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Chain-of-Thought Prompting Elicits Reasoning

in Large Language Models

Jason Wei

Xuezhi Wang

Dale Schuurmans

Maarten Bosma

Brian Ichter

Fei Xia

Ed H. Chi

Quoc V. Le

Denny Zhou

Google Research, Brain Team

{jasonwei,dennyzhou}@google.com

Abstract

We explore how generating a chain of thought—a series of intermediate reasoning

steps—significantly improves the ability of large language models to perform

complex reasoning. In particular, we show how such reasoning abilities emerge

naturally in sufficiently large language models via a simple method called chain-of-

thought prompting, where a few chain of thought demonstrations are provided as

exemplars in prompting.

Experiments on three large language models show that chain-of-thought prompting

improves performance on a range of arithmetic, commonsense, and symbolic

reasoning tasks. The empirical gains can be striking. For instance, prompting a

PaLM 540B with just eight chain-of-thought exemplars achieves state-of-the-art

accuracy on the GSM8K benchmark of math word problems, surpassing even

finetuned GPT-3 with a verifier.

A: The cafeteria had 23 apples originally. They used

20 to make lunch. So they had 23 - 20 = 3. They

bought 6 more apples, so they have 3 + 6 = 9. The

answer is 9.

Chain-of-Thought Prompting

Q: Roger has 5 tennis balls. He buys 2 more cans of

tennis balls. Each can has 3 tennis balls. How many

tennis balls does he have now?

A: The answer is 11.

Q: The cafeteria had 23 apples. If they used 20 to

make lunch and bought 6 more, how many apples

do they have?

A: The answer is 27.

Standard Prompting

Q: Roger has 5 tennis balls. He buys 2 more cans of

tennis balls. Each can has 3 tennis balls. How many

tennis balls does he have now?

A: Roger started with 5 balls. 2 cans of 3 tennis balls

each is 6 tennis balls. 5 + 6 = 11. The answer is 11.

Q: The cafeteria had 23 apples. If they used 20 to

make lunch and bought 6 more, how many apples

do they have?

Model Input

Model Output

Model Output

Model Input

Figure 1: Chain-of-thought prompting enables large language models to tackle complex arithmetic,

commonsense, and symbolic reasoning tasks. Chain-of-thought reasoning processes are highlighted.

36th Conference on Neural Information Processing Systems (NeurIPS 2022).

1 Introduction

Math Word Problems (GSM8K)

0

20

40

60

80

100

33

55

18

57

Solv

e

rate

(%)

Finetuned GPT-3 175B

Prior best

PaLM 540B: standard prompting

PaLM 540B: chain-of-thought prompting

Figure 2: PaLM 540B uses chain-of-

thought prompting to achieve new state-

of-the-art performance on the GSM8K

benchmark of math word problems.

Finetuned GPT-3 and prior best are from

Cobbe et al. (2021).

The NLP landscape has recently been revolutionized by

language models (Peters et al., 2018; Devlin et al., 2019;

Brown et al., 2020, inter alia). Scaling up the size of lan-

guage models has been shown to confer a range of benefits,

such as improved performance and sample efficiency (Ka-

plan et al., 2020; Brown et al., 2020, inter alia). However,

scaling up model size alone has not proved sufficient for

achieving high performance on challenging tasks such as

arithmetic, commonsense, and symbolic reasoning (Rae

et al., 2021).

This work explores how the reasoning ability of large

language models can be unlocked by a simple method

motivated by two ideas. First, techniques for arithmetic

reasoning can benefit from generating natural language

rationales that lead to the final answer. Prior work has

given models the ability to generate natural language inter-

mediate steps by training from scratch (Ling et al., 2017)

or finetuning a pretrained model (Cobbe et al., 2021), in

addition to neuro-symbolic methods that use formal lan-

guages instead of natural language (Roy and Roth, 2015;

Chiang and Chen, 2019; Amini et al., 2019; Chen et al.,

2019). Second, large language models offer the exciting

prospect of in-context few-shot learning via prompting. That is, instead of finetuning a separate

language model checkpoint for each new task, one can simply “prompt” the model with a few

input–output exemplars demonstrating the task. Remarkably, this has been successful for a range of

simple question-answering tasks (Brown et al., 2020).

