Mirror-Consistency: Harnessing Inconsistency in Majority Voting (2024)

Abstract: Self-Consistency, a widely-used decoding strategy, significantly boosts the reasoning capabilities of Large Language Models (LLMs). However, it depends on the plurality voting rule, which focuses on the most frequent answer while overlooking all other minority responses. These inconsistent minority views often illuminate areas of uncertainty within the model’s generation process. To address this limitation, we present Mirror-Consistency, an enhancement of the standard Self-Consistency approach. Our method incorporates a ‘reflective mirror’ into the self-ensemble decoding process and enables LLMs to critically examine inconsistencies among multiple generations. Additionally, just as humans use the mirror to better understand themselves, we propose using Mirror-Consistency to enhance the sample-based confidence calibration methods, which helps to mitigate issues of overconfidence. Our experimental results demonstrate that Mirror-Consistency yields superior performance in both reasoning accuracy and confidence calibration compared to Self-Consistency.

## introduction large language models (llms) have substantially influenced diverse sectors with their advanced applications @xcite @xcite @xcite . to further bolster llms' reasoning ability, self-consistency @xcite initially generates a wide range of reasoning pathways, then performs a marginalization to determine the most consistent response. although generally effective, this approach relies primarily on the plurality voting rule, which focuses only on the most frequent answer, thereby neglecting other minority responses. consequently, the crucial inconsistencies in the resampled answers, which could reveal majority voting 3 majority voting 2 candidate ans 1 candidate ans 2 candidate ans 3 majority voting 1 contrast 1 (no action) contrast 2 (reflection) candidate ans 4 contrast 3 (reflection) input input input input ... ... reflection on inconsistency conditional resampling simple resampling contrast 2 (reflection) contrast 1 (no action) candidate ans 1 candidate ans 2 candidate ans 3 input input input ... majority voting ignore the inconsistent minority opinions self-consistency mirror-consistency uncertainties and potential errors of llms, often do not receive the attention they merit. to address this limitation, we introduce mirror-consistency, which enables the llm to analyze and learn from discrepancies in its resampled responses. the complete process is illustrated in figure 1 . we sequentially resample new responses. each new response is then compared to the previous majority voting result. if the new response deviates from the majority's decision (i.e., it represents a minority opinion), we position the llm to act as an arbitrator. in this role, the llm reflects on the differences between the new response and the previous majority opinion and offers a feedback, which is then utilized to guide the generation of subsequent responses. this process effectively equips the standard self-consistency method with a 'mirror', enabling the llm to learn from incon-sistencies observed during the sampling process. we then delve into another application of mirror-consistency: the confidence calibration of llms @xcite . recent studies leverage the consistency of multiple generations to assess the llm's confidence in its responses @xcite @xcite @xcite . following this idea, we find that mirror-consistency, which involves repeatedly comparing and reflecting on the discrepancies between the majority and the minority opinions, provides a more robust quantification of uncertainty, particularly in cases of overconfidence. our motivation for using mirror consistency in confidence calibration stems from the idea that answers that consistently emerge as the majority after several rounds of comparisons with other candidate answers are likely more reliable. we conduct experiments on four reasoning datasets with four different llms to compare the performance of mirror-consistency with self-consistency. the results confirm the efficacy of reflecting on the inconsistencies during the sampling process, showing improvements in both reasoning accuracy and confidence calibration. ## mirror-consistency this section details the implementation of mirror-consistency. self-consistency depends on the plurality voting rule, which tends to overlook minority responses that may be inconsistent yet informative. to address this gap, we introduce a reflective form of consistency, termed mirror-consistency. mirror-consistency and self-consistency share procedural similarities, as both methods generate multiple responses and use majority voting to determine the final output. the key distinction is that mirror-consistency examines the inconsistencies within the sampling process, rather than merely repeat sampling independent answers. the mirror-consistency process begins with an initial sampling phase to produce the first response, denoted as r 0 . this is followed by a series of iterations that alternate between reflection on inconsistency and conditional resampling, as shown in algorithm 1. we next introduce these two steps in detail. the corresponding prompts are provided in appendix d. ## experiments in this section, we assess the efficacy of mirror-consistency from two distinct angles: first, we evaluate its reasoning accuracy in comparison to self-consistency across four reasoning datasets. second, we demonstrate how the reflective form of consistency embodied by mirror-consistency improves the sample-based calibration methods. ## conclusion mirror-consistency effectively remedies a crucial limitation in the standard self-consistency method: the disregard for minority viewpoints during sampling. our approach examines the discrepancies across various responses to identify uncertainties within the generative process. the experimental results demonstrates that mirror-consistency not only achieves higher reasoning accuracy compared to self-consistency but also enhances model calibration, especially when standard sample-based calibration methods face issues of overconfidence.