al. [2022]</span>
<span class="ltx_bibblock">
E. Zelikman, Y. Wu, J. Mu, and N. Goodman.

</span>
<span class="ltx_bibblock">Star: Bootstrapping reasoning with reasoning.

</span>
<span class="ltx_bibblock"><em id="bib.bib31.1.1" class="ltx_emph ltx_font_italic">Advances in Neural Information Processing Systems</em>,
35:15476–15488, 2022.

</span>
</li>
<li id="bib.bib32" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Zeng et al. [2022]</span>
<span class="ltx_bibblock">
A. Zeng, A. Wong, S. Welker, K. Choromanski, F. Tombari, A. Purohit, M. Ryoo,
V. Sindhwani, J. Lee, V. Vanhoucke, et al.

</span>
<span class="ltx_bibblock">Socratic models: Composing zero-shot multimodal reasoning with
language.

</span>
<span class="ltx_bibblock"><em id="bib.bib32.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:2204.00598</em>, 2022.

</span>
<span class="ltx_bibblock">URL <a target="_blank" href="https://arxiv.org/abs/2204.00598" title="" class="ltx_ref ltx_url ltx_font_typewriter">https://arxiv.org/abs/2204.00598</a>.

</span>
</li>
<li id="bib.bib33" class="ltx_bibitem">
<span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Ziegler et al. [2019]</span>
<span class="ltx_bibblock">
D. M. Ziegler, N. Stiennon, J. Wu, T. B. Brown, A. Radford, D. Amodei,
P. Christiano, and G. Irving.

</span>
<span class="ltx_bibblock">Fine-tuning language models from human preferences.

</span>
<span class="ltx_bibblock"><em id="bib.bib33.1.1" class="ltx_emph ltx_font_italic">arXiv preprint arXiv:1909.08593</em>, 2019.

</span>
</li>
</ul>
</section>
<div class="ltx_pagination ltx_role_newpage"></div>
<section id="A1" class="ltx_appendix">
<h2 class="ltx_title ltx_title_appendix">
<span class="ltx_tag ltx_tag_appendix">Appendix A </span>Appendix</h2>

<div id="A1.p1" class="ltx_para">
<p id="A1.p1.1" class="ltx_p">In this appendix, we provide additional analysis and visualizations of the debates used in the main paper in Section <a href="#A1.SS1" title="A.1 Additional Results ‣ Appendix A Appendix ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">A.1</span></a>. We further provide detailed experimental details on each dataset in Section <a href="#A1.SS2" title="A.2 Evaluation Details ‣ Appendix A Appendix ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">A.2</span></a>.</p>
</div>
<section id="A1.SS1" class="ltx_subsection">
<h3 class="ltx_title ltx_title_subsection">
<span class="ltx_tag ltx_tag_subsection">A.1 </span>Additional Results</h3>

<figure id="A1.F14" class="ltx_figure ltx_align_floatright"><img src="/html/2305.14325/assets/x13.png" id="A1.F14.g1" class="ltx_graphics ltx_centering ltx_img_landscape" width="461" height="307" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="A1.F14.3.1.1" class="ltx_text" style="font-size:90%;">Figure 14</span>: </span><span id="A1.F14.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Effect of Prompts on Consensus.<span id="A1.F14.4.2.1" class="ltx_text ltx_font_medium"> Using a short debate prompt induces faster consensus between agents</span></span></figcaption>
</figure>
<section id="A1.SS1.SSS0.Px1" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Consensus Between Agents.</h4>

<div id="A1.SS1.SSS0.Px1.p1" class="ltx_para">
<p id="A1.SS1.SSS0.Px1.p1.1" class="ltx_p">In Figure <a href="#A1.F14" title="Figure 14 ‣ A.1 Additional Results ‣ Appendix A Appendix ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">14</span></a>, we illustrate the consensus between agents using either short or long consensus prompts discussed in Figure <a href="#S2.F3" title="Figure 3 ‣ 2.1 Multiagent Language Generation ‣ 2 Language Generation through Multiagent Debate ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">3</span></a>. The use of debate prompts that encourage agents to adapt more to the opinions of other agents improves consensus.</p>
</div>
</section>
<section id="A1.SS1.SSS0.Px2" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Additional Qualitative Visualizations.</h4>

<div id="A1.SS1.SSS0.Px2.p1" class="ltx_para">
<p id="A1.SS1.SSS0.Px2.p1.1" class="ltx_p">We added additional qualitative visualizations of the debate process. In Figure <a href="#A1.F16" title="Figure 16 ‣ Chess Validity. ‣ A.2 Evaluation Details ‣ Appendix A Appendix ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">16</span></a>, Figure <a href="#A1.F17" title="Figure 17 ‣ Chess Validity. ‣ A.2 Evaluation Details ‣ Appendix A Appendix ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">17</span></a>, Figure <a href="#A1.F18" title="Figure 18 ‣ Chess Validity. ‣ A.2 Evaluation Details ‣ Appendix A Appendix ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">18</span></a>, Figure <a href="#A1.F19" title="Figure 19 ‣ Chess Validity. ‣ A.2 Evaluation Details ‣ Appendix A Appendix ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">19</span></a>, Figure <a href="#A1.F20" title="Figure 20 ‣ Chess Validity. ‣ A.2 Evaluation Details ‣ Appendix A Appendix ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">20</span></a>, we illustrate debates between agents in the GSM8K dataset which result in the correct answer. In Figure <a href="#A1.F21" title="Figure 21 ‣ Chess Validity. ‣ A.2 Evaluation Details ‣ Appendix A Appendix ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">21</span></a>, Figure <a href="#A1.F22" title="Figure 22 ‣ Chess Validity. ‣ A.2 Evaluation Details ‣ Appendix A Appendix ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">22</span></a>, Figure <a href="#A1.F23" title="Figure 23 ‣ Chess Validity. ‣ A.2 Evaluation Details ‣ Appendix A Appendix ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">23</span></a>, we further illustrate debates in GSM8K which lead to the incorrect answer. We further provide an example illustration of debate in arithmetic in Figure <a href="#A1.F24" title="Figure 24 ‣ Chess Validity. ‣ A.2 Evaluation Details ‣ Appendix A Appendix ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">24</span></a>, arithmetic with summarization of individual responses of agents in Figure <a href="#A1.F25" title="Figure 25 ‣ Chess Validity. ‣ A.2 Evaluation Details ‣ Appendix A Appendix ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">25</span></a>, MMLU in Figure <a href="#A1.F26" title="Figure 26 ‣ Chess Validity. ‣ A.2 Evaluation Details ‣ Appendix A Appendix ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">26</span></a>, a debate with the full contents biographies in Figure <a href="#A1.F27" title="Figure 27 ‣ Chess Validity. ‣ A.2 Evaluation Details ‣ Appendix A Appendix ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">27</span></a>, and debate in chess in Figure <a href="#A1.F28" title="Figure 28 ‣ Chess Validity. ‣ A.2 Evaluation Details ‣ Appendix A Appendix ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">28</span></a>. In general, we found that debate improved the performance of final generated answers, though sometimes answers would converge to the incorrect value.</p>
</div>
</section>
</section>
<section id="A1.SS2" class="ltx_subsection">
<h3 class="ltx_title ltx_title_subsection">
<span class="ltx_tag ltx_tag_subsection">A.2 </span>Evaluation Details</h3>

