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Large Language Models are Zero-Shot Reasoners | Pretrained large language models (LLMs) are widely used in many sub-fields of natural language processing (NLP) and generally known as excellent few-shot learners with task-specific exemplars. Notably, chain of thought (CoT) prompting, a recent technique for eliciting complex multi-step reasoning through step-by-step answer examples, achieved the state-of-the-art performances in arithmetics and symbolic reasoning, difficult system-2 tasks that do not follow the standard scaling laws for LLMs. While these successes are often attributed to LLMs' ability for few-shot learning, we show that LLMs are decent zero-shot reasoners by simply adding ``Let's think step by step'' before each answer. Experimental results demonstrate that our Zero-shot-CoT, using the same single prompt template, significantly outperforms zero-shot LLM performances on diverse benchmark reasoning tasks including arithmetics (MultiArith, GSM8K, AQUA-RAT, SVAMP), symbolic reasoning (Last Letter, Coin Flip), and other logical reasoning tasks (Date Understanding, Tracking Shuffled Objects), without any hand-crafted few-shot examples, e.g. increasing the accuracy on MultiArith from 17.7% to 78.7% and GSM8K from 10.4% to 40.7% with large-scale InstructGPT model (text-davinci-002), as well as similar magnitudes of improvements with another off-the-shelf large model, 540B parameter PaLM. The versatility of this single prompt across very diverse reasoning tasks hints at untapped and understudied fundamental zero-shot capabilities of LLMs, suggesting high-level, multi-task broad cognitive capabilities may be extracted by simple prompting. We hope our work not only serves as the minimal strongest zero-shot baseline for the challenging reasoning benchmarks, but also highlights the importance of carefully exploring and analyzing the enormous zero-shot knowledge hidden inside LLMs before crafting finetuning datasets or few-shot exemplars. | Experimental results demonstrate that the Zero-shot-CoT, using the same single prompt template, significantly outperforms zero-shot LLM performances on diverse benchmark reasoning tasks including arithmetics, symbolic reasoning, and other logical reasoning tasks, without any hand-crafted few-shot examples. | ## Large Language Models are Zero-Shot Reasoners
**Takeshi Kojima**
The University of Tokyo
```
[email protected]
```
**Shixiang Shane Gu**
Google Research, Brain Team
**Machel Reid** **Yutaka Matsuo** **Yusuke Iwasawa**
Google Research[∗] The University of Tokyo The University of Tokyo
**Abstract**
Pretrained large language models (LLMs) are widely used in many sub-fields of
natural language processing (NLP) and generally known as excellent few-shot
learners with task-specific exemplars. Notably, chain of thought (CoT) prompting,
a recent technique for eliciting complex multi-step reasoning through step-bystep answer examples, achieved the state-of-the-art performances in arithmetics
and symbolic reasoning, difficult system-2 tasks that do not follow the standard
scaling laws for LLMs. While these successes are often attributed to LLMs’
ability for few-shot learning, we show that LLMs are decent zero-shot reasoners
by simply adding “Let’s think step by step” before each answer. Experimental
results demonstrate that our Zero-shot-CoT, using the same single prompt template,
significantly outperforms zero-shot LLM performances on diverse benchmark
reasoning tasks including arithmetics (MultiArith, GSM8K, AQUA-RAT, SVAMP),
symbolic reasoning (Last Letter, Coin Flip), and other logical reasoning tasks (Date
Understanding, Tracking Shuffled Objects), without any hand-crafted few-shot
examples, e.g. increasing the accuracy on MultiArith from 17.7% to 78.7% and
GSM8K from 10.4% to 40.7% with large-scale InstructGPT model (text-davinci002), as well as similar magnitudes of improvements with another off-the-shelf
large model, 540B parameter PaLM. The versatility of this single prompt across
very diverse reasoning tasks hints at untapped and understudied fundamental
_zero-shot capabilities of LLMs, suggesting high-level, multi-task broad cognitive_
capabilities may be extracted by simple prompting. We hope our work not only
serves as the minimal strongest zero-shot baseline for the challenging reasoning
benchmarks, but also highlights the importance of carefully exploring and analyzing
the enormous zero-shot knowledge hidden inside LLMs before crafting finetuning
datasets or few-shot exemplars.
**1** **Introduction**
Scaling up the size of language models has been key ingredients of recent revolutions in natural
language processing (NLP) [Vaswani et al., 2017, Devlin et al., 2019, Raffel et al., 2020, Brown et al.,
2020, Thoppilan et al., 2022, Rae et al., 2021, Chowdhery et al., 2022]. The success of large language
models (LLMs) is often attributed to (in-context) few-shot or zero-shot learning. It can solve various
tasks by simply conditioning the models on a few examples (few-shot) or instructions describing the
task (zero-shot). The method of conditioning the language model is called “prompting” [Liu et al.,
2021b], and designing prompts either manually [Schick and Schütze, 2021, Reynolds and McDonell,
2021] or automatically [Gao et al., 2021, Shin et al., 2020] has become a hot topic in NLP.
_∗Work done while at The University of Tokyo._
36th Conference on Neural Information Processing Systems (NeurIPS 2022).
-----
(a) Few-shot (b) Few-shot-CoT
Q: Roger has 5 tennis balls. He buys 2 more cans of tennis
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
balls. Each can has 3 tennis balls. How many tennis balls does he have now?
he have now? A: Roger started with 5 balls. 2 cans of 3 tennis balls each is 6
A: The answer is 11. tennis balls. 5 + 6 = 11. The answer is 11.
Q: A juggler can juggle 16 balls. Half of the balls are golf balls, Q: A juggler can juggle 16 balls. Half of the balls are golf balls,
and half of the golf balls are blue. How many blue golf balls are and half of the golf balls are blue. How many blue golf balls are
there? there?
A: A:
_(Output) The answer is 8. X_ _(Output) The juggler can juggle 16 balls. Half of the balls are golf_
_balls. So there are 16 / 2 = 8 golf balls. Half of the golf balls are_
_blue. So there are 8 / 2 = 4 blue golf balls. The answer is 4. ✓_
(c) Zero-shot (d) Zero-shot-CoT (Ours)
Q: A juggler can juggle 16 balls. Half of the balls are golf balls, Q: A juggler can juggle 16 balls. Half of the balls are golf balls,
and half of the golf balls are blue. How many blue golf balls are and half of the golf balls are blue. How many blue golf balls are
there? there?
A: The answer (arabic numerals) is A: Let’s think step by step.
_(Output) 8 X_ _(Output)_ _There are 16 balls in total. Half of the balls are golf_
_balls. That means that there are 8 golf balls. Half of the golf balls_
_are blue. That means that there are 4 blue golf balls. ✓_
Figure 1: Example inputs and outputs of GPT-3 with (a) standard Few-shot ([Brown et al., 2020]), (b)
Few-shot-CoT ([Wei et al., 2022]), (c) standard Zero-shot, and (d) ours (Zero-shot-CoT). Similar to
Few-shot-CoT, Zero-shot-CoT facilitates multi-step reasoning (blue text) and reach correct answer
where standard prompting fails. Unlike Few-shot-CoT using step-by-step reasoning examples per
**task, ours does not need any examples and just uses the same prompt “Let’s think step by step” across**
_all tasks (arithmetic, symbolic, commonsense, and other logical reasoning tasks)._
In contrast to the excellent performance of LLMs in intuitive and single-step system-1 [Stanovich
and West, 2000] tasks with task-specific few-shot or zero-shot prompting [Liu et al., 2021b], even
language models at the scale of 100B or more parameters had struggled on system-2 tasks requiring
slow and multi-step reasoning [Rae et al., 2021]. To address this shortcoming, Wei et al. [2022],
Wang et al. [2022] have proposed chain of thought prompting (CoT), which feed LLMs with the
step-by-step reasoning examples rather than standard question and answer examples (see Fig. 1-a).
Such chain of thought demonstrations facilitate models to generate a reasoning path that decomposes
the complex reasoning into multiple easier steps. Notably with CoT, the reasoning performance then
satisfies the scaling laws better and jumps up with the size of the language models. For example,
when combined with the 540B parameter PaLM model [Chowdhery et al., 2022], chain of thought
prompting significantly increases the performance over standard few-shot prompting across several
benchmark reasoning tasks, e.g., GSM8K (17.9% → 58.1%).