Both of the above ideas, however, have key limitations. For rationale-augmented training and

finetuning methods, it is costly to create a large set of high quality rationales, which is much more

complicated than simple input–output pairs used in normal machine learning. For the traditional few-

shot prompting method used in Brown et al. (2020), it works poorly on tasks that require reasoning

abilities, and often does not improve substantially with increasing language model scale (Rae et al.,

2021). In this paper, we combine the strengths of these two ideas in a way that avoids their limitations.

Specifically, we explore the ability of language models to perform few-shot prompting for reasoning

tasks, given a prompt that consists of triples: 〈input, chain of thought, output〉. A chain of thought is

a series of intermediate natural language reasoning steps that lead to the final output, and we refer to

this approach as chain-of-thought prompting. An example prompt is shown in Figure 1.

We present empirical evaluations on arithmetic, commonsense, and symbolic reasoning benchmarks,

showing that chain-of-thought prompting outperforms standard prompting, sometimes to a striking

degree. Figure 2 illustrates one such result—on the GSM8K benchmark of math word problems

(Cobbe et al., 2021), chain-of-thought prompting with PaLM 540B outperforms standard prompting

by a large margin and achieves new state-of-the-art performance. A prompting only approach is

important because it does not require a large training dataset and because a single model checkpoint

can perform many tasks without loss of generality. This work underscores how large language models

can learn via a few examples with natural language data about the task (c.f. automatically learning

the patterns underlying inputs and outputs via a large training dataset).

2 Chain-of-Thought Prompting

Consider one’s own thought process when solving a complicated reasoning task such as a multi-step

math word problem. It is typical to decompose the problem into intermediate steps and solve each

before giving the final answer: “After Jane gives 2 flowers to her mom she has 10 ... then after she

gives 3 to her dad she will have 7 ... so the answer is 7.” The goal of this paper is to endow language

models with the ability to generate a similar chain of thought—a coherent series of intermediate

reasoning steps that lead to the final answer for a problem. We will show that sufficiently large

2

language models can generate chains of thought if demonstrations of chain-of-thought reasoning are

provided in the exemplars for few-shot prompting.

Figure 1 shows an example of a model producing a chain of thought to solve a math word problem

that it would have otherwise gotten incorrect. The chain of thought in this case resembles a solution

and can interpreted as one, but we still opt to call it a chain of thought to better capture the idea that it

mimics a step-by-step thought process for arriving at the answer (and also, solutions/explanations

typically come after the final answer (Narang et al., 2020; Wiegreffe et al., 2022; Lampinen et al.,

2022, inter alia)).

Chain-of-thought prompting has several attractive properties as an approach for facilitating reasoning

in language models.

1. First, chain of thought, in principle, allows models to decompose multi-step problems into

intermediate steps, which means that additional computation can be allocated to problems

that require more reasoning steps.

2. Second, a chain of thought provides an interpretable window into the behavior of the model,

suggesting how it might have arrived at a particular answer and providing opportunities

to debug where the reasoning path went wrong (although fully characterizing a model’s

computations that support an answer remains an open question).

3. Third, chain-of-thought reasoning can be used for tasks such as math word problems,

commonsense reasoning, and symbolic manipulation, and is potentially applicable (at least

in principle) to any task that humans can solve via language.

4. Finally, chain-of-thought reasoning can be readily elicited in sufficiently large off-the-shelf

language models simply by including examples of chain of thought sequences into the

exemplars of few-shot prompting.

In empirical experiments, we will observe the utility of chain-of-thought prompting for arithmetic

reasoning (Section 3), commonsense reasoning (Section 4), and symbolic reasoning (Section 5).

3 Arithmetic Reasoning

We begin by considering math word problems of the form in Figure 1, which measure the arithmetic

reasoning ability of language models. Though simple for humans, arithmetic reasoning is a task where

language models often struggle (Hendrycks et al., 2021; Patel et al., 2021, inter alia). Strikingly, chain-

of-thought prompting when used with the 540B parameter language model performs comparably with

task-specific finetuned models on several tasks, even achieving new state of the art on the challenging

GSM8K benchmark (Cobbe et al., 2021).