<div id="A1.SS2.p1" class="ltx_para">
<p id="A1.SS2.p1.1" class="ltx_p">We provided detailed evaluation details for each setting in the paper. We run all experiments using the <span id="A1.SS2.p1.1.1" class="ltx_text ltx_font_typewriter">gpt-3.5-turbo-0301</span> model. We provide a table listing the prompts used to prompt models and initialize debate in Table <a href="#A1.F15" title="Figure 15 ‣ Chess Validity. ‣ A.2 Evaluation Details ‣ Appendix A Appendix ‣ Improving Factuality and Reasoning in Language Models through Multiagent Debate" class="ltx_ref"><span class="ltx_text ltx_ref_tag">15</span></a>.</p>
</div>
<section id="A1.SS2.SSS0.Px1" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Arithmetic.</h4>

<div id="A1.SS2.SSS0.Px1.p1" class="ltx_para">
<p id="A1.SS2.SSS0.Px1.p1.1" class="ltx_p">To evaluate the arithmetic task, we generated six random integers for each task between 0 and 30. We then evaluated the extent to which the correct integer answer was correctly obtained. We evaluated models on one hundred generated arithmetic tasks.</p>
</div>
</section>
<section id="A1.SS2.SSS0.Px2" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Grade School Math.</h4>

<div id="A1.SS2.SSS0.Px2.p1" class="ltx_para">
<p id="A1.SS2.SSS0.Px2.p1.1" class="ltx_p">To evaluate the GSM8K task, we evaluated the accuracy at which models were able to obtain the final correct answer, as extracted from a box. We evaluated models on one hundred grade school math problems.</p>
</div>
</section>
<section id="A1.SS2.SSS0.Px3" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Chess.</h4>

<div id="A1.SS2.SSS0.Px3.p1" class="ltx_para">
<p id="A1.SS2.SSS0.Px3.p1.1" class="ltx_p">To evaluate the chess reasoning task, we used chess games from <a target="_blank" href="https://www.pgnmentor.com/players/Adams.zip" title="" class="ltx_ref ltx_url ltx_font_typewriter">https://www.pgnmentor.com/players/Adams.zip</a>. We asked chatGPT to predict the next move for white to move at turn 14 and reported the relative Stockfish pawn score with search depth 20 after executing the suggested move from chatGPT. We evaluated models on three hundred selected chess games.</p>
</div>
</section>
<section id="A1.SS2.SSS0.Px4" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Biographies.</h4>

<div id="A1.SS2.SSS0.Px4.p1" class="ltx_para">
<p id="A1.SS2.SSS0.Px4.p1.1" class="ltx_p">To evaluate the biographies task, we compare each generated bullet point biography for a person with a ground truth set of facts about the person extracted from Wikipedia. We iteratively loop through each ground truth fact, and validate the extent to which the generated biography matches a particular bullet by prompting chatGPT with the prompt: <em id="A1.SS2.SSS0.Px4.p1.1.1" class="ltx_emph ltx_font_italic">Consider the following biography of &lt;person&gt;: &lt;generated biography&gt; Is the above biography above consistent with the fact below? &lt;ground truth bullet&gt; Give a single-word answer, yes, no, or uncertain.</em> We then evaluate and report the percentage of ground bullets that chatGPT returns either yes or no on. We ignored ground truth bullets that chatGPT returns returned uncertain.</p>
</div>
<div id="A1.SS2.SSS0.Px4.p2" class="ltx_para">
<p id="A1.SS2.SSS0.Px4.p2.1" class="ltx_p">We found this evaluation metric provided a fast way to evaluate how relatively correct a generated bullet point biography is. However, we found that generated facts could contain incorrect information that was not captured in the ground truth bullet and thus could not be validated through this metric. Nevertheless, we believe this evaluation scheme estimates the relative accuracy of a generated biography.</p>
</div>
</section>
<section id="A1.SS2.SSS0.Px5" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">MMLU.</h4>

<div id="A1.SS2.SSS0.Px5.p1" class="ltx_para">
<p id="A1.SS2.SSS0.Px5.p1.1" class="ltx_p">To evaluate MMLU, we measured the accuracy in which models were able to select the correct multiple-choice answer in each problem. We evaluated models on one hundred selected MMLU questions randomly distributed across each of the subject areas.</p>
</div>
</section>
<section id="A1.SS2.SSS0.Px6" class="ltx_paragraph">
<h4 class="ltx_title ltx_title_paragraph">Chess Validity.</h4>