While the successes of CoT prompting [Wei et al., 2022], along those of many other task-specific
prompting work [Gao et al., 2021, Schick and Schütze, 2021, Liu et al., 2021b], are often attributed
to LLMs’ ability for few-shot learning [Brown et al., 2020], we show that LLMs are decent zero-shot
reasoners by adding a simple prompt, Let’s think step by step, to facilitate step-by-step thinking before
answering each question (see Figure 1). Despite the simplicity, our Zero-shot-CoT successfully
generates a plausible reasoning path in a zero-shot manner and reaches the correct answer in a
problem where the standard zero-shot approach fails. Importantly, our Zero-shot-CoT is versatile and
_task-agnostic, unlike most prior task-specific prompt engineering in the forms of examples (few-shot)_
or templates (zero-shot) [Liu et al., 2021b]: it can facilitate step-by-step answers across various
reasoning tasks, including arithmetic (MultiArith [Roy and Roth, 2015], GSM8K [Cobbe et al., 2021],
AQUA-RAT [Ling et al., 2017], and SVAMP [Patel et al., 2021]), symbolic reasoning (Last letter and
Coin flip), commonsense reasoning (CommonSenseQA [Talmor et al., 2019] and Strategy QA [Geva
et al., 2021]), and other logical reasoning tasks (Date understanding and Tracking Shuffled Objects
from BIG-bench [Srivastava et al., 2022]) without modifying the prompt per task.
We empirically evaluate Zero-shot-CoT against other prompting baselines in Table 2. While our
Zero-shot-CoT underperforms Few-shot-CoT with carefully-crafted and task-specific step-by-step examples, Zero-shot-CoT achieves enormous score gains compared to the zero-shot baseline, e.g. from
17.7% to 78.7% on MultiArith and from 10.4% to 40.7% on GSM8K with large-scale InstructGPT
-----
model (text-davinci-002). We also evaluate Zero-shot-CoT with another off-the-shelf large model,
540B parameter PaLM, showing similar magnitudes of improvements on MultiArith and GSM8K.
Importantly, with our single fixed prompt, zero-shot LLMs have a significantly better scaling curve
comparable to that of the few-shot CoT baseline. We also show that besides Few-shot-CoT requiring
human engineering of multi-step reasoning prompts, their performance deteriorates if prompt example
question types and task question type are unmatched, suggesting high sensitivity to per-task prompt
designs. In contrast, the versatility of this single prompt across diverse reasoning tasks hints at
untapped and understudied zero-shot fundamental capabilities of LLMs, such as higher-level broad
cognitive capabilities like generic logical reasoning [Chollet, 2019]. While the vibrant field of LLMs
started out from the premise of excellent few-shot learners [Brown et al., 2020], we hope our work
encourages more research into uncovering high-level and multi-task zero-shot capabilities hidden
inside those models.
**2** **Background**
We briefly review the two core preliminary concepts that form the basis of this work: the advent of
large language models (LLMs) and prompting, and chain of thought (CoT) prompting for multi-step
reasoning.
**Large language models and prompting** A language model (LM), is a model that looks to estimate
the probability distribution over text. Recently, scaling improvements through larger model sizes
(from a few million [Merity et al., 2016] to hundreds of millions [Devlin et al., 2019] to hundreds of
billions [Brown et al., 2020] parameters) and larger data (e.g. webtext corpora [Gao et al., 2020])
have enabled pre-trained large language models (LLMs) to be incredibly adept at many downstream
NLP tasks. Besides the classic “pre-train and fine-tune” paradigm [Liu et al., 2021b], models scaled
to 100B+ parameters exhibit properties conducive to few-shot learning [Brown et al., 2020], by way
of in context learning, where one can use a text or template known as a prompt to strongly guide the
generation to output answers for desired tasks, thus beginning an era of “pre-train and prompt” [Liu
et al., 2021a]. In work, we call such prompts with explicit conditioning on few task examples as
_few-shot prompts, and other template-only prompts as zero-shot prompts._
**Chain of thought prompting** Multi-step arithmetic and logical reasoning benchmarks have particularly challenged the scaling laws of large language models [Rae et al., 2021]. Chain of thought
(CoT) prompting [Wei et al., 2022], an instance of few-shot prompting, proposed a simple solution
by modifying the answers in few-shot examples to step-by-step answers, and achieved significant
boosts in performance across these difficult benchmarks, especially when combined with very large
language models like PaLM [Chowdhery et al., 2022]. The top row of Figure 1 shows standard
few-shot prompting against (few-shot) CoT prompting. Notably, few-shot learning was taken as a
given for tackling such difficult tasks, and the zero-shot baseline performances were not even reported
in the original work [Wei et al., 2022]. To differentiate it from our method, we call Wei et al. [2022]
as Few-shot-CoT in this work.
**3** **Zero-shot Chain of Thought**
We propose Zero-shot-CoT, a zero-shot template-based prompting for chain of thought reasoning.
It differs from the original chain of thought prompting [Wei et al., 2022] as it does not require
step-by-step few-shot examples, and it differs from most of the prior template prompting [Liu et al.,
2021b] as it is inherently task-agnostic and elicits multi-hop reasoning across a wide range of tasks
with a single template. The core idea of our method is simple, as described in Figure 1: add Let’s
_think step by step, or a a similar text (see Table 4), to extract step-by-step reasoning._
**3.1** **Two-stage prompting**
While Zero-shot-CoT is conceptually simple, it uses prompting twice to extract both reasoning and
answer, as explained in Figure 2. In contrast, the zero-shot baseline (see the bottom-left in Figure 1)
already uses prompting in the form of “The answer is”, to extract the answers in correct formats.
Few-shot prompting, standard or CoT, avoids needing such answer-extraction prompting by explicitly
designing the few-shot example answers to end in such formats (see the top-right and top-left
-----
【2nd prompt】
**Answer Extraction**
【1st prompt】
**Reasoning Extraction**
Q: On average Joe throws 25 punches per Q: On average Joe throws 25 punches per
minute. A fight lasts 5 rounds of 3 minutes. How minute. A fight lasts 5 rounds of 3 ・・・
many punches did he throw? A: Let's think step by step.
**A: Let's think step by step.**
In one minute, Joe throws 25 punches. ・・・In five
rounds, Joe throws 5 * 75 = 375 punches. .
**Therefore, the answer (arabic numerals) is**
LLM
LLM
In one minute, Joe throws 25 punches.
In three minutes, Joe throws 3 * 25 = 75 punches.
In five rounds, Joe throws 5 * 75 = 375 punches. 375.
Figure 2: Full pipeline of Zero-shot-CoT as described in § 3: we first use the first “reasoning” prompt
to extract a full reasoning path from a language model, and then use the second “answer” prompt to
extract the answer in the correct format from the reasoning text.
in Figure 1). In summary, Few-shot-CoT [Wei et al., 2022] requires careful human engineering of
a few prompt examples with specific answer formats per task, while Zero-shot-CoT requires less
engineering but requires prompting LLMs twice.
**1st prompt: reasoning extraction** In this step we first modify the input question x into a prompt
**x[′]** using a simple template “Q: [X]. A: [T]”, where [X] is an input slot for x and [T] is an slot
for hand-crafted trigger sentence t that would extract chain of though to answer the question x. For
example, if we use “Let’s think step by step” as a trigger sentence, the prompt x[′] would be “Q: [X].
A: Let’s think step by step.”. See Table 4 for more trigger examples. Prompted text x[′] is then fed into
a language model and generate subsequent sentence z. We can use any decoding strategy, but we
used greedy decoding throughout the paper for the simplicity.
**2nd prompt: answer extraction** In the second step, we use generated sentence z along with
prompted sentence x[′] to extract the final answer from the language model. To be concrete, we simply
concatenate three elements as with “[X[′]] [Z] [A]”: [X[′]] for 1st prompt x[′], [Z] for sentence z
generated at the first step, and [A] for a trigger sentence to extract answer. The prompt for this step
is self-augmented, since the prompt contains the sentence z generated by the same language model.
In experiment, we use slightly different answer trigger depending on the answer format. For example,
we use “Therefore, among A through E, the answer is” for multi-choice QA, and “Therefore, the
answer (arabic numerals) is” for math problem requiring numerical answer. See Appendix A.5 for
the lists of answer trigger sentences. Finally, the language model is fed the prompted text as input to
generate sentences ˆy and parse the final answer. See “Answer Cleansing” at §4 for the parser details.
**4** **Experiment**
**Tasks and datasets** We evaluate our proposal on 12 datasets from four categories of reasoning
tasks: arithmetic, commonsense, symbolic, and other logical reasoning tasks. See Appendix A.2 for
the detailed description of each datasets.
For arithmetic reasoning, we consider the following six datasets: (1) SingleEq [Koncel-Kedziorski
et al., 2015], (2) AddSub [Hosseini et al., 2014], (3) MultiArith [Roy and Roth, 2015], (4) AQUARAT [Ling et al., 2017], (5) GSM8K [Cobbe et al., 2021], and (6) SVAMP [Patel et al., 2021]. The
first three are from the classic Math World Problem Repository [Koncel-Kedziorski et al., 2016],
and the last three are from more recent benchmarks. SingleEq and AddSub contain easier problems,
which do not require multi-step calculation to solve the tasks. MultiArith, AQUA-RAT, GSM8k, and
SVAMP are more challenging datasets that require multi-step reasoning to solve.
