Chain-of-Thought Prompting Elicits Reasoning in Large Language Models

1 Introduction

• PaLM 540B achieves state-of-the-art GSM8K performance (Cobbe et al., 2021) with chain-of-thought prompting, outperforming standard prompting by a large margin.Evaluations also show improvements over standard prompting across arithmetic, commonsense, and symbolic reasoning benchmarks.Source: Figure 2 · p. 2, §1 · p. 2
• Chain-of-thought prompting uses input–reasoning–output exemplars, where intermediate natural-language steps lead to the final answer.The method combines natural-language rationale generation with in-context few-shot learning.Source: §1 · p. 2
• Scaling alone does not ensure strong reasoning, while rationale-augmented training requires costly collections of high-quality intermediate explanations.Traditional few-shot prompting (Brown et al., 2020) performs poorly on reasoning tasks and often improves little with increasing model scale (Rae et al., 2021).Source: §1 · p. 2
• A prompting-only approach avoids requiring a large training dataset and lets a single model checkpoint perform many tasks without losing generality.Models learn from a few examples containing natural-language information about the task.Source: §1 · p. 2

2 Chain-of-Thought Prompting

• Chain-of-thought prompting elicits reasoning in sufficiently large off-the-shelf language models using few-shot exemplars containing intermediate steps leading to a final answer.A chain of thought is a coherent sequence of intermediate reasoning steps.Source: §2 · pp. 2–3
• Decomposing multi-step problems into intermediate steps can, in principle, allocate additional computation to problems requiring more reasoning steps.Source: §2 · p. 3
• Chains of thought offer an interpretable view of possible reasoning paths and opportunities to debug errors, without fully characterizing the computations supporting an answer.Source: §2 · p. 3
• Chain-of-thought reasoning supports math word problems, commonsense reasoning, and symbolic manipulation, with potential applicability to any task humans can solve through language.Source: §2 · p. 3

3.1 Experimental Setup

• Eight manually written reasoning exemplars augment standard question–answer prompting across GSM8K, SVAMP, ASDiv, and MAWPS; multiple-choice AQuA instead uses four training-set exemplars.The shared exemplars did not undergo prompt engineering. Five language-model families were evaluated using greedy decoding; LaMDA results average five shuffled exemplar orders, while other models use one order.Source: §3.1 · pp. 3–4

3.2 Results

• ∼100B-parameter models begin benefiting from chain-of-thought prompting, with larger improvements on more complicated arithmetic problems.GSM8K performance more than doubled for the largest GPT and PaLM models, whereas SingleOp improvements were negative or very small. Smaller models produced fluent but illogical reasoning that reduced performance relative to standard prompting.Source: §3.2 · pp. 4–5
• 46% of incorrect LaMDA 137B GSM8K reasoning chains contained only minor mistakes; the remaining 54% had major semantic-understanding or coherence errors.Among 50 correct-answer examples, only two reasoning chains were not logically and mathematically correct. Scaling PaLM from 62B to 540B fixed many missing-step and semantic-understanding errors.Source: §3.2 · p. 5
• 540B-parameter PaLM achieves new state of the art on GSM8K, SVAMP, and MAWPS, and comes within 2% of state of the art on AQuA and ASDiv.These results compare favorably with prior methods that typically finetune task-specific models on labeled data. Standard prompting already surpassed the prior best on SVAMP.Source: §3 · p. 3, Figure 4 · p. 5, §3.2 · p. 5

3.3 Ablation Study

• Equation-only prompting offers little benefit on GSM8K but improves one- and two-step problems, where equations are easier to derive.The authors interpret this contrast as evidence that GSM8K questions are difficult to translate directly into equations without intermediate natural-language reasoning.Source: §3.3 · p. 5
• Extra computation without reasoning and reasoning placed after the answer perform near baseline, supporting the usefulness of sequential natural-language reasoning before answering.The computation-only variant generated dots matching the character count of the required equation. Placing reasoning after the answer tested whether benefits came merely from activating pretrained knowledge.Source: §3.3 · p. 6

3.4 Robustness of Chain of Thought

• All tested annotation styles substantially outperform standard prompting for LaMDA 137B on GSM8K and MAWPS, despite variation between reasoning annotations.Tests included independently written reasoning from two additional annotators and a more concise version from the original annotator, indicating that success does not require one linguistic style.Source: §3.4 · p. 6
• Randomly sampled GSM8K exemplars perform comparably to manually written prompts, while arithmetic reasoning remains robust to exemplar order and number.Three randomly sampled sets of eight exemplars substantially outperformed standard prompting. Robustness also extended across independently written reasoning and various language models.Source: §3.4 · pp. 6–7

