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There are several variants of chain of thought prompting that have been proposed in the literature. For example, Kojima et al. (2022) introduce Zero- shot-CoT, in which LLMs are simply prompted with the phrase “Let’s think step by step” after the input, in order to elicit reasoning without the need for few-shot demonstrations. Wang et al. (2022a) propose to iteratively prompt chain of thought. Shi et al. (2022) attempt to solve multilingual reason- ing tasks with CoT in the native language, CoT in English (regardless of the problem language), and CoT in English (with the problem translated to English). Chen (2022) apply CoT to table-based reasoning, i nding that LLMs can achieve strong performance on table tasks with only one exem- plar. Prystawski et al. (2022) demonstrate that CoT can improve LLMs’ performance on paraphrase selection for metaphors. 3.2.2Rationale Engineering The original version of chain of thought prompting, proposed by Wei et al. (2022b), relies on manually crafted examples of intermediate reasoning steps or through rationale exploration and rationale ver- if i cation, which involve exploring and verifying the rationales produced by LLMs. A summary of

raltionale engineering is illustrated in Figure 1. Rationale creation & ref i nement.The choice of exemplars can signif i cantly affect the few-shot per- formance of LLMs, as demonstrated in research such as Liu et al. (2022), which also appears in chain of thought prompting. Rationale creation & ref i nement aims to create and ref i ne rationale exam- ples that are better able to elicit reasoning in LLMs. Fu et al. (2022b) propose complexity-based prompt- ing to create rationales with more reasoning steps. Their experiments show that the performance of LLMs improves with the increased rationale com- plexity. Similarly, Zhou et al. (2022c) propose algo- rithmic prompting, which suggests that providing more thorough examples of solutions can help im- prove reasoning performance on some simple math calculations. Zhang et al. (2022) design Auto-CoT to automatically construct exemplars by partition- ing questions from a given dataset into clusters and then using Zero-Shot-CoT (Kojima et al., 2022) to generate the rationale for a representative question from each cluster. The analysis shows that making exemplars diverse is important in prompting LLMs to produce better rationales.

3.2.3Problem Decomposition Chain of thought prompting, while effective for eliciting reasoning in LLMs, can struggle with com- plex tasks, e.g., tasks that require compositional generalization (Lake and Baroni, 2018; Keysers et al., 2020). To solve a complex problem, it is helpful to i rst break it down into smaller, more manageable subproblems. By solving each of these subproblems, we can effectively solve the complex problem. This technique is called problem decom- position or divide and conquer (Talmor and Berant, 2018; Min et al., 2019; Perez et al., 2020; Yang et al., 2022).

Based on this idea, Zhou et al. (2022a) propose least-to-most prompting, which consists of two steps: decomposing the complex problem into sub- problems and solving these subproblems in a spe- cif i c order, with each subproblem being facilitated by the answers obtained from previously solved subproblems. As follow-up work, Drozdov et al. (2022) introduce dynamic least-to-most prompting, which is designed to solve more realistic seman- tic parsing problems by decomposing the problems with prompting-based syntactic parsing and dynam- ically selecting exemplars based on the decompo- sition. A similar idea is presented in Yang et al. (2022) earlier, who decompose the semantic pars- ing problem using a rule-based system and each subproblem is solved by an ensemble of a i netuned BART (Lewis et al., 2020) and a zero-shot model. In addition, Khot et al. (2022) design decomposed prompting, which breaks down a complex prob- lem into subproblems that can be handled by a shared library of prompting-based LLMs, each spe- cialized in a particular subproblem. Furthermore, Dua et al. (2022) develop successive prompting, which iteratively decomposes a complex problem into a simple problem, with the next subproblem prediction having access to the answers to the pre- vious subproblems. Overall, these techniques show promise for helping LLMs to solve complex tasks by decomposing the problem into smaller, more manageable subproblems. 3.2.4Others There are other techniques that have been devel- oped to facilitate reasoning in LLMs for specif i c tasks or settings.For instance, Creswell et al. (2022); Creswell and Shanahan (2022) introduce a selection-inference framework that uses LLMs as modules to select and infer reasoning steps from a set of facts that culminate in the i nal answer. Jung et al. (2022) propose a method for solving binary questions by prompting LLMs abductively and recursively to rationalize each option. Zhou et al. (2022b) design a technique for performing numerical reasoning on complex numbers by re- placing the complex numbers with simple numbers to produce simpler expressions, and then using these expressions to perform calculations on the complex numbers. Lu et al. (2022) apply chain of thought to solve multimodal science questions. There are also efforts to distill reasoning from large LLMs into smaller models, such as the work by Li et al. (2022a); Shridhar et al. (2022); Magister et al. (2022). Finally, we refer the reader to Dohan et al. (2022)’s position paper on language model cascade, which presents a unifying framework for understanding this line of work. 3.3Hybrid Method While “prompting” techniques can help elicit or better utilize reasoning in large language models to solve reasoning tasks, they do not actually im- prove the reasoning capabilities of the LLMs them- selves, as the parameters of the models remain un- changed. In contrast, the “hybrid approach” aims to simultaneously improve the reasoning capabilities of LLMs and make better use of these models in order to solve complex problems. This approach in- volves both enhancing the reasoning capabilities of the LLMs and using techniques such as prompting to effectively utilize these capabilities. 3.3.1Reasoning-Enhanced Training and Prompting One approach to improving the reasoning capabili- ties of LLMs is to pretrain or i netune the models on datasets that include “reasoning”. Lewkowycz et al. (2022) i nd that LLMs trained on datasets containing scientif i c and mathematical data can achieve better performance on reasoning tasks like quantitative reasoning problems when using CoT prompting3. Furthermore, Chung et al. (2022) de- velop Flan models by i netuning PaLM (Chowdh- ery et al., 2022) and T5 (Raffel et al., 2020) with 1.8k i netuning tasks, including CoT data, and i nd that CoT data are critical to keeping reasoning abil- ities. Anil et al. (2022) study the length gener- alization abilities of LLMs, i.e., whether LLMs learned with short problem instances can general- ize to long ones. They discover that the combina- tion of few-shot scratchpad (or chain of thought) i netuning and scratchpad prompting results in a signif i cant improvement in LLMs’ ability to gener- alize to longer problems, while this phenomenon is not observed in the standard fully supervised i netuning paradigm.

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