For commonsense reasoning, we use CommonsenseQA [Talmor et al., 2019] and StrategyQA [Geva
et al., 2021]. CommonsenseQA asks questions with complex semantics that often require reasoning
-----
based on prior knowledge [Talmor et al., 2019]. StrategyQA requires models to infer an implicit
multi-hop reasoning to answer questions [Geva et al., 2021].
For symbolic reasoning, we use Last Letter Concatenation and Coin Flip [Wei et al., 2022]. Last
letter Concatenation asks the model to concatenate the last letters of each word. We used randomly
selected four names for each sample. Coin Flip asks the model to answer whether a coin is still heads
up after people either flip or do not flip the coin. We created samples of four times flip or not flip
trials. Although these tasks are easy for humans, LMs typically exhibit a flat scaling curve.
For other logical reasoning tasks, we choose two evaluation sets from the BIG-bench effort [Srivastava
et al., 2022]: Date Understanding [2] and Tracking Shuffled Objects. Date Understanding asks models
to infer the date from a context. Tracking Shuffled Objects tests a model’s ability to infer the final
state of objects given its initial state and a sequence of object shuffling. We used a dataset of tracking
three shuffled objects for our experiment.
**Models** We experiment with 17 models in total. Main experiments are conducted with InstructGPT3 [Ouyang et al., 2022] (text-ada/babbage/curie/davinci-001 and text-davinci-002)[3], original
GPT3 [Brown et al., 2020] (ada, babbage, curie, and davinci)[4], and PaLM [Chowdhery et al., 2022]
(8B, 62B, and 540B). In addition, we used GPT-2[Radford et al., 2019], GPT-Neo[Black et al., 2021],
GPT-J[Wang and Komatsuzaki, 2021], T0 [Sanh et al., 2022], and OPT [Zhang et al., 2022] for model
scaling study. The size of LMs ranges from 0.3B to 540B. We include both standard (e.g. GPT-3 and
OPT), and instruction following variants (e.g. Instruct-GPT3 and T0). See Appendix A.3 for model
description details. Unless otherwise stated, we use text-davinci-002 throughout the experiments.
**Baselines** We compare our Zero-shot-CoT mainly to standard Zero-shot prompting to verify the
effectiveness of its chain of thought reasoning. For Zero-shot experiments, similar answer prompts
as Zero-shot-CoT are used as default. See Appendix A.5 for detail. To better evaluate the zero-shot
ability of LLMs on reasoning tasks, we also compare our method to Few-shot and Few-shot-CoT
baselines from [Wei et al., 2022], using the same in-context examples. Throughout the experiments,
we use greedy decoding across all the methods. For the zero-shot approaches, the results are therefore
deterministic. For the few-shot approaches, since the order of in-context examples could affect the
results [Lu et al., 2022], we run each experiment only once with a fixed seed across all methods and
datasets, for fair comparisons with the zero-shot methods. Wei et al. [2022] showed that the order of
examples did not cause large variance in CoT experiments.
**Answer cleansing** After the model outputs a text by answer extraction (see § 3 and Figure 2), our
method picks up only the part of the answer text that first satisfies the answer format. For example,
if the answer prompting outputs “probably 375 and 376” on arithmetic tasks, we extract the first
number “375” and set it as the model prediction. In the case of multiple-choice, the first large letter
we encounter is set as the prediction. See Appendix A.6 for more detail. Standard Zero-shot method
follows the same idea. For Few-shot and Few-shot-CoT methods, we follow [Wang et al., 2022] and
first extract the answer text after "The answer is " from the model output, and apply the same answer
cleansing to parse the answer text. If “The answer is” is not found in the model output, we search
from the back of the text and set the first text that satisfies the answer format as the prediction.
**4.1** **Results**
**Zero-shot-CoT vs. Zero-shot** Table 1 summarize accuracy of our method (Zero-shot-CoT) and
standard zero-shot prompting (Zero-shot) for each dataset. Zero-shot-CoT substantially outperforms
four out of six arithmetic reasoning tasks (MultiArith, GSM8K, AQUA, SVAMP), all symbolic
reasoning, and all other logical reasoning tasks (from BIG-bench [Srivastava et al., 2022]). For
2While prior work [Wei et al., 2022] categorized Date Understanding task into Common Sense reasoning,
our study categorized this task into logical reasoning because this task requires less prior knowledge and more
logical reasoning between dates.
3Our experiment for Instruct GPT-3 models includes both text-****-001 and text-davinci-002. Text-davinci002 differs from text-****-001 in that they use different fine-tuning data depending on the date range collected
from the APIs. Specifically, text-davinci-002 uses data up to Jun 2021, while text-****-001 uses data up to Oct
[2019. (See https://beta.openai.com/docs/engines/gpt-3)](https://beta.openai.com/docs/engines/gpt-3)
4Our experiments with GPT3 series are conducted by using OpenAI API between April-2022 and May-2022,
except for No.10-16 in Table 4 in Aug-2022.
-----
Table 1: Accuracy comparison of Zero-shot-CoT with Zero-shot on each tasks. The values on the left
side of each task are the results of using answer extraction prompts depending on answer format as
described at § 3. The values on the right side are the result of additional experiment where standard
answer prompt "The answer is" is used for answer extraction. See Appendix A.5 for detail setups.
Arithmetic
SingleEq AddSub MultiArith GSM8K AQUA SVAMP
zero-shot 74.6/78.7 **72.2/77.0** 17.7/22.7 10.4/12.5 22.4/22.4 58.8/58.7
zero-shot-cot **78.0/78.7** 69.6/74.7 **78.7/79.3** **40.7/40.5** **33.5/31.9** **62.1/63.7**
Common Sense Other Reasoning Tasks Symbolic Reasoning
Common Strategy Date Shuffled Last Letter Coin Flip
SenseQA QA Understand Objects (4 words) (4 times)
zero-shot **68.8/72.6** 12.7/54.3 49.3/33.6 31.3/29.7 0.2/- 12.8/53.8
zero-shot-cot 64.6/64.0 **54.8/52.3** **67.5/61.8** **52.4/52.9** **57.6/-** **91.4/87.8**
Table 2: Comparison with baseline methods using accuracies on MultiArith and GSM8K. text-davinci002 is used as the model if not specified. We used the same 8 examples as described in [Wei et al.,
2022] for Few-shot and Few-shot-CoT settings. (*1) To verify the variance of changing examples,
we report two results for 4-shot-cot by splitting the eight examples into two groups. (*2) We insert
“Let’s think step by step.” at the beginning of answer part of each exemplars for Few-shot-CoT to test
performance gains. Further experiment results with PaLM are found at Appendix D
MultiArith GSM8K
**Zero-Shot** **17.7** **10.4**
Few-Shot (2 samples) 33.7 15.6
Few-Shot (8 samples) 33.8 15.6
**Zero-Shot-CoT** **78.7** **40.7**
Few-Shot-CoT (2 samples) 84.8 41.3
Few-Shot-CoT (4 samples : First) (*1) 89.2 -
Few-Shot-CoT (4 samples : Second) (*1) 90.5 -
Few-Shot-CoT (8 samples) 93.0 48.7
**Zero-Plus-Few-Shot-CoT (8 samples) (*2)** **92.8** **51.5**
Finetuned GPT-3 175B [Wei et al., 2022] - 33
Finetuned GPT-3 175B + verifier [Wei et al., 2022] - 55
**PaLM 540B: Zero-Shot** **25.5** **12.5**
**PaLM 540B: Zero-Shot-CoT** **66.1** **43.0**
**PaLM 540B: Zero-Shot-CoT + self consistency** **89.0** **70.1**
PaLM 540B: Few-Shot [Wei et al., 2022] - 17.9
PaLM 540B: Few-Shot-CoT [Wei et al., 2022] - 56.9
PaLM 540B: Few-Shot-CoT + self consistency [Wang et al., 2022] - 74.4
example, Zero-shot-CoT achieves score gains from 17.7% to 78.7% on MultiArith and from 10.4% to
40.7% on GSM8K. Our method gives on-par performances for the remaining two arithmetic reasoning
tasks (SingleEq and AddSub), which is expected since they do not require multi-step reasoning.
In commonsense reasoning tasks, Zero-shot-CoT does not provide performance gains. It is expected
as Wei et al. [2022] also reports that even Few-shot-CoT does not provide performance gains on
Lambda (135B), but does improve StrategyQA when combined with substantially larger PaLM
(540B) model, which may also apply for ours. More importantly, we observe that many generated
chain of thought themselves are surprisingly logically correct or only contains human-understandable
mistakes (See Table 3), suggesting that Zero-shot-CoT does elicit for better commonsense reasoning
even when the task metrics do not directly reflect it. We provide samples generated by Zero-shot-CoT
for each dataset in Appendix B.