Motivation

• Chain of thought’s language-based format makes it applicable beyond arithmetic to commonsense reasoning about physical and human interactions using general background knowledge.The section motivates this extension by identifying commonsense reasoning as important for interacting with the world and beyond current natural language understanding systems (Talmor et al., 2021).Source: §4 · p. 7

Benchmarks

• Five benchmarks test commonsense knowledge, multi-hop reasoning, date inference, sports plausibility, and mapping instructions to robot-action sequences.The datasets are CSQA (Talmor et al., 2019), StrategyQA (Geva et al., 2021), BIG-bench Date Understanding and Sports Understanding (BIG-bench collaboration, 2021), and SayCan (Ahn et al., 2022).Source: §4 · p. 7

Prompts

• Few-shot prompts use manually composed reasoning chains with training-set exemplars for CSQA, StrategyQA, and SayCan, while BIG-bench tasks use evaluation-set exemplars.CSQA and StrategyQA exemplars were randomly selected; SayCan used six training examples from Ahn et al. (2022). Each BIG-bench task used its first ten evaluation examples as exemplars, with results reported on the remainder.Source: §4 · p. 7

Results

• 75.6% on StrategyQA and 95.4% on Sports Understanding let chain-of-thought-prompted PaLM 540B surpass prior state-of-the-art (69.4%) and unaided sports enthusiast (84%) baselines, respectively.Larger models improved under standard prompting, and chain-of-thought prompting provided further gains, apparently largest for PaLM 540B. Gains on CSQA were minimal.Source: Figure 7 · p. 7, §4 · p. 7

Tasks

• The two toy tasks require concatenating the last letters of words in a name or tracking whether a coin remains heads up after flip/no-flip actions.First-letter concatenation can already be performed without chain of thought. The experiments use manually composed chains of thought as few-shot exemplars.Source: §5 · p. 8

Results

• Almost 100% in-domain solve rates are achieved by PaLM 540B with chain-of-thought prompting on the two symbolic reasoning tasks.Standard prompting already solves coin flip with PaLM 540, though not with LaMDA 137B.Source: Figure 8 · p. 8, §5 · p. 8
• 100B model parameters mark the scale where abstract manipulation of unseen symbols emerges; smaller models fail even when exemplars supply perfect solution structures.In-domain tests require repeating the demonstrated steps with new symbols rather than discovering a new solution structure.Source: §5 · p. 8
• Chain-of-thought prompting supports generalization to longer sequences with improving performance as models scale, whereas standard prompting fails on both out-of-domain tasks.Performance remains below in-domain results. Exemplars contain two-word names or two potential flips; out-of-domain tests extend these to three and four.Source: §5 · p. 8, Figure 8 · p. 8

• Chain-of-thought prompting substantially improves arithmetic reasoning, outperforming ablations and remaining robust across annotators, exemplars, and language models.It provides a simple mechanism for eliciting multistep reasoning behavior.Source: §6 · p. 8
• Commonsense experiments demonstrate broad linguistic applicability, while symbolic experiments show out-of-distribution generalization to longer sequences.All experiments use prompting of off-the-shelf language models; no models were finetuned.Source: §6 · p. 9
• Chain-of-thought reasoning emerges with model scale (Wei et al., 2022b), yielding sharply increasing performance where standard prompting often has flat scaling curves.Standard prompting therefore provides only a lower bound on model capabilities; gains from further scaling and other prompting methods remain open questions.Source: §6 · p. 9
• Human-like chains of thought neither establish that models actually reason nor guarantee correct reasoning paths or answers.Improving factual generations remains an open research direction (Rashkin et al., 2021; Ye and Durrett, 2022; Wiegreffe et al., 2022, inter alia).Source: §6 · p. 9
• Manual chain-of-thought annotation costs are minimal for few-shot prompting but could become prohibitive for finetuning.Synthetic data generation or zero-shot generalization could potentially mitigate these costs.Source: §6 · p. 9
• Emergence only at large model scales makes chain-of-thought reasoning costly to serve in real-world applications.Inducing reasoning in smaller models is a direction for further research.Source: §6 · p. 9

Intermediate reasoning steps

• Ling et al. (2017) pioneered solving math word problems through intermediate steps expressed as natural-language rationales.This contrasts with reasoning through formal languages (Roy et al., 2015; Chiang and Chen, 2019; Amini et al., 2019; Chen et al., 2019).Source: §7 · p. 9
• Cobbe et al. (2021) extended Ling et al. (2017) with a larger dataset and pretrained-language-model finetuning rather than training from scratch.Source: §7 · p. 9
• Nye et al. (2021) showed that predicting intermediate computational results line by line outperformed directly predicting Python programs’ final outputs.Source: §7 · p. 9

