Generating and voting multiple answers is an effective method to mitigate reasoning inconsistencies of large language models (LLMs). Prior works have shown that multiple reasoning formats outperform a single format when generating multiple answers. However, previous works using multiple formats rely on formats labeled by humans, which could be unsuitable for all tasks and have high labeling costs. To address this issue, we adapt suitable formats to the given tasks by generating and selecting formats. We first propose how to measure the reasoning error when generating multiple answers. Then, we introduce Format-Adapter, which utilizes LLMs to generate and select suitable reasoning formats by minimizing the error measurement we present. We conduct experiments on math and commonsense reasoning tasks, where Format-Adapter achieves a 4.3% performance improvement on average over previous works, demonstrating the effectiveness.

Adapting state-of-the-art Large Language Models (LLMs) like GPT-4 and Gemini for specific tasks is challenging. Due to the opacity in their parameters, embeddings, and even output probabilities, existing fine-tuning adaptation methods are inapplicable. Consequently, adapting these black-box LLMs is only possible through their API services, raising concerns about transparency, privacy, and cost. To address these challenges, we introduce BBox-Adapter, a novel lightweight adapter for black-box LLMs. BBox-Adapter distinguishes target and source domain data by treating target data as positive and source data as negative. It employs a ranking-based Noise Contrastive Estimation (NCE) loss to promote the likelihood of target domain data while penalizing that of the source domain. Furthermore, it features an online adaptation mechanism, which incorporates real-time positive data sampling from ground-truth, human, or AI feedback, coupled with negative data from previous adaptations. Extensive experiments demonstrate BBox-Adapter's effectiveness and cost efficiency. It improves model performance by up to 6.77% across diverse tasks and domains, while reducing training and inference costs by 31.30x and 1.84x, respectively.