-----
Zero-shot Zero-shot-CoT
80
60
40
20
0
0.3B 1.3B 6.7B 175B
Zero-shot Zero-shot-CoT
80
60
40
20
0
S M L XL
Zero-shot Zero-shot-CoT
50
40
30
20
10
0
8B 62B 540B
(a) MultiArith on Original GPT-3
(b) MultiArith on Instruct GPT-3
(c) GMS8K on PaLM
Figure 3: Model scale study with various types of models. S: text-ada-001, M: text-babbage-001, L:
text-curie-001, XL: text-davinci-002. See Appendix A.3 and E for the detail.
Table 3: Examples generated by Zero-Shot-CoT on CommonsenseQA for Error Analysis.
|Example 1 (Reasoning is correct.)|Example 2 (Model cannot choose only one.)|
|---|---|
|Q: Where is a well used toy car likely to be found? Answer Choices: (A) child’s room (B) boy’s bed- room (C) own home (D) toy store (E) house A: Let’s think step by step. A toy car is likely to be found in a child’s room. A child’s room is likely to be found in a house. Therefore, a toy car is likely to be found in a house. Therefore, among A through E, the answer is E. (GT : A, Zero-shot: A)|Q: What would be necessary for getting in shape? Answer Choices: (A) good health (B) exercise (C) muscle tone (D) sweat (E) feel better A: Let’s think step by step. In order to get in shape, you need to be able to do three things: 1. Exercise regularly 2. Eat a healthy diet 3. Get enough sleep If you can do all three of those things, then you will be well on your way to getting in shape! Therefore, among A through E, the answer is B, C, and D. (GT : B, Zero-shot: B)|
|---|---|
**Comparison with other baselines** Table 2 compares the performances on two arithmetic reasoning
benchmarks (MultiArith and GSM8K) across Zero-shot-CoT and baselines. The large gap between
standard prompting (1st block) and chain of thought prompting (2nd block) suggests that these
tasks are difficult without eliciting multi-step reasoning. Major improvements are confirmed on
both Instruct GPT-3 (text-davinci-002) and PaLM (540B) models (4th block). While Zero-shot-CoT
naturally underperforms Few-shot-CoT, it substantially outperforms standard Few-shot prompting
with even 8 examples per task. For GSM8K, Zero-shot-CoT with Instruct GPT-3 (text-davinci-002)
also outperforms finetuned GPT-3 and standard few-shot prompting with large models (PaLM, 540B),
reported in Wei et al. [2022] (3rd and 4th block). See App. D for more experiment results with PaLM.
**Does model size matter for zero-shot reasoning?** Figure 3 compares performance of various
language models on MultiArith / GSM8K. Without chain of thought reasoning, the performance
does not increase or increases slowly as the model scale is increased, i.e., the curve is mostly flat. In
contrast, the performance drastically increases with chain of thought reasoning, as the model size
gets bigger, for Original/Instruct GPT-3 and PaLM. When the model size is smaller, chain of thought
reasoning is not effective. This result aligns with the few-shot experiment results in Wei et al. [2022].
Appendix E shows extensive experiment results using wider variety of language models, including
GPT-2, GPT-Neo, GPT-J, T0, and OPT. We also manually investigated the quality of generated chain
of thought, and large-scale models clearly demonstrate better reasoning (See Appendix B for the
sampled outputs for each model).
**Error Analysis** To better understand the behavior of Zero-shot-CoT, we manually investigated
randomly selected examples generated by Instruct-GPT3 with Zero-shot-CoT prompting. See Appendix C for examples, where some of the observations include: (1) In commonsense reasoning
(CommonsenseQA), Zero-shot-CoT often produces flexible and reasonable chain of thought even
when the final prediction is not correct. Zero-shot-CoT often output multiple answer choices when
the model find it is difficult to narrow it down to one (see Table 3 for examples). (2) In arithmetic
-----
Table 4: Robustness study against template measured on the MultiArith dataset with text-davinci-002.
(*1) This template is used in Ahn et al. [2022] where a language model is prompted to generate
step-by-step actions given a high-level instruction for controlling robotic actions. (*2) This template
is used in Reynolds and McDonell [2021] but is not quantitatively evaluated.
No. Category Template Accuracy
1 instructive Let’s think step by step. **78.7**
2 First, (*1) 77.3
3 Let’s think about this logically. 74.5
4 Let’s solve this problem by splitting it into steps. (*2) 72.2
5 Let’s be realistic and think step by step. 70.8
6 Let’s think like a detective step by step. 70.3
7 Let’s think 57.5
8 Before we dive into the answer, 55.7
9 The answer is after the proof. 45.7
10 misleading Don’t think. Just feel. 18.8
11 Let’s think step by step but reach an incorrect answer. 18.7
12 Let’s count the number of "a" in the question. 16.7
13 By using the fact that the earth is round, 9.3
14 irrelevant By the way, I found a good restaurant nearby. 17.5
15 Abrakadabra! 15.5
16 It’s a beautiful day. 13.1
- (Zero-shot) 17.7
Table 5: Robustness study of Few-shot-CoT against examples. When the examples are from entirely different tasks, the performance generally becomes worse, but when the answer formats are
matched (i.e. CommonsenseQA to AQUA-RAT, multiple-choice), the performance loss is less severe.
_†CommonsenseQA samples are used in this variation_
Zero-shot Few-shot-CoT _[†]_ Zero-shot-CoT Few-shot-CoT
AQUA-RAT 22.4 31.9 33.5 39.0
MultiArith 17.7 27.0 78.7 88.2
reasoning (MultiArith), Zero-shot-CoT and Few-shot-CoT show substantial differences regarding
the error patterns. First, Zero-shot-CoT tends to output unnecessary steps of reasoning after getting
the correct prediction, which results in changing the prediction to incorrect one. Zero-shot-CoT also
sometimes does not start reasoning, just rephrasing the input question. In contrast, Few-shot-CoT
tend to fail when generated chain of thought include ternary operation, e.g. (3 + 2) ∗ 4.
**How does prompt selection affect Zero-shot-CoT?** We validate the robustness of Zero-shot-CoT
against input prompts. Table 4 summarizes performance using 16 different templates with three
categories. Specifically, following Webson and Pavlick [2022], the categories include instructive
(encourage reasoning), misleading (discourage reasoning or encouraging reasoning but in a wrong
way), and irrelevant (nothing to do with reasoning). The results indicate that the performance is
improved if the text is written in a way that encourages chain of thought reasoning, i.e., the templates
are within "instructive" category. However, the difference in accuracy is significant depending on
the sentence. In this experiment, "Let’s think step by step." achieves the best results. Interestingly,
it is found that different templates encourage the model to express reasoning quite differently (see
Appendix B for sample outputs by each template). In contrast, when we use misleading or irrelevant
templates, the performance does not improve. It remains an open question how to automatically
create better templates for Zero-shot-CoT.
**How does prompt selection affect Few-shot-CoT?** Table 5 shows the performance of Fewshot-CoT when using examples from different datasets: CommonsenseQA to AQUA-RAT and
CommonsenseQA to MultiArith. The domains are different in both cases, but the answer format
-----
is the same in the former. Surprisingly, the chain of thought examples from different domains
(common sense to arithmetic) but with the same answer (multiple-choice) format provide substantial
performance gain over Zero-shot (to AQUA-RAT), measured relative to the possible improvements
from Zero-shot-CoT or Few-shot-CoT. In contrast, the performance gain becomes much less when
using examples with different answer types (to MultiArith), confirming prior work [Min et al., 2022]
that suggests LLMs mostly leverage the few-shot examples to infer the repeated format rather than
the task itself in-context. Nevertheless, for both cases the results are worse than Zero-shot-CoT,
affirming the importance of task-specific sample engineering in Few-shot-CoT.
**5** **Discussion and Related Work**
Table 6: Summary of related work on arithmetic/commonsense reasoning tasks. Category denotes the
training strategy. CoT denotes whether to output chain of thought. Task column lists the tasks that
are performed in corresponding papers. AR: Arithmetic Reasoning, CR: Commonsense Reasoning.