<div id="A1.SS2.SSS0.Px6.p1" class="ltx_para">
<p id="A1.SS2.SSS0.Px6.p1.1" class="ltx_p">To evaluate chess validity, we consider the BIG-Bench Chess-State Tracking Benchmark  <cite class="ltx_cite ltx_citemacro_cite">[<a href="#bib.bib27" title="" class="ltx_ref">27</a>]</cite>, where we used the hardest reported task in the benchmark <span id="A1.SS2.SSS0.Px6.p1.1.1" class="ltx_text ltx_font_typewriter">synthetic_short</span>. Each generated answer was deemed correct as long as it was one of the valid answers in the sequence. We evaluated models of one hundred selected chess validity tasks.</p>
</div>
<figure id="A1.SS2.SSS0.Px6.tab1" class="ltx_table">
<div class="ltx_flex_figure ltx_flex_table">
<div class="ltx_flex_cell ltx_flex_size_1">
<div id="A1.SS2.SSS0.Px6.tab1.1" class="ltx_inline-block ltx_figure_panel ltx_transformed_outer" style="width:448.0pt;height:489.4pt;vertical-align:-0.8pt;"><span class="ltx_transformed_inner" style="transform:translate(-56.0pt,61.1pt) scale(0.8,0.8) ;">
<table id="A1.SS2.SSS0.Px6.tab1.1.1" class="ltx_tabular ltx_align_middle">
<tbody class="ltx_tbody">
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.1.1" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.1.1.1" class="ltx_td ltx_align_center ltx_border_r" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="A1.SS2.SSS0.Px6.tab1.1.1.1.1.1.1" class="ltx_text ltx_font_bold" style="font-size:90%;">Task</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.1.1.2" class="ltx_td ltx_align_center ltx_border_r" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="A1.SS2.SSS0.Px6.tab1.1.1.1.1.2.1" class="ltx_text" style="font-size:90%;">Type</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.1.1.3" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="A1.SS2.SSS0.Px6.tab1.1.1.1.1.3.1" class="ltx_text ltx_font_bold" style="font-size:90%;">Prompt</span></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.2.2" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.2.2.1" class="ltx_td ltx_align_center ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;" rowspan="4"><span id="A1.SS2.SSS0.Px6.tab1.1.1.2.2.1.1" class="ltx_text" style="font-size:90%;">Arithmetic</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.2.2.2" class="ltx_td ltx_align_center ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;"><span id="A1.SS2.SSS0.Px6.tab1.1.1.2.2.2.1" class="ltx_text" style="font-size:90%;">Starting</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.2.2.3" class="ltx_td ltx_align_left ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.2.2.3.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">What is the result of <span id="A1.SS2.SSS0.Px6.tab1.1.1.2.2.3.1.1" class="ltx_text ltx_font_upright">{}</span>+<span id="A1.SS2.SSS0.Px6.tab1.1.1.2.2.3.1.2" class="ltx_text ltx_font_upright">{}</span>*<span id="A1.SS2.SSS0.Px6.tab1.1.1.2.2.3.1.3" class="ltx_text ltx_font_upright">{}</span>+<span id="A1.SS2.SSS0.Px6.tab1.1.1.2.2.3.1.4" class="ltx_text ltx_font_upright">{}</span>-<span id="A1.SS2.SSS0.Px6.tab1.1.1.2.2.3.1.5" class="ltx_text ltx_font_upright">{}</span>*<span id="A1.SS2.SSS0.Px6.tab1.1.1.2.2.3.1.6" class="ltx_text ltx_font_upright">{}</span>? Make sure to state your answer at the end of the response.</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.3.3" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.3.3.1" class="ltx_td ltx_align_center ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;" rowspan="3"><span id="A1.SS2.SSS0.Px6.tab1.1.1.3.3.1.1" class="ltx_text" style="font-size:90%;">Debate</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.3.3.2" class="ltx_td ltx_align_left ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.3.3.2.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">These are the recent/updated opinions from other agents: &lt;other agent responses&gt; Use these opinions</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.4.4" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.4.4.1" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.4.4.1.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">carefully as additional advice, can you provide an updated answer? Make sure to state your answer</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.5.5" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.5.5.1" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.5.5.1.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">at the end of the response.</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.6.6" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.6.6.1" class="ltx_td ltx_align_center ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;" rowspan="6"><span id="A1.SS2.SSS0.Px6.tab1.1.1.6.6.1.1" class="ltx_text" style="font-size:90%;">GSM8K</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.6.6.2" class="ltx_td ltx_align_center ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;" rowspan="2"><span id="A1.SS2.SSS0.Px6.tab1.1.1.6.6.2.1" class="ltx_text" style="font-size:90%;">Starting</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.6.6.3" class="ltx_td ltx_align_left ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.6.6.3.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">Can you solve the following math problem? &lt;Problem&gt; Explain your reasoning. Your final answer</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.7.7" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.7.7.1" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.7.7.1.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">should be a single numerical number, in the form \boxed<span id="A1.SS2.SSS0.Px6.tab1.1.1.7.7.1.1.1" class="ltx_text ltx_font_upright">{{</span>answer<span id="A1.SS2.SSS0.Px6.tab1.1.1.7.7.1.1.2" class="ltx_text ltx_font_upright">}}</span>, at the end of your response.</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.8.8" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.8.8.1" class="ltx_td ltx_align_center ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;" rowspan="4"><span id="A1.SS2.SSS0.Px6.tab1.1.1.8.8.1.1" class="ltx_text" style="font-size:90%;">Debate</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.8.8.2" class="ltx_td ltx_align_left ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.8.8.2.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">These are the solutions to the problem from other agents: &lt;other agent responses&gt; Using the solutions</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.9.9" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.9.9.1" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.9.9.1.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">from other agents as additional information, can you provide your answer to the math problem? The original</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.10.10" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.10.10.1" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.10.10.1.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">math problem is &lt;Problem&gt;. Your final answer should be a single numerical number, in the form</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.11.11" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.11.11.1" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.11.11.1.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">\boxed<span id="A1.SS2.SSS0.Px6.tab1.1.1.11.11.1.1.1" class="ltx_text ltx_font_upright">{{</span>answer<span id="A1.SS2.SSS0.Px6.tab1.1.1.11.11.1.1.2" class="ltx_text ltx_font_upright">}}</span>, at the end of your response.</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.12.12" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.12.12.1" class="ltx_td ltx_align_center ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;" rowspan="2"><span id="A1.SS2.SSS0.Px6.tab1.1.1.12.12.1.1" class="ltx_text" style="font-size:90%;">Chess</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.12.12.2" class="ltx_td ltx_align_center ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;" rowspan="3"><span id="A1.SS2.SSS0.Px6.tab1.1.1.12.12.2.1" class="ltx_text" style="font-size:90%;">Starting</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.12.12.3" class="ltx_td ltx_align_left ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.12.12.3.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">Here is the current sequence of moves in a chess game: &lt;moves&gt;. What is the best chess move I should</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.13.13" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.13.13.1" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.13.13.1.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">execute next? Give a single move suggestion of the form 14. &lt;XXX&gt; and make sure the chess move</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.14.14" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.14.14.1" class="ltx_td ltx_border_r" style="padding-left:5.5pt;padding-right:5.5pt;"></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.14.14.2" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.14.14.2.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">is valid in the current board state.</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.15.15" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.15.15.1" class="ltx_td ltx_border_r" style="padding-left:5.5pt;padding-right:5.5pt;"></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.15.15.2" class="ltx_td ltx_align_center ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;" rowspan="3"><span id="A1.SS2.SSS0.Px6.tab1.1.1.15.15.2.1" class="ltx_text" style="font-size:90%;">Debate</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.15.15.3" class="ltx_td ltx_align_left ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.15.15.3.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">Here are other chess move suggestions from other agents: &lt;other agent responses&gt; Using the chess suggestions</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.16.16" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.16.16.1" class="ltx_td ltx_border_r" style="padding-left:5.5pt;padding-right:5.5pt;"></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.16.16.2" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.16.16.2.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">from other agents as additional advice and your earlier generated solution, can you give me your updated thoughts</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.17.17" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.17.17.1" class="ltx_td ltx_border_r" style="padding-left:5.5pt;padding-right:5.5pt;"></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.17.17.2" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.17.17.2.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">on the best next chess move I should play given the chess sequence ? Give a single move suggestion of the form</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.18.18" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.18.18.1" class="ltx_td ltx_border_r" style="padding-left:5.5pt;padding-right:5.5pt;"></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.18.18.2" class="ltx_td ltx_border_r" style="padding-left:5.5pt;padding-right:5.5pt;"></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.18.18.3" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.18.18.3.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">14. &lt;XXX&gt; and make sure the chess move is valid in the current board state.</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.19.19" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.19.19.1" class="ltx_td ltx_align_center ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;" rowspan="4"><span id="A1.SS2.SSS0.Px6.tab1.1.1.19.19.1.1" class="ltx_text" style="font-size:90%;">Biographies</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.19.19.2" class="ltx_td ltx_align_center ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;" rowspan="2"><span id="A1.SS2.SSS0.Px6.tab1.1.1.19.19.2.1" class="ltx_text" style="font-size:90%;">Starting</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.19.19.3" class="ltx_td ltx_align_left ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.19.19.3.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">Give a bullet point biography of  highlighting their contributions and achievements as a computer scientist,</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.20.20" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.20.20.1" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.20.20.1.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">with each fact separated with a new line character.</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.21.21" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.21.21.1" class="ltx_td ltx_align_center ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;" rowspan="2"><span id="A1.SS2.SSS0.Px6.tab1.1.1.21.21.1.1" class="ltx_text" style="font-size:90%;">Debate</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.21.21.2" class="ltx_td ltx_align_left ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.21.21.2.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">Here are some bullet point biographies of &lt;person&gt; given by other agents: &lt;other agent response&gt; Closely</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.22.22" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.22.22.1" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.22.22.1.