Prompting

• Chain-of-thought prompting augments model outputs with intermediate reasoning, an orthogonal direction to approaches that improve or augment prompt inputs.Following the popularization of few-shot prompting by Brown et al. (2020), approaches include automatically learning prompts (Lester et al., 2021) and providing task instructions (Wei et al., 2022a; Sanh et al., 2022; Ouyang et al., 2022).Source: §7 · p. 9

8 Conclusions

• Chain-of-thought reasoning emerges with model scale, enabling sufficiently large language models to perform reasoning tasks that otherwise exhibit flat scaling curves.The experiments cover arithmetic, symbolic, and commonsense reasoning.Source: §8 · p. 9
• Chain-of-thought prompting offers a simple, broadly applicable method for enhancing reasoning in language models.The method’s demonstrated reasoning capability is qualified by the requirement for sufficiently large models.Source: §8 · p. 9
• The authors hope that broadening language models’ reasoning capabilities will inspire further work on language-based approaches to reasoning.Source: §8 · p. 9

Checklist

• Generated chains of thought are not always factual, and the authors do not recommend treating them as factual or using them in real-world scenarios.The authors do not expect direct negative societal impacts from the paper’s contributions.Source: Checklist · p. 15
• The checklist reports reproducibility materials and resource descriptions but omits a total compute estimate despite using proprietary models.Supplementary materials include LaMDA and GPT-3 inputs, outputs, and targets; GPT-3 results are described as fully reproducible. Tables 6 and 7 report LaMDA 137B standard deviations across seeds defined by exemplar order.Source: Checklist · p. 15

A.1 Why does increasing model scale improve chain-of-thought prompting?

• 10B parameters marks a scale below which chain-of-thought prompting hurt most models, making its eventual success unpredictable from smaller-model performance alone.Small models struggled with symbol mapping, arithmetic abilities discussed by Brown et al. (2020), and producing parseable final answers. The authors hypothesize multiple emergent abilities; causal roles of pretraining data, architecture, and optimization remain unresolved.Source: §A.1 · p. 16
• 540B-parameter PaLM fixed a substantial portion of PaLM 62B errors across semantic understanding, one step missing, and other categories.The analysis categorized 45 errors: semantic understanding (20), one step missing (18), and other errors (7), including hallucinations, repetition, and symbol mapping. Model scale is confounded with factors such as training compute.Source: Figure 9 · p. 16, §A.1 · p. 16

A.2 What is the role of prompt engineering?

• Three annotators’ chains of thought substantially outperformed the baseline across eight arithmetic, commonsense, and symbolic reasoning datasets despite different writing styles.Three randomly sampled sets of eight GSM8K exemplars, written by workers without machine-learning backgrounds, also beat the baseline on all four arithmetic datasets. Testing each set across those datasets suggests exemplars need not share the test distribution.Source: §A.2 · pp. 17–18
• Five datasets retained chain-of-thought gains across varying exemplar counts; increasing standard-prompt exemplars from 8 to 16 did not close the gap in preliminary experiments.Prompt-order standard deviations were generally small, except for coin flip. The authors suggest that consecutive same-category exemplars may bias classification outputs, following Zhao et al. (2021).Source: §A.2 · p. 18
• Identical chain-of-thought prompts improved performance across LaMDA, GPT-3, and PaLM, except GPT-3 on CSQA and StrategyQA, showing imperfect transfer across models.The authors identify pretraining datasets and model architectures as factors for future investigation.Source: §A.2 · p. 18
• 99.6% coin-flip performance for Annotator A versus 71.4% for Annotator C, both above standard prompting’s 50.0%, illustrates substantial prompt sensitivity.For reversing five items, two co-authors failed to create successful prompts while a third produced one that solved the task perfectly. Future work could automatically generate reasoning chains with a language model and potentially optimize them on validation data.Source: §A.2 · p. 18

A.3 Will chain-of-thought prompting improve performance for my task of interest?