3.1 Experimental Setup

We explore chain-of-thought prompting for various language models on multiple benchmarks.

Benchmarks. We consider the following five math word problem benchmarks: (1) the GSM8K

benchmark of math word problems (Cobbe et al., 2021), (2) the SVAMP dataset of math word

problems with varying structures (Patel et al., 2021), (3) the ASDiv dataset of diverse math word

problems (Miao et al., 2020), (4) the AQuA dataset of algebraic word problems, and (5) the MAWPS

benchmark (Koncel-Kedziorski et al., 2016). Example problems are given in Appendix Table 12.

Standard prompting. For the baseline, we consider standard few-shot prompting, popularized by

Brown et al. (2020), in which a language model is given in-context exemplars of input–output pairs

before outputting a prediction for a test-time example. Exemplars are formatted as questions and

answers. The model gives the answer directly, as shown in Figure 1 (left).

Chain-of-thought prompting. Our proposed approach is to augment each exemplar in few-shot

prompting with a chain of thought for an associated answer, as illustrated in Figure 1 (right). As most

of the datasets only have an evaluation split, we manually composed a set of eight few-shot exemplars

with chains of thought for prompting—Figure 1 (right) shows one chain of thought exemplar, and the

full set of exemplars is given in Appendix Table 20. (These particular exemplars did not undergo

prompt engineering; robustness is studied in Section 3.4 and Appendix A.2.) To investigate whether

chain-of-thought prompting in this form can successfully elicit successful reasoning across a range of

3

Q: Roger has 5 tennis balls. He buys

2 more cans of tennis balls. Each can

has 3 tennis balls. How many tennis

balls does he have now?

A: Roger started with 5 balls. 2 cans

of 3 tennis balls each is 6 tennis

balls. 5 + 6 = 11. The answer is 11.

Q: Sammy wanted to go to where the

people were. Where might he go?

Options: (a) race track (b) populated areas

(c) desert (d) apartment (e) roadblock

A: The answer must be a place with a

lot of people. Race tracks, desert,

apartments, and roadblocks don't

have a lot of people, but populated

areas do. So the answer is (b).

Q: Yes or no: Would a pear sink in

water?

A: The density of a pear is about 0.6

g/cm^3, which is less than water.

Thus, a pear would float. So the

answer is no.

Q: The concert was scheduled to be

on 06/01/1943, but was delayed by

one day to today. What is the date 10

days ago in MM/DD/YYYY?

A: One day after 06/01/1943 is

06/02/1943, so today is 06/02/1943.

10 days before today is 05/23/1943.

So the answer is 05/23/1943.

Q: Is the following sentence

plausible? "Joao Moutinho caught the

screen pass in the NFC

championship."

A: Joao Moutinho is a soccer player.

The NFC championship is part of

American football, not soccer. So the

answer is no.

Q: Take the last letters of the words

in “Lady Gaga” and concatenate

them.

A: The last letter of “Lady” is “y”. The

last letter of “Gaga” is “a”.

Concatenating them is “ya”. So the

answer is ya.

Q: A coin is heads up. Maybelle flips

the coin. Shalonda does not flip the

coin. Is the coin still heads up?

A: The coin was flipped by Maybelle.

So the coin was flipped 1 time, which

is an odd number. The coin started

heads up, so after an odd number of

flips, it will be tails up. So the answer

is no.

Math Word Problems (free response)

Math Word Problems (multiple choice)

CSQA (commonsense)

StrategyQA

Date Understanding

Sports Understanding

Last Letter Concatenation

Coin Flip (state tracking)

Q: How many keystrokes are needed

to type the numbers from 1 to 500?

Answer Choices: (a) 1156 (b) 1392 (c) 1480

(d) 1562 (e) 1788

A: There are 9 one-digit numbers

from 1 to 9. There are 90 two-digit

numbers from 10 to 99. There are

401 three-digit numbers from 100 to

500. 9 + 90(2) + 401(3) = 1392. The

answer is (b).

SayCan (Instructing a robot)

Human: How would you bring me

something that isn’t a fruit?