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">examine your biography and the biography of other agents and provide an updated bullet point biography.</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.23.23" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.23.23.1" class="ltx_td ltx_align_center ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;" rowspan="5"><span id="A1.SS2.SSS0.Px6.tab1.1.1.23.23.1.1" class="ltx_text" style="font-size:90%;">MMLU</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.23.23.2" class="ltx_td ltx_align_center ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;" rowspan="2"><span id="A1.SS2.SSS0.Px6.tab1.1.1.23.23.2.1" class="ltx_text" style="font-size:90%;">Starting</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.23.23.3" class="ltx_td ltx_align_left ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.23.23.3.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">Can you answer the following question as accurately as possible? : A) , B) , C) , D)  Explain your answer,</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.24.24" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.24.24.1" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.24.24.1.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">putting the answer in the form (X) at the end of your response.</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.25.25" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.25.25.1" class="ltx_td ltx_align_center ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;" rowspan="3"><span id="A1.SS2.SSS0.Px6.tab1.1.1.25.25.1.1" class="ltx_text" style="font-size:90%;">Debate</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.25.25.2" class="ltx_td ltx_align_left ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.25.25.2.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">These are the solutions to the problem from other agents: &lt;other agent responses&gt; Using the reasoning</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.26.26" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.26.26.1" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.26.26.1.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">from other agents as additional advice, can you give an updated answer? Examine your solution and</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.27.27" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.27.27.1" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.27.27.1.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">that other agents. Put your answer in the form (X) at the end of your response.</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.28.28" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.28.28.1" class="ltx_td ltx_align_center ltx_border_bb ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;" rowspan="6"><span id="A1.SS2.SSS0.Px6.tab1.1.1.28.28.1.1" class="ltx_text" style="font-size:90%;">Chess Validity</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.28.28.2" class="ltx_td ltx_align_center ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;" rowspan="3"><span id="A1.SS2.SSS0.Px6.tab1.1.1.28.28.2.1" class="ltx_text" style="font-size:90%;">Starting</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.28.28.3" class="ltx_td ltx_align_left ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.28.28.3.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">Given the chess game , give one valid destination square for the chess piece at . State the destination square</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.29.29" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.29.29.1" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.29.29.1.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">in the form (X), where X follows the regex [a-h][1-8], for example (e5). Give a one line explanation</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.30.30" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.30.30.1" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.30.30.1.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">of why your destination square is a valid move.</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.31.31" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.31.31.1" class="ltx_td ltx_align_center ltx_border_bb ltx_border_r ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;" rowspan="3"><span id="A1.SS2.SSS0.Px6.tab1.1.1.31.31.1.1" class="ltx_text" style="font-size:90%;">Debate</span></td>
<td id="A1.SS2.SSS0.Px6.tab1.1.1.31.31.2" class="ltx_td ltx_align_left ltx_border_t" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.31.31.2.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">Here are destination square suggestions from other agents: &lt;other agent responses&gt; Can you double</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.32.32" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.32.32.1" class="ltx_td ltx_align_left" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.32.32.1.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">check that your destination square is a valid move? Check the valid move justifications from other agents.</em></td>
</tr>
<tr id="A1.SS2.SSS0.Px6.tab1.1.1.33.33" class="ltx_tr">
<td id="A1.SS2.SSS0.Px6.tab1.1.1.33.33.1" class="ltx_td ltx_align_left ltx_border_bb" style="padding-left:5.5pt;padding-right:5.5pt;"><em id="A1.SS2.SSS0.Px6.tab1.1.1.33.33.1.1" class="ltx_emph ltx_font_italic" style="font-size:90%;">State your final answer in a newline with a 2 letter response following the regex [a-h][1-8].</em></td>
</tr>
</tbody>
</table>
</span></div>
</div>
<div class="ltx_flex_break"></div>
<div class="ltx_flex_cell ltx_flex_size_1">
<figure id="A1.F15" class="ltx_figure ltx_figure_panel ltx_align_center">
<figcaption class="ltx_caption" style="font-size:90%;"><span class="ltx_tag ltx_tag_figure">Figure 15: </span><span id="A1.F15.5.1" class="ltx_text ltx_font_bold">Prompts in each task.</span> List of prompts used in each task </figcaption>
</figure>
</div>
</div>
</figure>
<figure id="A1.F16" class="ltx_figure"><img src="/html/2305.14325/assets/x14.png" id="A1.F16.g1" class="ltx_graphics ltx_centering ltx_img_portrait" width="461" height="670" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="A1.F16.3.1.1" class="ltx_text" style="font-size:90%;">Figure 16</span>: </span><span id="A1.F16.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Example of a correct GSM8K Debate.</span></figcaption>
</figure>
<figure id="A1.F17" class="ltx_figure"><img src="/html/2305.14325/assets/x15.png" id="A1.F17.g1" class="ltx_graphics ltx_centering ltx_img_portrait" width="461" height="611" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="A1.F17.3.1.1" class="ltx_text" style="font-size:90%;">Figure 17</span>: </span><span id="A1.F17.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Example of Correct GSM8K Debate.</span></figcaption>
</figure>
<figure id="A1.F18" class="ltx_figure"><img src="/html/2305.14325/assets/x16.png" id="A1.F18.g1" class="ltx_graphics ltx_centering ltx_img_portrait" width="461" height="713" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="A1.F18.3.1.1" class="ltx_text" style="font-size:90%;">Figure 18</span>: </span><span id="A1.F18.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Example of Correct GSM8K Debate.</span></figcaption>
</figure>
<figure id="A1.F19" class="ltx_figure"><img src="/html/2305.14325/assets/x17.png" id="A1.F19.g1" class="ltx_graphics ltx_centering ltx_img_portrait" width="461" height="611" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="A1.F19.3.1.1" class="ltx_text" style="font-size:90%;">Figure 19</span>: </span><span id="A1.F19.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Example of Correct GSM8K Debate.</span></figcaption>
</figure>
<figure id="A1.F20" class="ltx_figure"><img src="/html/2305.14325/assets/x18.png" id="A1.F20.g1" class="ltx_graphics ltx_centering ltx_img_square" width="461" height="451" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="A1.F20.3.1.1" class="ltx_text" style="font-size:90%;">Figure 20</span>: </span><span id="A1.F20.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Example of Correct GSM8K Debate.</span></figcaption>
</figure>
<figure id="A1.F21" class="ltx_figure"><img src="/html/2305.14325/assets/x19.png" id="A1.F21.g1" class="ltx_graphics ltx_centering ltx_img_portrait" width="461" height="688" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="A1.F21.3.1.1" class="ltx_text" style="font-size:90%;">Figure 21</span>: </span><span id="A1.F21.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Example of Incorrect GSM8K Debate.</span></figcaption>
</figure>
<figure id="A1.F22" class="ltx_figure"><img src="/html/2305.14325/assets/x20.png" id="A1.F22.g1" class="ltx_graphics ltx_centering ltx_img_portrait" width="438" height="752" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="A1.F22.3.1.1" class="ltx_text" style="font-size:90%;">Figure 22</span>: </span><span id="A1.F22.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Example of Incorrect GSM8K Debate.</span></figcaption>
</figure>
<figure id="A1.F23" class="ltx_figure"><img src="/html/2305.14325/assets/x21.png" id="A1.F23.g1" class="ltx_graphics ltx_centering ltx_img_portrait" width="461" height="693" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="A1.F23.3.1.1" class="ltx_text" style="font-size:90%;">Figure 23</span>: </span><span id="A1.F23.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Example of Incorrect GSM8K Debate.</span></figcaption>
</figure>
<figure id="A1.F24" class="ltx_figure"><img src="/html/2305.14325/assets/x22.png" id="A1.F24.g1" class="ltx_graphics ltx_centering ltx_img_portrait" width="461" height="588" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="A1.F24.3.1.1" class="ltx_text" style="font-size:90%;">Figure 24</span>: </span><span id="A1.F24.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Example of Arithmetic Debate.</span></figcaption>
</figure>
<figure id="A1.F25" class="ltx_figure"><img src="/html/2305.14325/assets/x23.png" id="A1.F25.g1" class="ltx_graphics ltx_centering ltx_img_portrait" width="461" height="588" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="A1.F25.3.1.1" class="ltx_text" style="font-size:90%;">Figure 25</span>: </span><span id="A1.F25.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Example of Arithmetic Debate with Summarization.<span id="A1.F25.4.2.1" class="ltx_text ltx_font_medium"> Four separate agents participate in debate, with two illustrated above. Instruction contains the summarized responses across agents.</span></span></figcaption>
</figure>
<figure id="A1.F26" class="ltx_figure"><img src="/html/2305.14325/assets/x24.png" id="A1.F26.g1" class="ltx_graphics ltx_centering ltx_img_square" width="461" height="490" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="A1.F26.3.1.1" class="ltx_text" style="font-size:90%;">Figure 26</span>: </span><span id="A1.F26.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Example of MMLU Debate.</span></figcaption>
</figure>
<figure id="A1.F27" class="ltx_figure"><img src="/html/2305.14325/assets/x25.png" id="A1.F27.g1" class="ltx_graphics ltx_centering ltx_img_portrait" width="461" height="672" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="A1.F27.3.1.1" class="ltx_text" style="font-size:90%;">Figure 27</span>: </span><span id="A1.F27.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Example of Biography Debate.<span id="A1.F27.4.2.1" class="ltx_text ltx_font_medium"> While we found that generated biographies after debate to be more accurate, many facts remain incorrect.</span></span></figcaption>
</figure>
<figure id="A1.F28" class="ltx_figure"><img src="/html/2305.14325/assets/x26.png" id="A1.F28.g1" class="ltx_graphics ltx_centering ltx_img_landscape" width="461" height="305" alt="Refer to caption">
<figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure"><span id="A1.F28.3.1.1" class="ltx_text" style="font-size:90%;">Figure 28</span>: </span><span id="A1.F28.4.2" class="ltx_text ltx_font_bold" style="font-size:90%;">Example of Chess Debate.</span></figcaption>
</figure>
<div class="ltx_pagination ltx_role_newpage"></div>
</section>
</section>
</section>
</article>
</div>
<div class="ar5iv-footer"><a href="/html/2305.14324" class="ar5iv-nav-button ar5iv-nav-button-prev">◄</a>
    <a class="ar5iv-home-button" href="/"><img height="40" alt="ar5iv homepage" src="/assets/ar5iv.png"></a>
    <a href="/feeling_lucky" class="ar5iv-text-button">Feeling<br>lucky?</a>
    <a href="/log/2305.14325" class="ar5iv-text-button ar5iv-severity-warning">Conversion<br>report</a>
    <a class="ar5iv-text-button" target="_blank" href="https://github.com/dginev/ar5iv/issues/new?template=improve-article--arxiv-id-.md&title=Improve+article+2305.14325">Report<br>an issue</a>
    <a href="https://arxiv.org/abs/2305.14325" class="ar5iv-text-button arxiv-ui-theme">View&nbsp;original<br>on&nbsp;arXiv</a><a href="/html/2305.14326" class="ar5iv-nav-button ar5iv-nav-button-next">►</a>
</div><footer class="ltx_page_footer">
<a class="ar5iv-toggle-color-scheme" href="javascript:toggleColorScheme()" title="Toggle ar5iv color scheme"><span class="color-scheme-icon"></span></a>
<a class="ar5iv-footer-button" href="https://arxiv.org/help/license" target="_blank">Copyright</a>
<a class="ar5iv-footer-button" href="https://arxiv.org/help/policies/privacy_policy" target="_blank">Privacy Policy</a>