• The authors suggest three conditions maximize benefits: challenging multi-step reasoning, a large language model, and a relatively flat scaling curve.Benefits are smaller when one or more conditions are absent.Source: §A.3 · pp. 18–19
• Chain-of-thought prompting is applicable in principle to any text-to-text task, but this paper focuses on arithmetic, commonsense, and symbolic multi-step reasoning.The authors propose potential applications wherever humans use intermediate reasoning, leaving evaluation on diverse tasks such as machine translation to future work.Source: §A.3 · pp. 18–19
• Chain-of-thought prompting produces its largest arithmetic reasoning gain for PaLM 540B on GSM8K, which combines challenging multi-step problems with a flat scaling curve.This setting matches the authors’ proposed conditions for benefiting most from chain-of-thought prompting.Source: §A.3 · p. 19
• 90% or higher performance for PaLM 540B on MAWPS SingleOP, SingleEq, and AddSub leaves little improvement headroom, and chain-of-thought gains are small.These subsets require only one or two reasoning steps.Source: §A.3 · p. 19

A.4 Why is prompting with the equation only not enough for some arithmetic reasoning datasets?

• Equation-only prompting helps on SVAMP, ASDiv, and MAWPS, especially with few reasoning steps, but does not substantially improve GSM8K performance.The authors’ qualitative analysis suggests that GSM8K questions are too semantically challenging to translate directly into equations.Source: §A.4 · p. 19
• Natural-language intermediate steps let models reason about individual parts of a question rather than translate all its semantics directly into one equation.This provides the authors’ explanation for why equation-only prompting can be insufficient.Source: §A.4 · p. 19

B All Experimental Results

• Chain-of-thought prompting shows scale-dependent benefits on arithmetic and commonsense benchmarks and enables length generalization on two symbolic manipulation tasks.Arithmetic ablations place equation-only prompting between standard and chain-of-thought prompting; robustness tests retain large gains despite changing annotators or exemplars. These tests mostly use LaMDA 137B, with PaLM used for SayCan.Source: Table 1 · p. 20, Table 2 · p. 21, Table 4 · p. 22

C Extended Related Work

• Chain-of-thought prompting draws inspiration from prompting, natural language explanations, program synthesis and execution, numeric and logical reasoning, and intermediate language steps.Source: C Extended Related Work · p. 24

C.1 Prompting

• Chain-of-thought prompting belongs to general prompting approaches and augments model outputs rather than adding task instructions to inputs.Instruction-based approaches instead augment inputs (Raffel et al., 2020; Wei et al., 2022a; Ouyang et al., 2022; Sanh et al., 2022; Wang et al., 2022b).Source: §C.1 · p. 24

C.2 Natural language explanations

• Chain-of-thought prompting precedes the final answer and targets multi-hop task decomposition, with interpretability a side effect rather than its primary goal.Natural language explanation work often targets interpretability (Rajagopal et al., 2021) and generates explanations alongside or after predictions (Narang et al., 2020; Majumder et al., 2021; Wiegreffe et al., 2021, 2022).Source: §C.2 · p. 24

C.3 Program synthesis and execution

• Chain-of-thought prompting generalizes domain-specific program-execution primitives into open-domain natural language reasoning.An external Python calculator can evaluate generated equations and propagate corrected results to subsequent equations through string matching. This significantly improves chain-of-thought performance on most arithmetic tasks.Source: B All Experimental Results · p. 20, §C.3 · p. 24

C.4 Numeric and logical reasoning

• Chain-of-thought prompting handles a broad range of reasoning tasks without finetuning, unlike often task-specific numeric and logical reasoning approaches.Prior approaches include executable operations for BERT (Andor et al., 2019), graph neural networks (Ran et al., 2019), and specialized training procedures (Pi˛ekos et al., 2021).Source: §C.4 · pp. 24–25

C.5 Intermediate language steps

• Sufficiently large off-the-shelf models can produce intermediate reasoning through prompting, without extensive labeled annotations or gradient updates across reasoning tasks.This contrasts with approaches that typically obtain intermediate-step reasoning through training or finetuning on manually annotated or synthetic datasets.Source: §C.5 · p. 25

D.1 Correct Chain of Thought Analysis

• 49 of 50 correct-answer GSM8K chains from LaMDA 137B had correct logic and mathematics, although five contained minor imperfections.One chain reached the correct answer through incorrect reasoning. Incorrect reasoning paths were more likely to yield correct answers on multiple-choice or binary tasks, motivating further analysis of chain factuality.Source: §D.1 · pp. 25–26