Explanation: the user wants

something to eat that isn’t a fruit. An

energy bar is not a fruit, so I will bring

the user an energy bar.

Plan: 1. find(energy bar) 2.

pick(energy bar) 3. find(user) 4.

put(energy bar) 5. done().

Figure 3: Examples of 〈input, chain of thought, output〉 triples for arithmetic, commonsense, and

symbolic reasoning benchmarks. Chains of thought are highlighted. Full prompts in Appendix G.

math word problems, we used this single set of eight chain of thought exemplars for all benchmarks

except AQuA, which is multiple choice instead of free response. For AQuA, we used four exemplars

and solutions from the training set, as given in Appendix Table 21.

Language models. We evaluate five large language models. The first is GPT-3 (Brown et al.,

2020), for which we use text-ada-001, text-babbage-001, text-curie-001, and text-davinci-002, which

presumably correspond to InstructGPT models of 350M, 1.3B, 6.7B, and 175B parameters (Ouyang

et al., 2022).The second is LaMDA (Thoppilan et al., 2022), which has models of 422M, 2B, 8B,

68B, and 137B parameters. The third is PaLM, which has models of 8B, 62B, and 540B parameters.

The fourth is UL2 20B (Tay et al., 2022), and the fifth is Codex (Chen et al., 2021, code-davinci-002

in the OpenAI API). We sample from the models via greedy decoding (though follow-up work shows

chain-of-thought prompting can be improved by taking the majority final answer over many sampled

generations (Wang et al., 2022a)). For LaMDA, we report averaged results over five random seeds,

where each seed had a different randomly shuffled order of exemplars. As LaMDA experiments

did not show large variance among different seeds, to save compute we report results for a single

exemplar order for all other models.

3.2 Results

The strongest results of chain-of-thought prompting are summarized in Figure 4, with all experimental

outputs for each model collection, model size, and benchmark shown in Table 2 in the Appendix.

There are three key takeaways. First, Figure 4 shows that chain-of-thought prompting is an emergent

ability of model scale (Wei et al., 2022b). That is, chain-of-thought prompting does not positively

impact performance for small models, and only yields performance gains when used with models of

∼100B parameters. We qualitatively found that models of smaller scale produced fluent but illogical

chains of thought, leading to lower performance than standard prompting.

4

0

20

40

60

GSM8K

solve

rate

(%)

LaMDA

GPT

PaLM

Standard prompting

Chain-of-thought prompting

Prior supervised best

0

20

40

60

80

SV

AMP

solve

rate

(%)

0.4 8 137

0

25

50

75

100

MA

WPS

solve

rate

(%)

0.4 7 175 8 62 540

Model scale (# parameters in billions)

Figure 4: Chain-of-thought prompting enables

large language models to solve challenging math

problems. Notably, chain-of-thought reasoning

is an emergent ability of increasing model scale.

Prior best numbers are from Cobbe et al. (2021)

for GSM8K, Jie et al. (2022) for SVAMP, and Lan

et al. (2021) for MAWPS.

Second, chain-of-thought prompting has larger

performance gains for more-complicated prob-

lems. For instance, for GSM8K (the dataset

with the lowest baseline performance), perfor-

mance more than doubled for the largest GPT

and PaLM models. On the other hand, for Sin-

gleOp, the easiest subset of MAWPS which only

requires a single step to solve, performance im-

provements were either negative or very small

(see Appendix Table 3).

Third, chain-of-thought prompting via GPT-3

175B and PaLM 540B compares favorably to

prior state of the art, which typically finetunes a

task-specific model on a labeled training dataset.

Figure 4 shows how PaLM 540B uses chain-of-

thought prompting to achieve new state of the art

on GSM8K, SVAMP, and MAWPS (though note

that standard prompting already passed the prior

best for SVAMP). On the other two datasets,

AQuA and ASDiv, PaLM with chain-of-thought

prompting reaches within 2% of the state of the

art (Appendix Table 2).