<div class="ltx_page_logo">Generated  on Thu Feb 29 06:02:31 2024 by <a target="_blank" href="http://dlmf.nist.gov/LaTeXML/" class="ltx_LaTeXML_logo"><span style="letter-spacing:-0.2em; margin-right:0.1em;">L<span class="ltx_font_smallcaps" style="position:relative; bottom:2.2pt;">a</span>T<span class="ltx_font_smallcaps" style="font-size:120%;position:relative; bottom:-0.2ex;">e</span></span><span style="font-size:90%; position:relative; bottom:-0.2ex;">XML</span><img src="data:image/png;base64,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" alt="Mascot Sammy"></a>
</div></footer>
</div>

    <script>
      var canMathML = typeof(MathMLElement) == "function";
      if (!canMathML) {
        var body = document.querySelector("body");
        body.firstElementChild.setAttribute('style', 'opacity: 0;');
        var loading = document.createElement("div");
        loading.setAttribute("id", "mathjax-loading-spinner");
        var message = document.createElement("div");
        message.setAttribute("id", "mathjax-loading-message");
        message.innerText = "Typesetting Equations...";
        body.prepend(loading);
        body.prepend(message);

        var el = document.createElement("script");
        el.src = "https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js";
        document.querySelector("head").appendChild(el);

        window.MathJax = {
          startup: {
            pageReady: () => {
              return MathJax.startup.defaultPageReady().then(() => {
                body.removeChild(loading);
                body.removeChild(message);
                body.firstElementChild.removeAttribute('style');
              }); } } };
      }
    </script>
    <script>
    // Auxiliary function, building the preview feature when
    // an inline citation is clicked
    function clicked_cite(e) {
      e.preventDefault();
      let cite = this.closest('.ltx_cite');
      let next = cite.nextSibling;
      if (next && next.nodeType == Node.ELEMENT_NODE && next.getAttribute('class') == "ar5iv-bibitem-preview") {
        next.remove();
        return; }
      // Before adding a preview modal,
      // cleanup older previews, in case they're still open
      document.querySelectorAll('span.ar5iv-bibitem-preview').forEach(function(node) {
        node.remove();
      })