D.2 Incorrect Chain of Thought Analysis

• 17.3% GSM8K solve rate was achieved by LaMDA 137B with an external Python calculator, versus 14.3% without it.Calculator errors were the only problem in 8% of sampled incorrect chains. Another 34% contained calculator errors alongside other errors.Source: §D.2 · p. 27
• 16% of sampled incorrect chains involved symbol-mapping errors, while 22% could be corrected by adding one missing reasoning step.Symbol-mapping errors required changing only number symbols and equations—not words—to make the entire reasoning process correct. These categories were assessed independently of calculator errors.Source: §D.2 · p. 27
• 54% (27 of 50) of sampled incorrect chains required substantial edits, nearly always involving semantic-understanding errors; eight of these also contained incoherent reasoning.The authors manually categorized 50 randomly sampled incorrect LaMDA 137B GSM8K outputs by the changes needed to correct them. Incoherent statements failed to follow prior statements or violated basic world knowledge.Source: §D.2 · pp. 27–28
• Generated reasoning is not guaranteed to be coherent or factually correct, and flawed reasoning can produce accidentally correct answers.Accidental correctness is more likely in binary classification than free response, and improving factuality might improve multistep reasoning. Generating multiple reasoning paths and scoring them could improve decoding, but requires training a verifier (Cobbe et al., 2021; Shen et al., 2021; Thoppilan et al., 2022).Source: §D.2 · p. 28

D.3 Additional Robustness Analysis

• Chain-of-thought prompting consistently outperformed standard prompting across varying exemplar counts in five datasets tested with LaMDA 137B.These datasets had mostly flat scaling curves under standard prompting. The main experiments used eight exemplars, constrained by a 1024-token input limit.Source: §D.3 · p. 28, Figure 11 · p. 29

Version Control

• Successive versions added PaLM, GPT-3, Codex, and UL2 results, expanded evaluations and appendices, and corrected Figure 3 typos.Additions included SVAMP and AQuA math evaluations, SayCan commonsense evaluation, commonsense and symbolic-reasoning ablations, extended related work, an FAQ, and raw results.Source: Version Control · p. 30

E.2 Computational Resources

• All three evaluated language models used prompting-only inference without finetuning; LaMDA and PaLM ran on TPUs, while GPT-3 used the public API.LaMDA 137B used TPU v3 in an 8x8 configuration with 64 chips and 128 cores. PaLM 540B used TPU v4 in a 4x4x12 configuration with 192 chips and 384 cores.Source: §E.2 · p. 30

E.3 Dataset Details and Licenses

• The dataset appendix documents arithmetic and commonsense dataset details and licenses; symbolic reasoning datasets were created synthetically.The synthetic dataset construction is described in Section 4.Source: §E.3 · p. 30

Arithmetic reasoning

• GSM8K (Cobbe et al., 2021) and SVAMP use MIT licenses; MultiArith (Roy and Roth, 2015) uses CC BY 4.0.The arithmetic inventory also lists AddSub, ASDiv (Miao et al., 2020), and AQuA (Ling et al., 2017), providing dataset locations and an AQuA license reference.Source: Arithmetic reasoning · p. 30

Commonsense reasoning

• StrategyQA (Geva et al., 2021) uses the open-domain, question-only set from BIG-bench collaboration (2021).The inventory also includes CSQA (Talmor et al., 2019), Date Understanding and Sports Understanding (BIG-bench collaboration, 2021), and SayCan (Ahn et al., 2022). Listed licenses are MIT for original StrategyQA, Apache License v.2 for the two BIG-Bench tasks, and CC BY 4.0 for SayCan.Source: Commonsense reasoning · pp. 30–31

F Appendix: Input/Output Examples

• The output appendix presents correct and incorrect chains of thought from LaMDA 137B on symbolic and commonsense tasks and PaLM 540B on SayCan.Illustrated tasks include letter concatenation, coinflip, StrategyQA, Date Understanding, and Sports Understanding.Source: Table 13 · p. 32, Table 14 · p. 32, Table 16 · p. 33

G Appendix: Full Prompts

• Math-word-problem prompts share one exemplar set except for AQuA, while letter concatenation and coinflip tasks receive separate chain-of-thought prompts.The math exemplars demonstrate intermediate reasoning followed by an explicit final answer.Source: Table 20 · p. 35, G Appendix: Full Prompts · p. 35, Table 21 · p. 36
• Full chain-of-thought prompts also cover CSQA, StrategyQA, Date Understanding, Sports Understanding, and SayCan robot planning.CSQA answer choices retain separating newlines in the actual prompt, although the table omits them for space.Source: Table 24 · p. 38, Table 25 · p. 39, Table 26 · p. 39

H Appendix: Alternate Annotators for MWP

• Alternate math-word-problem prompts retain the same exemplars but replace Annotator A’s chains of thought with versions written by Annotators B and C.The annotators were co-authors familiar with the goal of chain-of-thought prompting.Source: Table 29 · p. 42, Table 30 · p. 43