Method Category CoT Task Model
Rajani et al. [2019] Fine-Tuning ✓ CR GPT
Cobbe et al. [2021] Fine-Tuning ✓ AR GPT-3
Zelikman et al. [2022] Fine-Tuning ✓ AR,CR GPT-3, etc
Nye et al. [2022] Fine-Tuning[5] ✓ AR Transformer(Decoder)
Brown et al. [2020] Few/Zero-Shot CR GPT-3
Smith et al. [2022] Few/Zero-Shot AR,CR MT-NLG
Rae et al. [2021] Few-Shot AR,CR Gopher
Wei et al. [2022] Few-Shot ✓ AR,CR PaLM, LaMBDA, GPT-3
Wang et al. [2022] Few-Shot ✓ AR,CR PaLM, etc
Chowdhery et al. [2022] Few-Shot ✓ AR,CR PaLM
Shwartz et al. [2020] Zero-Shot ✓ CR GPT-2, etc
Reynolds and McDonell [2021] Zero-Shot ✓ AR GPT-3
Zero-shot-CoT (Ours) Zero-Shot ✓ AR,CR PaLM, Instruct-GPT3, GPT-3, etc
**Reasoning Ability of LLMs** Several studies have shown that pre-trained models usually are not
good at reasoning [Brown et al., 2020, Smith et al., 2022, Rae et al., 2021], but its ability can be
substantially increased by making them produce step-by-step reasoning, either by fine-tuning [Rajani
et al., 2019, Cobbe et al., 2021, Zelikman et al., 2022, Nye et al., 2022] or few-shot prompting [Wei
et al., 2022, Wang et al., 2022, Chowdhery et al., 2022] (See Table 6 for summary of related work).
Unlike most prior work, we focus on zero-shot prompting and show that a single fixed trigger prompt
substantially increases the zero-shot reasoning ability of LLMs across a variety of tasks requiring
complex multi-hop thinking (Table 1), especially when the model is scaled up (Figure 3). It also
generates reasonable and understandable chain of thought across diverse tasks (Appendix B), even
when the final prediction is wrong (Appendix C). Similar to our work, Reynolds and McDonell
[2021] demonstrate a prompt, “Let’s solve this problem by splitting it into steps”, would facilitate
the multi-step reasoning in a simple arithmetic problem. However, they treated it as a task-specific
example and did not evaluate quantitatively on diverse reasoning tasks against baselines. Shwartz et al.
[2020] propose to decompose a commonsense question into a series of information seeking question,
such as “what is the definition of [X]”. It does not require demonstrations but requires substantial
manual prompt engineering per each reasoning task. Our results strongly suggest that LLMs are
decent zero-shot reasoners, while prior work [Wei et al., 2022] often emphasize only few-shot learning
and task-specific in-context learning, e.g. no zero-shot baselines were reported. Our method does
not require time-consuming fine-tuning or expensive sample engineering, and can be combined with
any pre-trained LLM, serving as the strongest zero-shot baseline for all reasoning tasks.
**Zero-shot Abilities of LLMs** Radford et al. [2019] show that LLMs have excellent zero-shot
abilities in many system-1 tasks, including reading comprehension, translation, and summarization.
5Nye et al. [2022] also evaluates few-shot settings, but the few-shot performances on their domains are worse
than the fine-tuning results.
-----
Sanh et al. [2022], Ouyang et al. [2022] show that such zero-shot abilities of LLMs can be increased
by explicitly fine-tuning models to follow instructions. Although these work focus on the zero-shot
performances of LLMs, we focus on many system-2 tasks beyond system-1 tasks, considered a grand
challenge for LLMs given flat scaling curves. In addition, Zero-shot-CoT is orthogonal to instruction
tuning; it increases zero-shot performance for Instruct GPT3, vanilla GPT3, and PaLM (See Figure 3).
**From Narrow (task-specific) to Broad (multi-task) Prompting** Most prompts are task-specific.
While few-shot prompts are naturally so due to task-specific in-context samples [Brown et al., 2020,
Wei et al., 2022], majority of zero-shot prompts have also focused on per-task engineering (of
templates) [Liu et al., 2021b, Reynolds and McDonell, 2021]. Borrowing terminologies from Chollet
[2019] which builds on hierarchical models of intelligence [McGrew, 2005, Johnson and Bouchard Jr,
2005], these prompts are arguably eliciting “narrow generalization” or task-specific skills from LLMs.
On the other hand, our method is a multi-task prompt and elicits “broad generalization” or broad
cognitive abilities in LLMs, such as logical reasoning or system-2 itself. We hope our work can serve
as a reference for accelerating not just logical reasoning research with LLMs, but also discovery of
other broad cognitive capabilities within LLMs.
**Training Dataset Details** A limitation of the work is the lack of public information on the details
of training datasets used for LLMs, e.g. 001 vs 002 for GPT models, original GPT3 vs InstructGPT [Ouyang et al., 2022], and data for PaLM models [Chowdhery et al., 2022]. However, big
performance increases from Zero-shot to Zero-shot-CoT in all recent large models (InstructGPT
001 or 002, Original GPT3, and PaLM) and consistent improvements in both arithmetic and nonarithmetic tasks suggest that the models are unlikely simply memorizing, but instead capturing a
task-agnostic multi-step reasoning capability for generic problem solving. While most results are
based on InstructGPT since it is the best performing open-access LLM, key results are reproduced
on PaLM, and dataset details in InstructGPT (Appendix A, B, and F in Ouyang et al. [2022]) also
confirm that it is not specially engineered for multi-step reasoning.
**Limitation and Social Impact** Our work is based on prompting methods for large language models.
LLMs have been trained on large corpora from various sources on the web (also see “Training Dataset
Details”), and have shown to capture and amplify biases found in the training data. Prompting is a
method that looks to take advantage of the patterns captured by language models conducive to various
tasks, and therefore it has the same shortcomings. This being said, our approach is a more direct way
to probe complex reasoning inside pre-trained LLMs, removing the confounding factor of in-context
learning in prior few-shot approaches, and can lead to more unbiased study of biases in LLMs.
**6** **Conclusion**
We have proposed Zero-shot-CoT, a single zero-shot prompt that elicits chain of thought from large
language models across a variety of reasoning tasks, in contrast to the few-shot (in-context) approach
in previous work that requires hand-crafting few-shot examples per task. Our simple method not only
is the minimalist and strongest zero-shot baseline for difficult multi-step system-2 reasoning tasks
that long evaded the scaling laws of LLMs, but also encourages the community to further discover
similar multi-task prompts that elicit broad cognitive abilities instead of narrow task-specific skills.
**Acknowledgements**
This work has been supported by the Mohammed bin Salman Center for Future Science and Technology for Saudi-Japan Vision 2030 at The University of Tokyo (MbSC2030). Computational resource
of AI Bridging Cloud Infrastructure (ABCI) provided by National Institute of Advanced Industrial
Science and Technology (AIST) was used for experiments other than PaLM. We also thank Jason
Wei and Denny Zhou for discussions and support on running PaLM experiments, and Sharan Narang
and Aakanksha Chowdhery for generic support on PaLM infrastructures.
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-----
**Checklist**
1. For all authors...
(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s
contributions and scope? [Yes]
(b) Did you describe the limitations of your work? [Yes]
(c) Did you discuss any potential negative societal impacts of your work? [Yes]
(d) Have you read the ethics review guidelines and ensured that your paper conforms to
them? [Yes]
2. If you are including theoretical results...
(a) Did you state the full set of assumptions of all theoretical results? [N/A]
(b) Did you include complete proofs of all theoretical results? [N/A]
3. If you ran experiments...
(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes]
(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they
were chosen)? [Yes]
(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [No] Our paper mainly used GPT-3 API with greedy decoding,
and there are no randomness for the experiments.
(d) Did you include the total amount of compute and the type of resources used (e.g., type
of GPUs, internal cluster, or cloud provider)? [Yes]
4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
(a) If your work uses existing assets, did you cite the creators? [Yes]
(b) Did you mention the license of the assets? [Yes]
(c) Did you include any new assets either in the supplemental material or as a URL? [Yes]
(d) Did you discuss whether and how consent was obtained from people whose data you’re
using/curating? [Yes]
(e) Did you discuss whether the data you are using/curating contains personally identifiable
information or offensive content? [Yes]
5. If you used crowdsourcing or conducted research with human subjects...
(a) Did you include the full text of instructions given to participants and screenshots, if
applicable? [N/A]
(b) Did you describe any potential participant risks, with links to Institutional Review
Board (IRB) approvals, if applicable? [N/A]
(c) Did you include the estimated hourly wage paid to participants and the total amount
spent on participant compensation? [N/A]
-----
**A** **Details of Experimental Setup**
**A.1** **Code**
[Code is available at https://github.com/kojima-takeshi188/zero_shot_cot.](https://github.com/kojima-takeshi188/zero_shot_cot)
**A.2** **Datasets**
**A.2.1** **Dataset Description**
Table 7 summarizes the description of each dataset used in our experiment.
Table 7: Dataset Description. Our experiments used publicly available datasets except for “Last
Letters” and “Coin Flip” datasets. We created these two datasets. See Appendix A.2.2 for the details.
(*1) N : Number, M : Pick up one from multiple choices, Y : Answer Yes or No, F : Free Format.
(*2) Average number of words in questions texts.