      // Create the preview
      preview = document.createElement('span');
      preview.setAttribute('class','ar5iv-bibitem-preview');
      let target = document.getElementById(this.getAttribute('href').slice(1));
      target.childNodes.forEach(function (child) {
        preview.append(child.cloneNode(true));
      });
      let close_x = document.createElement('button');
      close_x.setAttribute("aria-label","Close modal for bibliography item preview");
      close_x.textContent = "×";
      close_x.setAttribute('class', 'ar5iv-button-close-preview');
      close_x.setAttribute('onclick','this.parentNode.remove()');
      preview.append(close_x);
      preview.querySelectorAll('.ltx_tag_bibitem').forEach(function(node) {
        node.remove();
      });
      cite.parentNode.insertBefore(preview, cite.nextSibling);
      return;
    }
    // Global Document initialization:
    // - assign the preview feature to all inline citation links
    document.querySelectorAll(".ltx_cite .ltx_ref").forEach(function (link) {
      link.addEventListener("click", clicked_cite);
    });
    </script>
    </body>
</html>

2305.14325
Large language models (LLMs)  have demonstrated remarkable capabilities in language generation, understanding, and few-shot learning in recent years. An extensive body of work has explored how their performance may be further improved through the tools of prompting, ranging from verification, self-consistency, or intermediate scratchpads.
In this paper, we present a complementary approach to improve language responses
where multiple language model instances propose and debate their individual responses and reasoning processes over multiple rounds to arrive at a common final answer.
Our findings indicate that this approach significantly enhances mathematical and strategic reasoning across a number of tasks. We also demonstrate that our approach improves the factual validity of generated content, reducing fallacious answers and hallucinations that contemporary models are prone to. Our approach may be directly applied to existing black-box models and uses identical procedure and prompts for all tasks we investigate.
Overall, our findings suggest that such "society of minds" approach has the potential to significantly advance the capabilities of LLMs and pave the way for further breakthroughs in language generation and understanding. Project website athttps://composable-models.github.io/llm_debate/.
abstract
Improving Factuality and Reasoning in Language Models through Multiagent Debate
Abstract
2305.14325
1IntroductionLarge language models (LLMs)  have demonstrated remarkable language generation, understanding, and few-shot learning capabilities in recent years. These methods are trained on a massive corpus of text on the internet, where the quality and accuracy of extracted natural language may not be ensured. Thus, current models may suffer from confidently hallucinating facts or making implausible jumps in chains of reasoning. An extensive body of recent work has focused on improving factual accuracy and reasoning in language models. These range from prompting models with few or zero-shot chain-of-thought demonstrations, use of verification, self-consistency, or intermediate scratchpads.We note that these techniques are applied over a single model instance. Instead, we propose a complementary approach inspired byThe Society of Mindand multi-agent settings, where multiple language model instances (or agents)  individually propose and jointly debate their responses and reasoning processes to arrive at a single common answer. More specifically, given a query, multiple instances of a language model first generate individual candidate answers to a query. Then each individual model instance reads and critiques the responses of all other models and uses this content to update its own answer. This step is then repeated over several rounds. This process induces models to construct answers that are consistent with both their internal critic as well as sensible in light of the responses of other agents. The resulting quorum of models can hold and maintain multiple chains of reasoning and possible answers simultaneously before proposing the final answer.We find that our debate approach outperforms single model baselines such as zero-shot chain of thoughtand reflectionon a variety of six reasoning, factuality, and question-answering tasks. Using both multiple model agents and multiple rounds of debate are important to achieve the best performance. Given an initial query, we find that individual model instances propose a diverse range of answers despite being the same model class (although we also investigate the case of mixing different model types, such as chatGPTand Bard) . After debating and examining the responses of other model instances, we find that the population almost always converges on a single and more accurate common answer. Debate results are also less likely to include false facts that models are internally uncertain of. This is because as the debate progresses, individual model instances tend to disagree on uncertain facts and omit them from the answer (Figure7) . Lastly, we find that debate does not just act to amplify one correct answer in a model quorum - we find many cases where all the models initially make incorrect predictions, but then arrive at the correct answer as debate progresses (Figure4,11) .We use the same methodology and prompt templates for all our tasks and require only black-box access to language model generations – no model-internal information such as likelihoods or gradients is needed. This allows our method to be used with common public models serving interfaces. The method is also orthogonal to other model generation improvements such as retrieval or prompt engineering (in fact, we combine our debate method with zero-shot chain of thought) . While the debate process is more costly, requiring multiple model instances and rounds, it arrives at significantly improved answers and may be used to generate additional model training data, effectively creating a model self-improvement loop.To help evaluate the effect of our approach on factual accuracy, we introduce a new benchmark and dataset evaluating factual accuracy of famous computer scientist biographies. We find that contemporary language models have an especially high tendency to hallucinate factually incorrect biographies, often misrepresenting the relevant institutions and dates. Moreover, these facts often inconsistent across different language model instances. By asking models to come to a consensus across their answers, such inconsistent facts may be either removed or corrected.In summary, our work contributes the following. First, we present a novel approach to improving factual correctness and reasoning accuracy in contemporary language models, leveraging a multi-agent debate process between models. Second, we introduce a new benchmark of factual correctness which contemporary language models struggle with. Finally, we evaluate the performance of our debate procedure in language generation, both in terms of the number of agents, the underlying rounds of debate, and the prompts that elicit such behavior across a set of six different reasoning and factual accuracy tasks.Figure 1:Multiagent Debate Improves Reasoning and Factual Accuracy.Accuracy of traditional inference and our multi-agent debate over six benchmarks (chess move optimality reported as a normalized score) 
introduction
Improving Factuality and Reasoning in Language Models through Multiagent Debate
1Introduction
2305.14325
2Language Generation through Multiagent DebateWe present an approach to generate language responses through multiagent debate. We provide an overview of our approach in Section2.1. We further discuss convergence to consensus in the debate process in Section2.2. The overall overview of our approach is shown in Figure2.Figure 2:Illustration of Debate.Illustration of the debate procedure.2.1Multiagent Language GenerationConsider your work process when solving the following math question on an exam:“What is the area of a triangle with side lengths of 3, 4, 5?". In one thread of work, you may recognize that the triangle side-lengths directly correspond to a right triangle, and thus directly compute the area as. To make sure that you have the right answer, you may then try to solve the problem differently by estimating an anglein the triangle using the Law of Cosines, and then obtain the area by using the formula, arriving at another answer to the given exam problem.When these lines of work give the same answer, your confidence about the answer increases. In contrast, when these answers are different, individual lines of work may engage in a mental “debate" procedure, where you closely cross-examine the reasoning and assumptions of each line of work and refine solutions until a consistent answer.Similarly, consider writing a biography of a historical figure. To ensure the factuality of the biography, you may consult multiple different sources on each fact. Facts that are consistent in each source increase your confidence about the fact. In contrast, facts that are inconsistent require careful cross-examination between sources to determine the final consistent data.To mimic the above multi-threaded
