Our focus in this work is on perturbation attacks, where we aim to provide learners that remain robust even when the test data points are perturbed. A distribution shift refers to the phenomenon where the training distribution differs from the test distribution which often leads to a degradation in the learner's performance. Let H be any hypothesis class. Let H be any hypothesis class. Note that the supremum exists here since a union of open sets is also open.

Our focus in this work is on perturbation attacks, where we aim to provide learners that remain robust even when the test data points are perturbed. A distribution shift refers to the phenomenon where the training distribution differs from the test distribution which often leads to a degradation in the learner's performance. Let H be any hypothesis class. Let H be any hypothesis class. Note that the supremum exists here since a union of open sets is also open.

Majority voting is considered an effective method to enhance chain-of-thought reasoning, as it selects the answer with the highest "self-consistency" among different reasoning paths (Wang et al., 2023). However, previous chain-of-thought reasoning methods typically generate only a single answer in each trial, thereby ignoring the possibility of other potential answers. As a result, these alternative answers are often overlooked in subsequent voting processes. In this work, we propose to generate ranked answers in each reasoning process and conduct ranked voting among multiple ranked answers from different responses, thereby making the overall self-consistency more reliable. Specifically, we use three ranked voting methods: Instant-runoff voting, Borda count voting, and mean reciprocal rank voting. We validate our methods on six datasets, including three multiple-choice and three open-ended question-answering tasks, using both advanced open-source and closed-source large language models. Extensive experimental results indicate that our proposed method outperforms the baselines, showcasing the potential of leveraging the information of ranked answers and using ranked voting to improve reasoning performance. The code is available at https://github.com/szu-tera/RankedVotingSC.

Chain-of-thought (CoT) prompting is a simple and effective method for improving the reasoning capabilities of Large language models (LLMs). The basic idea of CoT is to let LLMs break down their thought processes step-by-step by putting exemplars in the input prompt. However, the densely structured prompt exemplars of CoT may cause the cognitive overload of LLMs. Inspired by human cognition, we introduce CoT-Sep, a novel method that strategically employs separators at the end of each exemplar in CoT prompting. These separators are designed to help the LLMs understand their thought processes better while reasoning. It turns out that CoT-Sep significantly improves the LLMs' performances on complex reasoning tasks (e.g., GSM-8K, AQuA, CSQA), compared with the vanilla CoT, which does not use separators. We also study the effects of the type and the location of separators tested on multiple LLMs, including GPT-3.5-Turbo, GPT-4, and LLaMA-2 7B. Interestingly, the type/location of separators should be chosen appropriately to boost the reasoning capability of CoT.

Performing inference on large volumes of samples with large language models (LLMs) can be computationally and financially costly in industry and real-world use. We propose batch prompting, a simple yet effective prompting approach that enables the LLM to run inference in batches, instead of one sample at a time. Our method reduces both token and time costs while retaining downstream performance. We theoretically demonstrate that under a few-shot in-context learning setting, the inference costs decrease almost inverse linearly with the number of samples in each batch. We extensively validate the effectiveness of batch prompting on ten datasets across commonsense QA, arithmetic reasoning, and NLI/NLU: batch prompting significantly~(up to 5x with six samples in batch) reduces the LLM (Codex) inference token and time costs while achieving better or comparable performance. For state-of-the-art Chat-based LLMs, e.g., GPT-3.5 and GPT-4, we show the benefits of batch prompting also hold. Further analysis shows that the number of samples in each batch and the complexity of tasks affect its performance. Moreover, batch prompting can be applied across different reasoning methods using LLMs. Our code can be found at the site https://github.com/xlang-ai/batch-prompting.

While large language models (LLMs) such as ChatGPT and PaLM have demonstrated remarkable performance in various language understanding and generation tasks, their capabilities in complex reasoning and intricate knowledge utilization still fall short of human-level proficiency. Recent studies have established the effectiveness of prompts in steering LLMs towards generating desired outputs. Building on these insights, we introduce a novel framework that harnesses the potential of large-scale pre-trained language models, to iteratively enhance performance of the LLMs. Our framework incorporates three components: \textit{Normal CoT}, a \textit{Convincer}, and an \textit{Answerer}. It processes the output of a typical few-shot chain-of-thought prompt, assesses the correctness of the response, scrutinizes the answer, refines the reasoning, and ultimately produces a new solution. Experimental results on the 7 datasets of miscellaneous problems validate the efficacy of the Self-Convince framework, achieving substantial improvements compared to the baselines. This study contributes to the burgeoning body of research focused on integrating pre-trained language models with tailored prompts and iterative refinement processes to augment their performance in complex tasks.

Recently, Chain-of-Thought (CoT) prompting has delivered success on complex reasoning tasks, which aims at designing a simple prompt like ``Let's think step by step'' or multiple in-context exemplars with well-designed rationales to elicit Large Language Models (LLMs) to generate intermediate reasoning steps. However, the generated rationales often come with mistakes, making unfactual and unfaithful reasoning chains. To mitigate this brittleness, we propose a novel Chain-of-Knowledge (CoK) prompting, where we aim at eliciting LLMs to generate explicit pieces of knowledge evidence in the form of structure triple. This is inspired by our human behaviors, i.e., we can draw a mind map or knowledge map as the reasoning evidence in the brain before answering a complex question. Benefiting from CoK, we additionally introduce a F^2-Verification method to estimate the reliability of the reasoning chains in terms of factuality and faithfulness. For the unreliable response, the wrong evidence can be indicated to prompt the LLM to rethink. Extensive experiments demonstrate that our method can further improve the performance of commonsense, factual, symbolic, and arithmetic reasoning tasks.