To better understand why chain-of-thought

prompting works, we manually examined model-

generated chains of thought by LaMDA 137B

for GSM8K. Of 50 random examples where the

model returned the correct final answer, all of

the generated chains of thought were also log-

ically and mathematically correct except two

that coincidentally arrived at the correct answer

(see Appendix D.1, and Table 8 for examples

of correct model-generated chains of thought).

We also randomly examined 50 random sam-

ples for which the model gave the wrong answer.

The summary of this analysis is that 46% of the

chains of thought were almost correct, barring

minor mistakes (calculator error, symbol map-

ping error, or one reasoning step missing), and that the other 54% of the chains of thought had major

errors in semantic understanding or coherence (see Appendix D.2). To provide a small insight into

why scaling improves chain-of-thought reasoning ability, we performed a similar analysis of errors

made by PaLM 62B and whether those errors were fixed by scaling to PaLM 540B. The summary

is that scaling PaLM to 540B fixes a large portion of one-step missing and semantic understanding

errors in the 62B model (see Appendix A.1).

3.3 Ablation Study

The observed benefits of using chain-of-thought prompting raises the natural question of whether the

same performance improvements can be conferred via other types of prompting. Figure 5 shows an

ablation study with three variations of chain of thought described below.

Equation only. One reason for why chain-of-thought prompting might help is that it produces the

mathematical equation to be evaluated, and so we test a variation where the model is prompted

to output only a mathematical equation before giving the answer. Figure 5 shows that equation

only prompting does not help much for GSM8K, which implies that the semantics of the questions

in GSM8K are too challenging to directly translate into an equation without the natural language

reasoning steps in chain of thought. For datasets of one-step or two-step problems, however, we find

that equation only prompting does improve performance, since the equation can be easily derived

from the question (see Appendix Table 6).

5

LaMDA

PaLM

0

20

40

60

GSM8K

solv

e

rate

(%)

Standard prompting

Equation only

Variable compute only

Reasoning after answer

Chain-of-thought prompting

Figure 5: Ablation study for dif-

ferent variations of prompting us-

ing LaMDA 137B and PaLM 540B.

Results for other datasets are given

in Appendix Table 6 and Table 7.

Variable compute only. Another intuition is that chain of

thought allows the model to spend more computation (i.e.,

intermediate tokens) on harder problems. To isolate the effect

of variable computation from chain-of-thought reasoning, we

test a configuration where the model is prompted to output a

only sequence of dots (...) equal to the number of characters in

the equation needed to solve the problem. This variant performs

about the same as the baseline, which suggests that variable

computation by itself is not the reason for the success of chain-

of-thought prompting, and that there appears to be utility from

expressing intermediate steps via natural language.

Chain of thought after answer. Another potential benefit of

chain-of-thought prompting could simply be that such prompts

allow the model to better access relevant knowledge acquired

during pretraining. Therefore, we test an alternative configura-

tion where the chain of thought prompt is only given after the

answer, isolating whether the model actually depends on the

produced chain of thought to give the final answer. This variant

performs about the same as the baseline, which suggests that

the sequential reasoning embodied in the chain of thought is

useful for reasons beyond just activating knowledge.

3.4 Robustness of Chain of Thought

GSM8K

0

5

10

15

20

Solv

e

rate

(%)

Standard prompting

Chain-of-thought prompting

� different annotator (B)

� different annotator (C)

� intentionally concise style

� exemplars from GSM8K (α)

� exemplars from GSM8K (β)

� exemplars from GSM8K (γ)

MAWPS

0

20

40

60

Figure 6: Chain-of-thought prompting

has variance for different prompt exam-

ples (as expected) but outperforms stan-

dard prompting for various annotators as

well as for different exemplars.

Sensitivity to exemplars is a key consideration of prompt-

ing approaches—for instance, varying the permutation of

few-shot exemplars can cause the accuracy of GPT-3 on

SST-2 to range from near chance (54.3%) to near state of

the art (93.4%) (Zhao et al., 2021). In this final subsec-

tion, we evaluate robustness to chains of thought written

by different annotators. In addition to the results above,

which used chains of thought written by an Annotator

A, two other co-authors of this paper (Annotators B and

C) independently wrote chains of thought for the same

few-shot exemplars (shown in Appendix H). Annotator A

also wrote another chain of thought that was more concise

than the original, following the style of solutions given in

Cobbe et al. (2021).1

Figure 6 shows these results for LaMDA 137B on GSM8K

and MAWPS (ablation results for other datasets are given

in Appendix Table 6 / Table 7). Although there is variance

among different chain of thought annotations, as would be

expected when using exemplar-based prompting (Le Scao

and Rush, 2021; Reynolds and McDonell, 2021; Zhao

et al., 2021), all sets of chain of thought prompts outper-

form the standard baseline by a large margin. This result

implies that successful use of chain of thought does not

depend on a particular linguistic style.