reasoning process and multi-source factuality checking processes, we propose to generate answers subject to a multi-agent debate procedure between multiple instances of large language models. Given a question, multiple agents represented as copies of a large language model, generate answers to the question. Each response serves as a possible thought process or source of information which agents may re-examine to find consistent final answers.After initial responses are generated from different agents, we initiate a round of debate between agents. Individual responses from other agents are concatenated and given as context to each agent, with each agent instructed to construct a new response based on such responses. Each language agent is thus responsible for both verifying the collection of responses given by other agents, and refining its own response based on other agents’ responses. We iteratively repeat this debate procedure over multiple rounds for improved performance.Concretely, we first prompt each agent to independently solve the given problem or task. After each agent generates a response, we feed each agent a consensus prompt, illustrated in Figure3, where each agent is instructed to update their responses based on the responses of other agents. This resultant consensus prompt may then be repeatedly given, using the updated responses of each agent.
We illustrate an overview of this multiagent debate procedure in Figure2.Note that our proposed approach operates in an orthogonal manner to existing approaches to prompt language models. Given a question, we may apply additional techniques for prompting language models to further improve our debate procedure by eliciting additional more detailed responses from language models. We illustrate the synergy of our approach with existing approaches to prompting language models in Figure6and directly apply zero-shot chain-of-thought reasoning in our evaluations.Debate LengthPromptShort" These are the solutions to the problem from other agents: [other answers]Based off the opinion of other agents, can you give an updated response"Long" These are the solutions to the problem from other agents: [other answers]Using the opinion of other agents as additional advice, can you give an updated response"Figure 3:Prompts to induce long and short form debate.Responses of other agents to questions are are inserted in the middle of the prompt (indicated with[other answers]) 2.2Consensus in DebatesGiven multiple rounds of debate, how can we ensure that a set of language model agents will converge to a final consensus answer? In general, debate can be seen as a multi-agent game, where convergence is not guaranteed. Empirically, however, we find that language models are able to converge on a single shared answer after multiple rounds of debate (Figure4) .We found that we could control the duration of debates by how changing how much a language model trusts its own outputs over those generated by other models through different prompts. We illustrate two prompts below in Figure3, which we use to induce different debate durations between language models, and illustrate the effect of such prompts in Figure12. In general, we found that prompts that encouraged models to be more “stubborn’ based on their own solutions led to longer debates and better final solutions. Overall, we observed that language model agents were relatively "agreeable", perhaps as a result of instruction tuning or reinforcement learning based on human feedback.
body
Improving Factuality and Reasoning in Language Models through Multiagent Debate
2Language Generation through Multiagent Debate
2305.14325
3ExperimentsIn our experiments, we evaluate our multiagent debate procedure and answer the following questions:(1) To what extent does multiagent debate improve reasoning?(2) To what extent does multiagent debate improve factual validity?(3) What design choices enable multiagent debate to improve language generation performance?Figure 4:Illustration of Solving Math.Reasoning between agents is omitted.Figure 5:Illustration of Solving Grade School Math.Reasoning between agents omitted.ModelArithmetic (%) Grade School Math (%) Chess (PS) Single Agent67.04.777.04.291.410.6Single Agent (Reflection) 72.14.575.04.3102.111.9Multi-Agent (Majority) 69.04.681.03.9102.26.2Multi-Agent (Debate) 81.82.385.03.5122.97.6Table 1:Multiagent Debate Improves ReasoningMulti-agent debate improves the reasoning abilities of language models. Multi-agent results in the table are run with 3 agents and two rounds of debate.3.1Improving Reasoning with Multiagent DebateWe first evaluate the extent to which multiagent debate improves the underlying reasoning process in language models.Tasks.We evaluate our approach on three reasoning tasks of increasing difficulty:•Arithmetic.We first evaluate the ability of models to correctly evaluate an arithmetic expression (containing addition, multiplication, and subtraction)  consisting of six different two-digit numbers. For example:What is the result of 12+15*21+0-3*27?•GSM8K.Next, we consider harder mathematical reasoning tasks. Using the GSM8K dataset, the models must correctly solve grade school mathematical reasoning tasks.•Chess Move Prediction.Finally, we consider the strategic reasoning of the ability of models, and ask models to predict the best next move in a game of chess, given the first 14 moves of a chess game between two chess grand-masters described in PGN notation.We report the accuracy of final answers in arithmetic and GSM8K tasks and report the pawn score (advantage)  of predicted moves, as estimated by Stockfish in the Chess move prediction tasks. Additional details may be found in the Appendix.Figure 6:Synergy with Other Methods.Performance of debate increases with use of Chain of Thought prompting.Figure 7:Illustration of Generating Biographies.Illustration of generating bullet biographies of computer scientists. For brevity, only the first 3 generated bullets are shown.Figure 8:Illustration of MMLU.Illustration of debate when answering factual tasks. Reasoning omitted.Baselines.We compare our approach to three alternative approaches to generate responses for reasoning problems. First, we ask agents to directly generate responses (single agent) . Next, we consider asking language models to generate and then "self-reflect" on the responses generated. Finally, we consider generating responses using multiple agents and performing majority voting. As the focus of our experiments is to verify the effectiveness of multiagent agent debate, we run both baselines and our approach, using the identical starting prompt and language model across all evaluations. We evaluate models in a zero-shot setting, with prompts found in the Appendix of the paper. We use chatGPT-based language modelin all our experiments except those in Figure11where we compare multiple language models.Due to computational expense, we evaluate our approach across benchmarks mainly using three agents with two rounds of debates, although we found further gains with both more agents and rounds of debate (Figure10) . Additional evaluation details are found in the Appendix.Quantitative Results.In Table1, we report the results of each approach on arithmetic, grade school math, and chess reasoning task. In each task, we observe that utilizing multiple different agents to generate solutions improves performance over using a single language model agent to generate a solution. Simultaneously, we also see that reflection, where a language model is asked to critique its early generation, generally gives a modest boost in performance. Multiagent debate, which may be seen as a combination of both reflection and multiagent generation, gives a substantial boost in reasoning across each of the tasks.Qualitative Results.In Figure4,5, we provide qualitative illustrations of the debate procedure between models. Interestingly, we find cases in which all models initially give an incorrect response, yet the result of debate still obtains the correct answer as agents critique each others’ reasoning. Thus, the purpose of our debate isn’t just to amplify a correct answer – all models can initially be wrong but arrive at the correct answer through the debate process.Compatibility with other reasoning methods.Our multiagent generation procedure operates orthogonally approach to other prompting methods which focus on single-agent generation. In Figure6, we illustrate the performance of multi-agent debate with and without zero-shot chain-of-thought promptingon GSM8K. In both settings, multiagent generation is beneficial.ModelBiographiesMMLUChess Move ValiditySingle Agent66.02.263.94.829.32.6Single Agent (Reflection) 68.32.957.75.038.82.9Multi-Agent (Debate) 73.82.371.14.645.22.9Table 2:Multiagent Debate Improves Factual AccuracyMulti-agent debate improves the factual accuracy.Figure 9:Expressing Uncertainty with Multiple Answers.For facts that a language model is uncertain about, different language agents generate different facts. Debate causes agents to converge to one fact that is more accurate, but not necessarily always factually correct.Figure 10:(a)  Performance with Increased Agents.Performance improves as the number of underlying agents involved in debate increases.(b)  Performance with Increased Rounds.Performance rises as the number of rounds of underlying debate increases.3.2Extracting Factual Information from Multiagent DebateWe next evaluate the extent to which multiagent debate improves the underlying factuality in language models.Tasks.We evaluate the factuality of language models in three different settings:•Biographies.To evaluate the factuality of language models, we introduce a novel task of accurately generating historical biographies of people. In preliminary testing, we found that existing language models had a tendency to hallucinate many facts on this task. We constructed ground truth bullet point biographies of 524 well-known computer scientists. We then asked language models to generate bullet point biographies for each person, and evaluated the accuracy at which each ground truth bullet point agreed with generated bullets. We report additional evaluation details in the Appendix.