Dataset Answer
Format
(*1)
# of Avg #
samples words
(*2)
Data split (filename) License
used for our experiment
[SingleEq](https://gitlab.cs.washington.edu/ALGES/TACL2015) N 508 27.4 questions.json No License
[AddSub](https://github.com/wangxr14/Algebraic-Word-Problem-Solver) N 395 31.5 AddSub.json Unspecified
[MultiArith](https://github.com/wangxr14/Algebraic-Word-Problem-Solver) N 600 31.8 MultiArith.json Unspecified
[GSM8K](https://github.com/openai/grade-school-math) N 1319 46.9 test.jsonl MIT License
[AQUA-RAT](https://github.com/deepmind/AQuA) M 254 51.9 test.jsonl Apache-2.0
[SVAMP](https://github.com/arkilpatel/SVAMP) N 1000 31.8 SVAMP.json MIT License
[CommonsenseQA](https://github.com/jonathanherzig/commonsenseqa) M 1221 27.8 dev_rand_split.jsonl Unspecified
[StrategyQA](https://github.com/google/BIG-bench/tree/main/bigbench/benchmark_tasks/strategyqa) Y 2290 9.6 task.json Apache-2.0
[Date Understanding](https://github.com/google/BIG-bench/tree/main/bigbench/benchmark_tasks/date_understanding) M 369 35.0 task.json Apache-2.0
[Shuffled Objects](https://github.com/google/BIG-bench/tree/main/bigbench/benchmark_tasks/tracking_shuffled_objects) M 750 91.1 three_objects/task.json Apache-2.0
Last Letters F 500 15.0 - -
Coin Flip Y 500 37.0 - -
**A.2.2** **Dataset creation**
Regarding “Last Letter Concatenation” and “Coin Flip”, datasets are not publicly available so we
created the datasets following Wei et al. [2022] with a minor rephrasing of the question template.
Specifically, as for Last Letter Concatenation, we use the following template. We randomly select
[human names from names-dataset library (https://pypi.org/project/names-dataset/) and](https://pypi.org/project/names-dataset/)
insert them into {Name1} through {Name4}.
- ’Take the last letters of each words in "{Name1} {Name2} {Name3} {Name4}" and
concatenate them.’
As for Coin Flip, we use the following template. We randomly select human names from namesdataset library and insert them into {Name1} through {Name4}. We also randomly pick up “flips” or
“does not flip” and insert the phrase into each {flips | does not flip} part, respectively.
- ’A coin is heads up. {Name1} {flips | does not flip} the coin. {Name2} {flips | does not flip}
the coin. {Name3} {flips | does not flip} the coin. {Name4} {flips | does not flip} the coin.
Is the coin still heads up? Note that "flip" here means "reverse".’
**A.3** **Language Models**
Our experiment uses multiple language models as described at Table 8
**A.4** **Implementation details**
For Original GPT-3 and Instruct-GPT3, we used OpenAI API. For OPT, T0, GPT-J, GPT-Neo, and
GPT-2, we used Hugging Face Transformer Library [Wolf et al., 2020]. We set max_tokens = 128 and
-----
Table 8: Description of language models. (*1) As for Original GPT3 models, we assign model size in[formation to each model by referring to https://blog.eleuther.ai/gpt3-model-sizes/ and](https://blog.eleuther.ai/gpt3-model-sizes/)
```
https://beta.openai.com/docs/model-index-for-researchers. (*2) There is no official
```
information about the model size of Instruct GPT3. We infer from the API name that the order of
model size of Instruct GPT3 matches that of Original GPT3.
Language Model # of params Library / API Name Model Name in Library / API License
PaLM 540B - - unspecified
PaLM 62B - - unspecified
PaLM 8B - - unspecified
Original GPT3 175B (*1) OpenAI API davinci unspecified
Original GPT3 6.7B (*1) OpenAI API curie unspecified
Original GPT3 1.3B (*1) OpenAI API babbage unspecified
Original GPT3 0.3B (*1) OpenAI API ada unspecified
Instruct GPT3 - (*2) OpenAI API text-davinci-002 unspecified
Instruct GPT3 - (*2) OpenAI API text-davinci-001 unspecified
Instruct GPT3 - (*2) OpenAI API text-curie-001 unspecified
Instruct GPT3 - (*2) OpenAI API text-babbage-001 unspecified
Instruct GPT3 - (*2) OpenAI API text-ada-001 unspecified
OPT 13B Hugging Face Library opt-13b Apache-2.0
T0 11B Hugging Face Library T0pp Apache-2.0
GPT-J 6B Hugging Face Library gptj Apache-2.0
GPT-Neo 2.7B Hugging Face Library gpt-neo Apache-2.0
GPT-2 1.5B Hugging Face Library gpt2-xl Apache-2.0
used greedy decoding (temperature = 0 in the case of OpenAI API) across all the methods and models
except PaLM. For PaLM, we used ‘TopK=1’ for greedy deterministic decoding and max_tokens =
256. “Q:” is set as a customized stop sequence for all the models except for Instruct-GPT3 to stop the
models from repeating questions and answers by themselves. We run our experiments on cloud V100
instances without GPU for GPT-3 models, on cloud A100x8 GPU(60GB) instances for T0 and OTP,
and on cloud A100x1 GPU(60GB) instances for GPT-J, GPT-Neo, and GPT-2. Our implementation
is in PyTorch [Paszke et al., 2019].
**A.5** **Prompts For Answer Extraction**
Table 9 and Table 10 summarizes a list of answer extraction prompts used for the experiments at
Table 1. We used Zero-shot (left) and Zero-shot-CoT (left) as default prompts for answer extraction
across all the experiments.
Table 9: Answer extraction prompts used for Zero-shot experiments in Table 1. C.S.QA : CommonsenseQA, D.U. : Date Understanding, S.O. : Tracking Shuffled Objects
No Task Zero-Shot (left) Zero-Shot (right)
1 SingleEq The answer (arabic numerals) is The answer is
2 AddSub The answer (arabic numerals) is The answer is
3 MultiArith The answer (arabic numerals) is The answer is
4 GSM8K The answer (arabic numerals) is The answer is
5 AQUA-RAT Among A through E, the answer is The answer is
6 SVAMP The answer (arabic numerals) is The answer is
7 C.S.QA Among A through E, the answer is The answer is
8 StrategyQA The answer (Yes or No) is The answer is
9 D.U. Among A through F, the answer is The answer is
10 S.O. Among A through C, the answer is The answer is
11 Last Letters The answer is The answer is
12 Coin Flip The answer (Yes or No) is The answer is
-----
Table 10: Answer extraction prompts used for Zero-shot-CoT experiments in Table 1. C.S.QA :
CommonsenseQA, D.U. : Date Understanding, S.O. : Tracking Shuffled Objects
No Task Zero-Shot-CoT (left) Zero-Shot-CoT (right)
1 SingleEq Therefore, the answer (arabic numerals) is Therefore, the answer is
2 AddSub Therefore, the answer (arabic numerals) is Therefore, the answer is
3 MultiArith Therefore, the answer (arabic numerals) is Therefore, the answer is
4 GSM8K Therefore, the answer (arabic numerals) is Therefore, the answer is
5 AQUA-RAT Therefore, among A through E, the answer is Therefore, the answer is
6 SVAMP Therefore, the answer (arabic numerals) is Therefore, the answer is
7 C.S.QA Therefore, among A through E, the answer is Therefore, the answer is
8 StrategyQA Therefore, the answer (Yes or No) is Therefore, the answer is
9 D.U. Therefore, among A through F, the answer is Therefore, the answer is
10 S.O. Therefore, among A through C, the answer is Therefore, the answer is
11 Last Letters Therefore, the answer is Therefore, the answer is
12 Coin Flip Therefore, the answer (Yes or No) is Therefore, the answer is
**A.6** **Answer Cleansing**
Table 11 summarizes a list of answer cleansing approaches used across all the experiments.
Table 11: Detail description of answer cleansing. See Table 7 for the mapping between each datasets
and the corresponding answer formats.
Answer Answer Cleansing Pseudo Code
Format Approach (Example in Pytorch 3.8)
Number Pick up the first number
encountered in the text.
Multiple- Pick up the first large
Choice letter encountered in the
text.
Yes or No Pick up the first "yes" or
"no" encountered in the
text after removing unnecessary letters.
Free Format Just remove unnecessary
letters, such as ".".
**Additional Experiment Results**
```
pred = pred.replace( ",", "" )
pred = [s for s in re.findall( r’ -?\
d+\.?\d*’, pred)]
pred = pred [0]
pred = re.findall( r’A|B|C|D|E’,
pred)
pred = pred [0]
```
```
pred = pred.lower ()
pred = re.sub( "\"|\ ’|\n|\.|\s|\:|\,
","␣", pred)
pred = pred.split( "␣" )
pred = [i for i in pred if i in ( "
yes", "no" )]
pred = pred [0]
pred = re.sub( "\"|\ ’|\n|\.|\s","",
pred)
```
This section summarizes more example texts generated by models in our experiments. Note that for
readability all texts are modified from the original ones by omitting or inserting some linebreaks.