To confirm that successful chain-of-thought prompting

works for other sets of exemplars, we also run experiments

with three sets of eight exemplars randomly sampled from the GSM8K training set, an independent

1For instance, whereas original chain of thought uses several short sentences (“’There were originally 9

computers. For each of 4 days, 5 more computers were added. So 5 * 4 = 20 computers were added. 9 + 20 is

29.”), the concise chain of thought would read “5 * 4 = 20 new computers were added. So there are 9 + 20 = 29

new computers in the server room now”.

6

source (examples in this dataset already included reasoning steps like a chain of thought).2 Fig-

ure 6 shows that these prompts performed comparably with our manually written exemplars, also

substantially outperforming standard prompting.

In addition to robustness to annotators, independently-written chains of thought, different exemplars,

and various language models, we also find that chain-of-thought prompting for arithmetic reasoning

is robust to different exemplar orders and varying numbers of exemplars (see Appendix A.2).

4 Commonsense Reasoning

Although chain of thought is particularly suitable for math word problems, the language-based nature

of chain of thought actually makes it applicable to a broad class of commonsense reasoning problems,

which involve reasoning about physical and human interactions under the presumption of general

background knowledge. Commonsense reasoning is key for interacting with the world and is still

beyond the reach of current natural language understanding systems (Talmor et al., 2021).

Benchmarks. We consider five datasets covering a diverse range of commonsense reasoning types.

The popular CSQA (Talmor et al., 2019) asks commonsense questions about the world involving

complex semantics that often require prior knowledge. StrategyQA (Geva et al., 2021) requires

models to infer a multi-hop strategy to answer questions. We choose two specialized evaluation sets

from the BIG-bench effort (BIG-bench collaboration, 2021): Date Understanding, which involves

inferring a date from a given context, and Sports Understanding, which involves determining whether

a sentence relating to sports is plausible or implausible. Finally, the SayCan dataset (Ahn et al.,

2022) involves mapping a natural language instruction to a sequence of robot actions from a discrete

set. Figure 3 shows examples with chain of thought annotations for all datasets.

Prompts. We follow the same experimental setup as the prior section. For CSQA and StrategyQA,

we randomly selected examples from the training set and manually composed chains of thought for

them to use as few-shot exemplars. The two BIG-bench tasks do not have training sets, so we selected

the first ten examples as exemplars in the evaluation set as few-shot exemplars and report numbers on

the rest of the evaluation set. For SayCan, we use six examples from the training set used in Ahn et al.

(2022) and also manually composed chains of thought.

Results. Figure 7 highlights these results for PaLM (full results for LaMDA, GPT-3, and different

model scales are shown in Table 4). For all tasks, scaling up model size improved the performance

of standard prompting; chain-of-thought prompting led to further gains, with improvements appear-

ing to be largest for PaLM 540B. With chain-of-thought prompting, PaLM 540B achieved strong

performance relative to baselines, outperforming the prior state of the art on StrategyQA (75.6% vs

69.4%) and outperforming an unaided sports enthusiast on sports understanding (95.4% vs 84%).

These results demonstrate that chain-of-thought prompting can also improve performance on tasks

requiring a range of commonsense reasoning abilities (though note that gain was minimal on CSQA).