•MMLU.Next, we assess the factuality of language models in responding to different factual knowledge questions typically learned and assessed in different exams. We utilize the existing MMLU datasetto benchmark the accuracy of responses.•Chess Move Validity.Lastly, we study the hallucinations in language models when planning under to the given rules of an existing environment or game. Specifically, we measure the validity of possible moves in a game of Chess given by BIG-Bench Chess-State Tracking Benchmarktask of chess-move prediction. In this task, an agent is given a set of next moves, and must make a valid next move of a piece on a board.Baselines.We use the same baselines as in Section3.1. The multiagent (majority)  is not directly applicable in this setting as individual responses are not easily comparable, and so we omit baseline comparison with the majority voting in this setting.Results.We analyze the performance of each method in Table2. We found that approaches based on reflection led to poor performance in the factuality setting. In contrast, debate gives the best performance in this setting also, and significantly outperforms each baseline. We illustrate a debate between agents on the biography task in Figure7and on MMLU in Figure8. We found that multiagent debate improved and settled on bullets that were more consistent across agents.We found that different language agents tended to give different answers when the underlying language model was uncertain about the question. However, directly asking each agent about their confidenceof the answer led to high confidence assessments on each answer. However, when these different language agents were asked to communicate with each other, each agent would quickly change their opinion to a consensus answer which was more accurate. We illustrate this in Figure9. Interestingly, we found that on facts that the language model was confident in (i.e. many instances of the same model all gave the same answer) , it was very difficult to convince an agent to change their opinion, suggesting that “ease of persuasion” may be a method to assess factual confidence.Figure 11:Debate Between chatGPT and BardIllustration of debate between different models.3.3Analysis: Understanding Multiagent DebateFinally, we analyze how multiagent debate improves the underlying language generation procedure in language models.Number of Agents.First, we analyze the impact of agents number in debate. In Figure10(a) , we increase the number of agents used in debate, while fixing the debate length to be two. On arithmetic, performance monotonically increases with the increased number of agents. For larger number of agents, we first summarize all agent responses with chatGPT instead of directly concatenating responses due to context length error.Rounds of DebateNext, we analyze the impact of the number of rounds of debate in multiagent debate. In Figure10(b) , we increase the debate length between agents, while fixing the number of agents to three. We find that on the arithmetic task, the performance also monotonically increases with debate length. However, we found that additional debate rounds above four led to a similar final performance to 4 rounds of debate.Figure 12:Performance vs Debate Length.Prompts which induce longer debate improve performance.Effect of Debate Length on AccuracyAs discussed in Section2.2, the underlying convergence time in the debate between agents can be controlled by the extent to which agents are encouraged to maintain their opinions.
In Figure12, we consider the effect of short and long-form prompts discussed in Figure3. We find that debates using longer prompts lead to slower convergence to correct answers, but also lead to a better final consensus on the correct answer. We provide an analysis of consensus between agents in Figure14.Using Different Initialization PromptsIn our experiments we use the same prompts for all agents. We also consider the effect of using different questions, where we first instruct each language model to behave like a different persona (professor, doctor, mathematician)  on the MMLU dataset. We found that improved performance on MMLU from 71.1 to 74.2 with different agents, suggesting further gains can be obtained with different initialization prompts.Figure 13:Effect of Summarization.When there are many agents in a debate, responses from other agents may be first summarized and then given as context, reducing context length. This operation improves performance.Summarization.While in the majority of experiments in the paper we directly concatenate the responses of other agents as context for an agent to generate a new response, this is expensive when the number of agents involved in debate gets large. We may alternatively first summarize the responses from all other agents into a single response that we provide to agent at each round for more efficient debate. We apply this strategy in Figure10to enable the use of five or more agents in debate. In Figure13, we analyze the effect compared to directly concatenating the responses of other agents. We find this improves the performance of debate, suggesting that summarization is another tool that can further improve multiagent debate.Utilizing Different Language ModelsOur existing debate results are reported using multiple instances of a chatGPT language model. We further assess the impact of using two different language models, where we ask chatGPT and Bardlanguage models to debate with each other on a set of 20 GSM8K math problems. In this set, we find that multi-agent debate improves the performance of both agents, with Bard solving 11 problems, chatGPT solving 14 problems, and joint multi-agent debate solving 17 problems. We qualitatively illustrate a debate between agents in Figure11. While both agents initially provide incorrect answers to the problem, chatGPT is able to utilize the incorrect response given by Bard to generate the final correct answer.
body
Improving Factuality and Reasoning in Language Models through Multiagent Debate
3Experiments
2305.14325
4Related WorkReasoning and Factuality in Language Models.A wide range of work has explored how to enable reasoning and factuality in language models. To improve reasoning, approaches have relied on prompting techniques such as scratchpads, verification, chain-of-thought demonstrations, and intermediate self-reflectionand finetuning. To improve factuality, approaches have relied on training techniques such as RLHF, pruning truthful datasets, external knowledge retrievaland training-free methods based off likelihood estimation.Our work provides an alternative way to obtain reasoning and factuality in language models using multiagent debates, which only requires black-box access to a language generator. Prior work also has explored how to take the majority vote across different modelswhile in this work, we use the power of a language model to combine different answers. Most similar to our work,also proposes a debate procedure to verify the accuracy and safety of powerful AI agents. In contrast to our approach, in their work, agents are asked to alternatively provide proof of a input, and humans are tasked with assessing these debates and determining safety.Compositional Generation.Our work is also related to existing works that focus on text generation by combining different models. Most similar to our work,propose to combine multiple different large pretrained models together for multimodal reasoning. In contrast, in our work, we aim to use communication between different language models to enable more effective reasoning and factuality in language models.
body
Improving Factuality and Reasoning in Language Models through Multiagent Debate
4Related Work
2305.14325
5Limitations and DiscussionIn this paper, we present an orthogonal approach to improve the performance of language models using multi-agent debate. We find that the approach is simple and effective across a wide set of different reasoning and validity language modeling tasks.Limitations.In comparison to other prompting techniques, our multiagent debate procedure is more computationally expensive, as it requires both multiple language generations, and an underlying debate procedure. However, we believe that this approach may be seen as a method to generate additional data that may be distilled back to self-improve the original base model.Further, we observed that as debates became longer in duration, current language models sometimes struggled to fully process the entire debate input, and typically only focused on the most recent generations. We believe that this performance will be alleviated with longer-context and improved language models or by summarizing early portions of the debate.Finally, we found that while debates typically converged into single final answers, these answers were not necessarily correct. Despite answers being incorrect, language models would confidently affirm that their answer is correct and consistent with all other agent responses. We believe this result is in part due to the fact that LMs do not correctly express their uncertainty when generating responses, and believe that other orthogonal approaches to improve this performance would improve the results of multiagent debate.
conclusion
Improving Factuality and Reasoning in Language Models through Multiagent Debate
5Limitations and Discussion