Collective Reasoning Among LLMs A Framework for Answer Validation Without Ground Truth

We present a collaborative framework where multiple large language models, namely GPT-4-0125-preview, Meta-LLaMA-3-70B-Instruct, Claude-3-Opus, and Gemini-1.5-Flash, work together to generate and respond to complex PhD-level probability questions in the absence of definitive ground truth. This study explores how inter-model consensus enhances response reliability and serves as a proxy for assessing the quality of generated questions. To quantify agreement and consistency, we employ statistical methods including chi-square tests, Fleiss' Kappa, and confidence interval analysis, measuring both response precision and question clarity. Our findings highlight that Claude and Gemini generate well-structured and less ambiguous questions, leading to higher inter-model agreement. This is reflected in their narrower confidence intervals and stronger alignment with answering models. Conversely, LLaMA demonstrates increased variability and lower reliability in question formulation, as indicated by broader confidence intervals and reduced consensus rates. These results suggest that multi-model collaboration not only enhances the reliability of responses but also provides a valuable framework for assessing and improving question quality in the absence of explicit ground truth. This research offers meaningful insights into optimizing AI-driven reasoning through collaborative large-language model interactions.

Enhancing Answer Reliability Through Inter-Model Consensus of Large Language Models

We explore the collaborative dynamics of an innovative language model interaction system involving advanced models such as GPT-4-0125-preview, Meta-LLaMA-3-70B-Instruct, Claude-3-Opus, and Gemini-1.5-Flash. These models generate and answer complex, PhD-level statistical questions without exact ground-truth answers. Our study investigates how inter-model consensus enhances the reliability and precision of responses. By employing statistical methods such as chi-square tests, Fleiss' Kappa, and confidence interval analysis, we evaluate consensus rates and inter-rater agreement to quantify the reliability of collaborative outputs. Key results reveal that Claude and GPT-4 exhibit the highest reliability and consistency, as evidenced by their narrower confidence intervals and higher alignment with question-generating models. Conversely, Gemini and LLaMA show more significant variability in their consensus rates, as reflected in wider confidence intervals and lower reliability percentages. These findings demonstrate that collaborative interactions among large language models (LLMs) significantly improve response reliability, offering novel insights into autonomous, cooperative reasoning and validation in AI systems.

LLMs Are Not Intelligent Thinkers: Introducing Mathematical Topic Tree Benchmark for Comprehensive Evaluation of LLMs

Large language models (LLMs) demonstrate impressive capabilities in mathematical reasoning. However, despite these achievements, current evaluations are mostly limited to specific mathematical topics, and it remains unclear whether LLMs are genuinely engaging in reasoning. To address these gaps, we present the Mathematical Topics Tree (MaTT) benchmark, a challenging and structured benchmark that offers 1,958 questions across a wide array of mathematical subjects, each paired with a detailed hierarchical chain of topics. Upon assessing different LLMs using the MaTT benchmark, we find that the most advanced model, GPT-4, achieved a mere 54\% accuracy in a multiple-choice scenario. Interestingly, even when employing Chain-of-Thought prompting, we observe mostly no notable improvement. Moreover, LLMs accuracy dramatically reduced by up to 24.2 percentage point when the questions were presented without providing choices. Further detailed analysis of the LLMs' performance across a range of topics showed significant discrepancy even for closely related subtopics within the same general mathematical area. In an effort to pinpoint the reasons behind LLMs performances, we conducted a manual evaluation of the completeness and correctness of the explanations generated by GPT-4 when choices were available. Surprisingly, we find that in only 53.3\% of the instances where the model provided a correct answer, the accompanying explanations were deemed complete and accurate, i.e., the model engaged in genuine reasoning.