Step-by-step reasoning approaches like chain-of-thought (CoT) have proved to be a very effective technique to induce reasoning capabilities in large language models. However, the success of the CoT approach depends primarily on model size, and often billion parameter-scale models are needed to get CoT to work. In this paper, we propose a knowledge distillation approach, that leverages the step-by-step CoT reasoning capabilities of larger models and distils these reasoning abilities into smaller models. Our approach Decompositional Distillation learns a semantic decomposition of the original problem into a sequence of subproblems and uses it to train two models: a) a problem decomposer that learns to decompose the complex reasoning problem into a sequence of simpler sub-problems and b) a problem solver that uses the intermediate subproblems to solve the overall problem. On a multi-step math word problem dataset (GSM8K), we boost the performance of GPT-2 variants up to 35% when distilled with our approach compared to CoT. We show that using our approach, it is possible to train a GPT-2-large model (775M) that can outperform a 10X larger GPT-3 (6B) model trained using CoT reasoning. Finally, we also demonstrate that our approach of problem decomposition can also be used as an alternative to CoT prompting, which boosts the GPT-3 performance by 40% compared to CoT prompts.

Language models (LMs) have demonstrated remarkable performance on downstream tasks, using in-context exemplars or human instructions. Recent works have shown that chain-of-thought (CoT) prompting can elicit models to solve complex reasoning tasks, step-by-step. However, the efficacy of prompt-based CoT methods is restricted to very large LMs such as GPT-3 (175B), thus limiting deployability. In this paper, we revisit the fine-tuning approach to enable complex reasoning in smaller LMs, optimized to efficiently perform a specific task. We propose Fine-tune-CoT, a method that leverages the capabilities of very large LMs to generate reasoning samples and teach smaller models via fine-tuning. We evaluate our method on publicly available LMs across a wide range of complex tasks and model sizes. We find that Fine-tune-CoT enables substantial reasoning capability in small models, whereas previous prompt-based baselines exhibit near-random performance. Student models can even outperform the teacher in some tasks while reducing model size requirements by several orders of magnitude. We conduct extensive ablations and sample studies to understand the reasoning capabilities of student models. We also identify several important nuances that have been overlooked in concurrent fine-tuning works on CoT and address them in our analysis.

Chain of thought prompting successfully improves the reasoning capabilities of large language models, achieving state of the art results on a range of datasets. However, these reasoning capabilities only appear to emerge in models with a size of over 100 billion parameters. In this paper, we explore the transfer of such reasoning capabilities to models with less than 100 billion parameters via knowledge distillation. Specifically, we finetune a student model on the chain of thought outputs generated by a larger teacher model. Our experiments show that the proposed method improves task performance across arithmetic, commonsense and symbolic reasoning datasets. For example, the accuracy of T5 XXL on GSM8K improves from 8.11% to 21.99% when finetuned on PaLM-540B generated chains of thought.

Large language models have recently shown promising progress in mathematical reasoning when fine-tuned with human-generated sequences walking through a sequence of solution steps. However, the solution sequences are not formally structured and the resulting model-generated sequences may not reflect the kind of systematic reasoning we might expect an expert human to produce. In this paper, we study how to build stronger reasoning capability in language models using the idea of relational abstractions. We introduce new types of sequences that more explicitly provide an abstract characterization of the transitions through intermediate solution steps to the goal state. We find that models that are supplied with such sequences as prompts can solve tasks with a significantly higher accuracy, and models that are trained to produce such sequences solve problems better than those that are trained with previously used human-generated sequences and other baselines. Our work thus takes several steps toward elucidating and improving how language models perform on tasks requiring multi-step mathematical reasoning.