8 62 540

20

40

60

80

100

Solve

rate

(%)

CSQA

8 62 540

50

60

70

80

90

StrategyQA

Standard prompting

Chain of thought

Prior supervised best

Human

8 62 540

0

20

40

60

80

Model scale (# parameters in billions)

Date

8 62 540

40

60

80

100

Sports

8 62 540

20

40

60

80

100

SayCan

Figure 7: Chain-of-thought prompting also improves the commonsense reasoning abilities of

language models. The language model shown here is PaLM. Prior best numbers are from the

leaderboards of CSQA (Talmor et al., 2019) and StrategyQA (Geva et al., 2021) (single-model only,

as of May 5, 2022). Additional results using various sizes of LaMDA, GPT-3, and PaLM are shown

in Table 4.

2We sample examples ≤ 60 tokens to fit into our input context window, and also limit the examples to ≤ 2

steps to solve for a fair comparison with the eight exemplars that we composed.

7

5 Symbolic Reasoning

0

25

50

75

100

Solve

rate

(%)

Letter Concat: 2

(in domain)

Letter Concat: 4

(OOD)

Standard prompting

Chain-of-thought prompting

8

62 540

40

60

80

100

Solve

rate

(%)

Coin Flip: 2

(in domain)

8

62 540

Model scale (# parameters in billions)

Coin Flip: 4

(OOD)

Figure 8:

Using chain-of-thought

prompting facilitates generalization to

longer sequences in two symbolic rea-

soning tasks.

Our final experimental evaluation considers symbolic rea-

soning, which is simple for humans but potentially chal-

lenging for language models. We show that chain-of-

thought prompting not only enables language models to

perform symbolic reasoning tasks that are challenging in

the standard prompting setting, but also facilitates length

generalization to inference-time inputs longer than those

seen in the few-shot exemplars.

Tasks. We use the following two toy tasks.

• Last letter concatenation. This task asks the model

to concatenate the last letters of words in a name (e.g.,

“Amy Brown” → “yn”). It is a more challenging version

of first letter concatenation, which language models can

already perform without chain of thought.3 We generate

full names by randomly concatenating names from the

top one-thousand first and last names from name census

data (https://namecensus.com/).

• Coin flip. This task asks the model to answer whether

a coin is still heads up after people either flip or don’t

flip the coin (e.g., “A coin is heads up. Phoebe flips the

coin. Osvaldo does not flip the coin. Is the coin still

heads up?” → “no”).

As the construction of these symbolic reasoning tasks is

well-defined, for each task we consider an in-domain test

set for which examples had the same number of steps as

the training/few-shot exemplars, as well as an out-of-domain (OOD) test set, for which evaluation

examples had more steps than those in the exemplars. For last letter concatenation, the model only

sees exemplars of names with two words, and then performs last letter concatenation on names with 3

and 4 words.4 We do the same for the number of potential flips in the coin flip task. Our experimental

setup uses the same methods and models as in the prior two sections. We again manually compose

chains of thought for the few-shot exemplars for each task, which are given in Figure 3.

Results. The results of these in-domain and OOD evaluations are shown in Figure 8 for PaLM,

with results for LaMDA shown in Appendix Table 5. With PaLM 540B, chain-of-thought prompting

leads to almost 100% solve rates (note that standard prompting already solves coin flip with PaLM

540, though not for LaMDA 137B). Note that these in-domain evaluations are “toy tasks” in the

sense that perfect solution structures are already provided by the chains of thought in the few-shot

exemplars; all the model has to do is repeat the same steps with the new symbols in the test-time

example. And yet, small models still fail—the ability to perform abstract manipulations on unseen

symbols for these three tasks only arises at the scale of 100B model parameters.

As for the OOD evaluations, standard prompting fails for both tasks. With chain-of-thought prompting,

language models achieve upward scaling curves (though performance is lower than in the in-domain

setting). Hence, chain-of-thought prompting facilitates length generalization beyond seen chains of

thought for language models of sufficient scale.

6 Discussion

We have explored chain-of-thought prompting as a simple mechanism for eliciting multi-step rea-

soning behavior in large language models. We first saw that chain-of-thought prompting improves

performance by a large margin on arithmetic reasoning, yielding improvements that are much stronger

than ablations and robust to different annotators, exemplars, and language models (Section 3). Next,

3We tested 10 common names using GPT-3 davinci and it got all but one correct.

4For names of length longer than 2 words, we concatenate multiple first and last names together.