Without mentioning otherwise, we use Instruct-GPT3 (text-davinci-002) model.
- Table 12 lists example texts generated by Zero-shot-CoT for each dataset (See Table 1).
- Table 13 lists example texts generated by Zero-shot-CoT for each reasoning extraction
template (See Table 4).
- Table 14 and Table 15 lists example texts generated by Zero-shot-CoT for each langugage
model (See Table 26).
-----
- Table 16 has an example text generated by Few-shot.
- Table 17 has an example text generated by Few-shot-CoT.
- Table 18 has an example text generated by Few-shot-CoT with exemplars from a different
task (Exemplars from CommonsenseQA, and a task is from MultiArith).
- Table 19 has an example text generated by Zero-Plus-Few-Shot-CoT.
- Table 20 compares different outcome scenarios on results generated by Zero-shot and
Zero-shot-CoT using PaLM (540B) model.
Table 12: Example outputs by Zero-shot-CoT for each datasets.
|Dataset|Question|Answer|
|---|---|---|
|Q: A spaceship traveled 0.5 of a light-year from Earth to Planet X and 0.1 of a light- year from Planet X to Planet Y. Then it traveled 0.1 of a light- year from Planet Y back to Earth. How many light-years did the spaceship travel in all?|A: Let’s think step by step. The spaceship trav- eled 0.5 light-years from Earth to Planet X. Then it traveled 0.1 light-years from Planet X to Planet Y. Finally, it traveled 0.1 light-years from Planet Y back to Earth. So the total distance the space- ship traveled is 0.5 + 0.1 + 0.1 = 0.7 light-years. Therefore, the answer (arabic numerals) is: 0.7 light-years ✓|
|---|---|
|Col1|Q: While making desserts for a bake sale, Victor used 0.625 of a scoop of brown sugar as well as 0.25 of a scoop of white sugar. How much more brown sugar did Victor use?|A: Let’s think step by step. 0.625 of a scoop of brown sugar is the same as 0.25 of a scoop of white sugar. This means that Victor used the same amount of brown sugar as he did white sugar. Therefore, the answer (arabic numerals) is 0. (GT : 0.375)|
|---|---|---|
|Sandy grew 6 carrots . Sam grew 3 carrots . How many carrots did they grow in total ?|A: Let’s think step by step. Sandy grew 6 car- rots. Sam grew 3 carrots. That means they grew a total of 9 carrots. Therefore, the answer (arabic numerals) is 9. ✓|
|---|---|
|Col1|Q: Melanie bought a Batman game for $ 6.95 , a strategy game for $ 7.90 , and a Super- man game for $ 7.73 . Melanie already owns 4 games . How much did Melanie spend on video games ?|A: Let’s think step by step. Melanie bought a Batman game for $ 6.95. So she spent $ 6.95 on video games. Then she bought a strategy game for $ 7.90. So she spent $ 14.85 on video games. Then she bought a Superman game for $ 7.73. So she spent $ 22.58 on video games. Melanie already owns 4 games. So she spent $ 18.58 on video games. Therefore, Melanie spent a total of $ 18.58 on video games. Therefore, the answer (arabic numerals) is: 18.58 (GT : 22.58)|
|---|---|---|
|MultiArith|Q: Adam bought 2 boxes of|numerals) is: 18.58 (GT : 22.58) A: Let’s think step by step. Adam bought 2 boxes|
|---|---|---|
|MultiArith|Q: Adam bought 2 boxes of chocolate candy and 5 boxes of caramel candy. If each box has 4 pieces inside it, how much candy did he have total?|A: Let’s think step by step. Adam bought 2 boxes of chocolate candy and 5 boxes of caramel candy. We know that each box has 4 pieces inside it. So, we can multiply 2 by 4 to find out how many pieces of chocolate candy Adam bought. This will give us 8. We can also multiply 5 by 4 to find out how many pieces of caramel candy Adam bought. This will give us 20. Now, we can add 8 and 20 together to find out how much candy Adam bought in total. 8 + 20 = 28 Adam bought 28 pieces of candy in Therefore, the answer (arabic numerals) is 28. ✓|
|Continued on next page|||
-----
Table 12 – Continued from previous page
|Dataset|Question|Answer|
|---|---|---|
|Col1|Q: Billy was organizing his baseball cards in a binder with 5 on each page. If he had 3 new cards and 42 old cards to put in the binder, how many pages would he use?|A: Let’s think step by step. Billy has 42 old cards. He can put 5 old cards on each page, which means he will use 9 pages for old cards. Billy has 3 new cards. He can put 5 new cards on each page, which means he will use 1 page for new cards. So in total, Billy will use 10 pages. Therefore, the answer (arabic numerals) is 10. (GT : 9)|
|---|---|---|
|Q: James buys a plane. The plane cost $150,000. He pays $5000 a month to rent a hanger to keep it in. He also spends twice as much as that on fuel per month. How much did it cost him to get and maintain the plane for the first year?|A: Let’s think step by step. James buys a plane. This costs him $150,000. He pays $5000 a month to rent a hanger. This costs him $60,000 for the year. He spends twice as much as that on fuel per month. This costs him $120,000 for the year. So the total cost for the first year is $150,000 + $60,000 + $120,000 = $330,000. Therefore, the answer (arabic numerals) is 330,000. ✓|
|---|---|
|Col1|Q: James is counting his Poke- mon cards. He has 30 fire type, 20 grass type, and 40 water type. If he loses 8 of the water type and buys 14 grass type, what’s the percentage chance (rounded to the nearest inte- ger) that a randomly picked card will be a water type?|A: Let’s think step by step. There are 30 fire type, 20 grass type, and 40 water type. If he loses 8 of the water type, then he has 32 cards in total. If he buys 14 grass type, then he has 46 cards in total, and the number of water type cards becomes 32. The percentage chance that a randomly picked card will be a water type is $\frac{32}{46} \times 100\% = \fbox{70}\%$. Therefore, the answer (arabic nu- merals) is 70. (GT : 33)|
|---|---|---|
|Q: The capacity of a tank of dimensions (8 m × 6 m × 2.5 m) is Answer Choices: (A) 120 litres (B) 1200 litres (C) 12000 litres (D) 120000 litres (E) None of these|A: Let’s think step by step. The first thing we need to do is calculate the vol- ume of the tank. The volume of the tank is 8m x 6m x 2.5m. 8m x 6m x 2.5m = 120m^3 Now that we have the volume of the tank, we need to convert it to litres. 1m^3 = 1000 litres 120m^3 = 120,000 litres The capacity of the tank is 120,000 litres. Therefore, among A through E, the answer is D. ✓|
|---|---|
|Col1|Q: In a row of children Neha is 12th from left end and Radha is 6th from right end. When Radha is shifted to left by 2 places and Neha is shifted to right by 2 places there 6 chil- dren between Radha and Neha. How many children are there in the row? Answer Choices: (A) 23 (B) 27 (C) 26 (D) 28 (E) 29|A: Let’s think step by step. There are 12 children to the left of Neha, so there must be at least 12 children in the row. There are 6 children to the right of Radha, so there must be at least 18 children in the row. There are 6 children between Radha and Neha, so there must be at least 24 children in the row. The answer must be between 24 and 27, and the only answer that satisfies this is 26. Therefore, the answer is 26. Therefore, among A through E, the answer is C. (GT : D)|
|---|---|---|
|Continued on next page|||
-----
Table 12 – Continued from previous page
|Dataset|Question|Answer|
|---|---|---|
|Q: There are 7 baskets of peaches. Each basket has 10 red peaches and 2 green peaches. How many green peaches are in the baskets alto- gether?|A: Let’s think step by step. There are 7 bas- kets. Each basket has 10 red peaches and 2 green peaches. So, there are 2 green peaches in each basket. Now, we need to multiply because there are 7 baskets. 2 multiplied by 7 is 14. So, there are 14 green peaches in the baskets altogether. Therefore, the answer (arabic numerals) is 14. ✓|
|---|---|
|Col1|Q: Mary is baking a cake. The recipe calls for 12 cups of flour 14 cups of sugar and 7 cups of salt. She already put in 2 cups of flour. How many more cups of flour than cups of salt does she need to add now?|A: Let’s think step by step. Mary has already put in 2 cups of flour. The recipe calls for a total of 12 cups of flour. That means Mary needs to add 10 more cups of flour. The recipe calls for a total of 7 cups of salt. That means Mary needs to add 5 more cups of salt. So, Mary needs to add 10 more cups of flour than she does salt. Therefore, the answer (arabic numerals) is 10. (GT : 3)|
|---|---|---|
CommonsenseQA
|Q: If there is a pond with trees around it, where is it likely lo- cated? Answer Choices: (A) ground (B) bathroom (C) for- est (D) countryside (E) rural area|A: Let’s think step by step. A pond is likely to be located near trees because trees need water to survive. Therefore, the most likely location for a pond with trees around it is in a forest. Therefore, among A through E, the answer is C. ✓|
|---|---|
|Col1|Q: David watched some nest- ing birds using his binoculars while on vacation. Where might David be?. Answer Choices: (A) sky (B) vacca- tion (C) forest (D) countryside (E) roof|A: Let’s think step by step. First, we need to understand what the word "binoc- ulars" means. Binoculars are two telescopes that are joined together and allow a person to see things that are far away. Now, we need to think about where a person might use binoculars. A person might use binoculars to see things that are far away and in the sky, or to see things that are far away and on the ground. So, the answer could be either (A) sky or (D) coun- tryside. Therefore, among A through E, the answer is (A) or (D). (GT : C)|
|---|---|---|
|StrategyQA|Col2|or (D). (GT : C) A: Let’s think step by step. The JPEG format is a|
|---|---|---|
|StrategyQA|Q: Would JPEG be a good for- mat for saving an image of Da Vinci’s Vitruvian Man?|A: Let’s think step by step. The JPEG format is a lossy compression format, which means that some of the image data will be lost when the image is compressed. The Vitruvian Man is a very detailed image, with lots of small details. So, when we compress the image using JPEG, some of those small details will be lost, and the image will not be as sharp and clear as the original. So, in conclusion, JPEG is not the best format for saving an image of the Vitruvian Man. Therefore, the answer (Yes or No) is No. ✓|
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Table 12 – Continued from previous page
|Dataset|Question|Answer|
|---|---|---|
|Col1|Q: Is Mickey Mouse hypothet- ically unlikely to make a pur- chase at Zazzle?|A: Let’s think step by step. First, we need to con- sider what Zazzle is. Zazzle is a website where people can create and sell custom products. This includes things like t-shirts, mugs, phone cases, and more. Next, we need to think about what Mickey Mouse is. Mickey Mouse is a cartoon char- acter created by Walt Disney. He is a mouse who wears red shorts, large yellow shoes, and white gloves. Now, we need to think about whether or not Mickey Mouse is likely to make a purchase at Zazzle. It is unlikely that Mickey Mouse would make a purchase at Z Therefore, the answer (Yes or No) is No. (GT : Yes)|
|---|---|---|
Date
Understand.