Answering complex questions that require making latent decisions is a challenging task, especially when limited supervision is available. Recent works leverage the capabilities of large language models (LMs) to perform complex question answering in a few-shot setting by demonstrating how to output intermediate rationalizations while solving the complex question in a single pass. We introduce ``Successive Prompting'', where we iteratively break down a complex task into a simple task, solve it, and then repeat the process until we get the final solution. Successive prompting decouples the supervision for decomposing complex questions from the supervision for answering simple questions, allowing us to (1) have multiple opportunities to query in-context examples at each reasoning step (2) learn question decomposition separately from question answering, including using synthetic data, and (3) use bespoke (fine-tuned) components for reasoning steps where a large LM does not perform well. The intermediate supervision is typically manually written, which can be expensive to collect. We introduce a way to generate a synthetic dataset which can be used to bootstrap a model's ability to decompose and answer intermediate questions. Our best model (with successive prompting) achieves an improvement of ~5% absolute F1 on a few-shot version of the DROP dataset when compared with a state-of-the-art model with the same supervision.

Reasoning, as an essential ability for complex problem-solving, can provide back-end support for various real-world applications, such as medical diagnosis, negotiation, etc. This paper provides a comprehensive survey of cutting-edge research on reasoning with language model prompting. We introduce research works with comparisons and summaries and provide systematic resources to help beginners. We also discuss the potential reasons for emerging such reasoning abilities and highlight future research directions.

Multi-hop reading comprehension requires not only the ability to reason over raw text but also the ability to combine multiple evidence. We propose a novel learning approach that helps language models better understand difficult multi-hop questions and perform "complex, compositional" reasoning. Our model first learns to decompose each multi-hop question into several sub-questions by a trainable question decomposer. Instead of answering these sub-questions, we directly concatenate them with the original question and context, and leverage a reading comprehension model to predict the answer in a sequence-to-sequence manner. By using the same language model for these two components, our best seperate/unified t5-base variants outperform the baseline by 7.2/6.1 absolute F1 points on a hard subset of DROP dataset.

在有问题的回答需要常识的问题上，语言模型（例如，GPT-3）已用于生成表达有助于提高性能的背景知识的文本。然而，使用此类模型的成本很高。在这项工作中，我们对较小的语言模型产生有用的中间上下文，此处称为阐述。我们的框架在更新两个语言模型之间交替使用 - 阐述生成器和一个答案预测变量 - 允许每个语言都影响彼此。我们的模型使用少于GPT-3的参数的0.5％优于具有相似尺寸的替代方案，并在四个常识性问题上回答基准测试的GPT-3上的差距缩小。人类评估表明，生成的阐述的质量很高。

Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving math problems and proving theorems has garnered significant interest in the fields of machine learning and natural language processing. For example, mathematics serves as a testbed for aspects of reasoning that are challenging for powerful deep learning models, driving new algorithmic and modeling advances. On the other hand, recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning. In this survey paper, we review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade. We also evaluate existing benchmarks and methods, and discuss future research directions in this domain.

Reasoning is a fundamental aspect of human intelligence that plays a crucial role in activities such as problem solving, decision making, and critical thinking. In recent years, large language models (LLMs) have made significant progress in natural language processing, and there is observation that these models may exhibit reasoning abilities when they are sufficiently large. However, it is not yet clear to what extent LLMs are capable of reasoning. This paper provides a comprehensive overview of the current state of knowledge on reasoning in LLMs, including techniques for improving and eliciting reasoning in these models, methods and benchmarks for evaluating reasoning abilities, findings and implications of previous research in this field, and suggestions on future directions. Our aim is to provide a detailed and up-to-date review of this topic and stimulate meaningful discussion and future work.

Large language models (LLMs) can acquire strong code-generation capabilities through few-shot learning. In contrast, supervised fine-tuning is still needed for smaller models to achieve good performance. Such fine-tuning demands a large number of task-specific NL-code pairs, which are expensive to obtain. In this paper, we attempt to transfer the code generation ability of an LLM to a smaller model with the aid of weakly-supervised data. More specifically, we propose explicit knowledge transfer (EKT), which uses the few-shot capabilities of a teacher LLM to create NL-code pairs that we then filter for correctness and fine-tune the student on. We evaluate EKT on the task of generating code solutions to math word problems from the GSM8k dataset. We find that EKT not only yields better performance than training with expert iteration, but also outperforms knowledge distillation, another form of knowledge transfer. A GPT-Neo 1.3B model trained using EKT with a GPT-J teacher achieves a 12.4% pass@100 on GSM8k, while the same student and teacher trained with knowledge distillation yield only a 3.7% pass@100. We also show that it is possible for a student model to outperform the teacher using EKT.