8

experiments on commonsense reasoning underscored how the linguistic nature of chain-of-thought

reasoning makes it generally applicable (Section 4). Finally, we showed that for symbolic reasoning,

chain-of-thought prompting facilitates OOD generalization to longer sequence lengths (Section 5). In

all experiments, chain-of-thought reasoning is elicited simply by prompting an off-the-shelf language

model. No language models were finetuned in the process of writing this paper.

The emergence of chain-of-thought reasoning as a result of model scale has been a prevailing theme

(Wei et al., 2022b). For many reasoning tasks where standard prompting has a flat scaling curve, chain-

of-thought prompting leads to dramatically increasing scaling curves. Chain-of-thought prompting

appears to expand the set of tasks that large language models can perform successfully—in other

words, our work underscores that standard prompting only provides a lower bound on the capabilities

of large language models. This observation likely raises more questions than it answers—for instance,

how much more can we expect reasoning ability to improve with a further increase in model scale?

What other prompting methods might expand the range of tasks that language models can solve?

As for limitations, we first qualify that although chain of thought emulates the thought processes of

human reasoners, this does not answer whether the neural network is actually “reasoning,” which

we leave as an open question. Second, although the cost of manually augmenting exemplars with

chains of thought is minimal in the few-shot setting, such annotation costs could be prohibitive for

finetuning (though this could potentially be surmounted with synthetic data generation, or zero-shot

generalization). Third, there is no guarantee of correct reasoning paths, which can lead to both correct

and incorrect answers; improving factual generations of language models is an open direction for

future work (Rashkin et al., 2021; Ye and Durrett, 2022; Wiegreffe et al., 2022, inter alia). Finally,

the emergence of chain-of-thought reasoning only at large model scales makes it costly to serve in

real-world applications; further research could explore how to induce reasoning in smaller models.

7 Related Work

This work is inspired by many research areas, which we detail in an extended related work section

(Appendix C). Here we describe two directions and associated papers that are perhaps most relevant.

The first relevant direction is using intermediate steps to solve reasoning problems. Ling et al. (2017)

pioneer the idea of using natural language rationales to solve math word problems through a series

of intermediate steps. Their work is a remarkable contrast to the literature using formal languages

to reason (Roy et al., 2015; Chiang and Chen, 2019; Amini et al., 2019; Chen et al., 2019). Cobbe

et al. (2021) extend Ling et al. (2017) by creating a larger dataset and using it to finetune a pretrained

language model rather than training a model from scratch. In the domain of program synthesis,

Nye et al. (2021) leverage language models to predict the final outputs of Python programs via

first line-to-line predicting the intermediate computational results, and show that their step-by-step

prediction method performs better than directly predicting the final outputs.

Naturally, this paper also relates closely to the large body of recent work on prompting. Since the

popularization of few-shot prompting as given by Brown et al. (2020), several general approaches

have improved the prompting ability of models, such as automatically learning prompts (Lester et al.,

2021) or giving models instructions describing a task (Wei et al., 2022a; Sanh et al., 2022; Ouyang

et al., 2022). Whereas these approaches improve or augment the input part of the prompt (e.g.,

instructions that are prepended to inputs), our work takes the orthogonal direction of augmenting the

outputs of language models with a chain of thought.

8 Conclusions

We have explored chain-of-thought prompting as a simple and broadly applicable method for enhanc-

ing reasoning in language models. Through experiments on arithmetic, symbolic, and commonsense

reasoning, we find that chain-of-thought reasoning is an emergent property of model scale that allows

sufficiently large language models to perform reasoning tasks that otherwise have flat scaling curves.

Broadening the range of reasoning tasks that language models can perform will hopefully inspire

further work on language-based approaches to reasoning.

9

Acknowledgements

We thank Jacob Devlin, Claire Cui, Andrew Dai, and Ellie Pavlick for providing feedback on the

paper. We thank Jacob Austin, Yuhuai Wu, Henryk Michalewski, Aitor Lewkowycz, Charles Sutton,

and Aakanksha Chowdhery for helpful discussions. We thank Sid Maxwell for notifying us about a

mistake in the manual error analysis in the original manuscript.

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