语言模型在需要自然语言理解的各种任务上取得了非凡的表现。然而，最先进的模型通常在需要定量推理的任务上挣扎，例如在大学一级解决数学，科学和工程问题。为了帮助缩小这一差距，我们介绍了Minerva，Minerva是一种在一般自然语言数据上鉴定的大型语言模型，并进一步培训了技术内容。该模型在不使用外部工具的情况下实现了技术基准测试的最新性能。我们还评估了我们在需要定量推理的物理学，生物学，化学，经济学和其他科学方面的200多个本科生问题上评估我们的模型，并发现该模型可以正确回答其中几乎三分之一。

大型语言模型在各种任务上显示出令人印象深刻的几次结果。但是，当知识是此类结果的关键时，就像问题回答和事实检查之类的任务一样，似乎需要存储知识的大量参数计数。众所周知，检索增强模型可以在不需要多个参数的情况下在知识密集的任务上表现出色，但是目前尚不清楚它们是否在几个弹药设置中工作。在这项工作中，我们介绍了地图集，这是一个经过精心设计和预先训练的增强语言模型，能够通过很少的培训示例学习知识密集型任务。我们对包括MMLU，苏格兰短裙和归类等各种任务进行评估，并研究文档索引内容的影响，表明它可以很容易地进行更新。值得注意的是，在自然问题上仅使用64个示例在自然问题上达到超过42 \％的准确性，尽管参数少了50倍，但比540B参数模型的表现优于540b参数模型。

Recently, there has been significant progress in teaching language models to perform step-by-step reasoning to solve complex numerical reasoning tasks. Chain-of-thoughts prompting (CoT) is by far the state-of-art method for these tasks. CoT uses language models to perform both reasoning and computation in the multi-step `thought' process. To disentangle computation from reasoning, we propose `Program of Thoughts' (PoT), which uses language models (mainly Codex) to express the reasoning process as a program. The computation is relegated to an external computer, which executes the generated programs to derive the answer. We evaluate PoT on five math word problem datasets (GSM, AQuA, SVAMP, TabMWP, MultiArith) and three financial-QA datasets (FinQA, ConvFinQA, TATQA) for both few-shot and zero-shot setups. Under both few-shot and zero-shot settings, PoT can show an average performance gain over CoT by around 12\% across all the evaluated datasets. By combining PoT with self-consistency decoding, we can achieve SoTA performance on all math problem datasets and near-SoTA performance on financial datasets. All of our data and code are released in Github\footnote{\url{https://github.com/wenhuchen/Program-of-Thoughts}}.

我们探索如何产生一系列思想 - 一系列中间推理步骤 - 显着提高了大语言模型执行复杂推理的能力。特别是，我们通过一种称为“思想链”提示的简单方法在足够大的语言模型中自然出现这种推理能力，在此过程中，一些思想示范被作为提示的示例提供了。三种大语模型的实验表明，促使思想链提高了一系列算术，常识和象征性推理任务的性能。经验收益可能会引人注目。例如，仅使用八个思想范围的540B参数语言模型才能在数学单词问题的GSM8K基准上实现最新的精度，甚至超过了带有验证器的Fineted GPT-3。

最近的研究表明，理性或逐步思想链可用于改善多步推理任务的性能。我们重新考虑了理由的提示，提示了几次射击中的内部学习学习，其中（输入 - >输出）提示将扩展到（输入，理由 - >输出）提示。对于以理由为提示的提示，我们证明了现有的方法（依赖手动及时工程）如何受到可能损害绩效的次级理由。为了减轻这种脆弱性，我们提出了一个统一的授权合奏的统一框架，在该框架中，我们将输出空间中的理由抽样确定为可鲁棒提高性能的关键组成部分。该框架是一般的，可以轻松地扩展到常见的自然语言处理任务，即使传统上不利于中间步骤的任务，例如问题回答，单词感官歧义和情感分析。我们证明，与现有的提示方法相比，以理由为原理的合奏获得了更准确和可解释的结果 - 包括标准提示，没有理由和基于理由的链链链，同时通过相关理性同时提高了模型预测的解释性。

Large-scale pre-trained language models (PLMs) bring new opportunities to challenge problems, especially those that need high-level intelligence, such as the math word problem (MWPs). However, directly applying existing PLMs to MWPs can fail as the generation process lacks sufficient supervision and thus lacks fast adaptivity as humans. We notice that human reasoning has a dual reasoning framework that consists of an immediate reaction system (system 1) and a delicate reasoning system (system 2), where the entire reasoning is determined by their interaction. This inspires us to develop a cooperative reasoning-induced PLM for solving MWPs, called Cooperative Reasoning (CoRe), resulting in a human-like reasoning architecture with system 1 as the generator and system 2 as the verifier. In our approach, the generator is responsible for generating reasoning paths, and the verifiers are used to supervise the evaluation in order to obtain reliable feedback for the generator. We evaluate our CoRe framework on several mathematical reasoning datasets and achieve decent improvement over state-of-the-art methods, up to 9.8% increase over best baselines.

GPT-3和Palm等大型语言模型在几次学习中表现出色。但是，他们仍然在推理任务（例如算术基准GSM8K）上挣扎。最近的进步故意指导语言模型在产生最终答案之前生成一系列推理步骤，从而成功地将GSM8K基准从17.9％提高到58.1％，以解决问题的解决率。在本文中，我们提出了一种新的方法，即多样化的方法（关于推理步骤的多样化验证者），以进一步提高其推理能力。多样性首先探索不同的提示，以增强推理路径的多样性。其次，Diverse介绍了一个验证者，以区分好的答案和不良答案，从而获得更好的权重投票。最后，多样性验证每个步骤的正确性，而不是整体上的所有步骤。我们使用最新的语言型号Davinci-002进行广泛的实验，并证明多样化可以在八分之六的推理基准中实现新的最先进的性能（例如，GSM8K 74.4％至83.2％），超过棕榈具有540B参数的模型。

Despite the success of large language models (LLMs) in various natural language processing (NLP) tasks, the stored knowledge in these models may inevitably be incomplete, out-of-date, or incorrect. This motivates the need to utilize external knowledge to assist LLMs. Unfortunately, current methods for incorporating external knowledge often require additional training or fine-tuning, which can be costly and may not be feasible for LLMs. To address this issue, we propose a novel post-processing approach, rethinking with retrieval (RR), which retrieves relevant external knowledge based on the decomposed reasoning steps obtained from the chain-of-thought (CoT) prompting. This lightweight approach does not require additional training or fine-tuning and is not limited by the input length of LLMs. We evaluate the effectiveness of RR through extensive experiments with GPT-3 on three complex reasoning tasks: commonsense reasoning, temporal reasoning, and tabular reasoning. Our results show that RR can produce more faithful explanations and improve the performance of LLMs.

最近已被证明大型语言模型在各种任务集中获得合理的零射普通化（Brown等，2020）。它已经假设这是语言模型的隐式多任务学习的结果，在语言模型中的预押（Radford等，2019）。可以通过明确的多任务学习直接引起零拍常规化？为了以缩放测试这个问题，我们开发一个系统，以便轻松地将任何自然语言任务映射到人类可读的提示表单中。我们转换一组大量的监督数据集，每个数据集都有多个提示，具有不同的措辞。这些提示的数据集允许基准测试模型执行完全看不见的任务的能力。我们介绍了一个普拉克尔编码器 - 解码器模型（Raffel等，2020; Lester等，2021），覆盖各种任务。该模型在多个标准数据集中达到强大的零点性能，通常优于其尺寸的型号超过16倍。此外，我们的方法对来自Big-替补基准测试的任务子集具有强烈性能，优于其尺寸的6倍。所有提示和培训的型号都可以在https://github.com/ bigscience-workshop / protectsource / httpsource / https：//huggingface.co/bigscience/t0pp。