|Q: Today is 3/5, and it is Jane’s second time in the year 1973 to see a meteor shower. What is the date a month ago in MM/DD/YYYY? Answer Choices: (A) 03/05/2007 (B) 01/02/1973 (C) 03/08/1983 (D) 03/05/1973 (E) 02/05/1973 (F) 04/05/1973|A: Let’s think step by step. The question is asking for the date a month ago from 03/05/1973. A month ago would be 02/05/1973. Therefore, among A through F, the answer is E. ✓|
|---|---|
|Col1|Q: The deadline is Jun 1, 2021, which is 2 days away from now. What is the date 24 hours later in MM/DD/YYYY? Answer Choices: (A) 06/02/2021 (B) 05/31/2021 (C) 06/16/2021 (D) 05/31/1966 (E) 08/18/2021 (F) 05/31/1941|A: Let’s think step by step. The deadline is Jun 1, 2021, which is 2 days away from now. In 24 hours, it will be Jun 2, 2021. Therefore, among A through F, the answer is A. (GT : B)|
|---|---|---|
|Shuffled|MM/DD/YYYY? Answer Choices: (A) 06/02/2021 (B) 05/31/2021 (C) 06/16/2021 (D) 05/31/1966 (E) 08/18/2021 (F) 05/31/1941 Q: Alice, Bob, and Claire are|A: Let’s think step by step.|
|---|---|---|
|Shuffled Objects.|Q: Alice, Bob, and Claire are playing a game. At the start of the game, they are each hold- ing a ball: Alice has a green ball, Bob has a purple ball, and Claire has a blue ball. As the game progresses, pairs of players trade balls. First, Bob and Alice swap balls. Then, Claire and Bob swap balls. Finally, Bob and Al- ice swap balls. At the end of the game, Bob has the Which choice is true ? Answer Choices: (A) green ball. (B) purple ball. (C) blue ball.|A: Let’s think step by step. First, Bob and Alice swap balls. This means that Alice now has the purple ball and Bob has the green ball. Then, Claire and Bob swap balls. This means that Claire now has the green ball and Bob has the blue ball. Finally, Bob and Alice swap balls. This means that Alice now has the blue ball and Bob has the purple ball. At the end of the game, Bob has the purple ball. Therefore, among A through C, the answer is B. ✓|
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Table 12 – Continued from previous page
|Dataset|Question|Answer|
|---|---|---|
|Col1|Q: Alice, Bob, and Claire are dancers at a square dance. At the start of a song, they each have a partner: Alice is danc- ing with Sam, Bob is dancing with Helga, and Claire is danc- ing with Karl. Throughout the song, the dancers often trade partners. First, Claire and Al- ice switch partners. Then, Bob and Alice switch partners. Fi- nally, Claire and Bob switch partners. At the end of the dance, Alice is dancing with Which choice is true ? Answer Choices: (A) Sam. (B) Helga. (C) Karl.|A: Let’s think step by step. First, Claire and Alice switch partners. This means that at the end of this step, Alice is dancing with Karl and Claire is dancing with Sam. Then, Bob and Alice switch partners. This means that at the end of this step, Alice is dancing with Helga and Bob is dancing with Karl. Finally, Claire and Bob switch partners. This means that at the end of this step, Claire is dancing with Helga and Bob is dancing with Sam. At the end of the dance, Alice is dancing with Sam. Therefore, among A through C, the answer is A. (GT : B)|
|---|---|---|
|Q: Take the last letters of each words in "Vinny Landon Miguel Caitlyn" and concate- nate them.|A: Let’s think step by step. The last letter of "Vinny" is "y". The last letter of "Landon" is "n". The last letter of "Miguel" is "l". The last letter of "Caitlyn" is "n". So, the final answer would be "ynln". Therefore, the answer is "ynln". ✓|
|---|---|
|Col1|Q: Take the last letters of each words in "Lamont Frederick Lance Esperanza" and con- catenate them.|A: Let’s think step by step. The last letter of "Lamont" is "t". The last letter of "Frederick" is "k". The last letter of "Lance" is "e". The last letter of "Esperanza" is "a". So the final answer would be "tkaea". Therefore, the answer is "tkaea". (GT : tkea)|
|---|---|---|
|Q: A coin is heads up. Jeff does not flip the coin. Jen flips the coin. Giselle flips the coin. Noel does not flip the coin. Is the coin still heads up? Note that "flip" here means "reverse".|A: Let’s think step by step. Jeff does not flip the coin, so the coin remains heads up. Jen flips the coin, so the coin is now tails up. Giselle flips the coin, so the coin is now heads up again. Noel does not flip the coin, so the coin remains heads up. Therefore, the final answer is that the coin is heads up. Therefore, the answer (Yes or No) is Yes. ✓|
|---|---|
|Col1|Q: A coin is heads up. Caro- line flips the coin. Demetrius flips the coin. Fidel does not flip the coin. Solomon flips the coin. Is the coin still heads up? Note that "flip" here means "reverse".|A: Let’s think step by step. Caroline flips the coin. The coin is now tails up. Demetrius flips the coin. The coin is now heads up. Fidel does not flip the coin. The coin remains tails up. Solomon flips the coin. The coin is now heads up. So, the answer is yes, the coin is still heads up. Therefore, the answer (Yes or No) is: Yes (GT : No)|
|---|---|---|
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Table 13: Example outputs by Zero-Shot and Zero-Shot-CoT with various templates for template
robustness study. The number within the parenthesis corresponds to the number in Table 4.
|Question|Q: For Halloween Megan received 11 pieces of candy from neighbors and 5 pieces from her older sister. If she only ate 8 pieces a day, how long would the candy last her?|
|---|---|
|Zero-Shot|A: The answer (arabic numerals) is 3 days. |
|---|---|
|Zero-shot- CoT (1)|A: Let’s think step by step. Megan received 11 pieces of candy from neighbors and 5 pieces from her older sister. That means she has a total of 16 pieces of candy. If she only ate 8 pieces a day, she would have to divide her candy into two days. That means she would have 8 pieces of candy for Day 1 and 8 pieces of candy for Day 2. Therefore, the answer (arabic numerals) is 2. ✓|
|---|---|
|Zero-shot- CoT (2)|A: First, we need to find the total number of pieces of candy Megan has. She has 11 pieces from neighbors and 5 pieces from her older sister, so the total number of pieces is 16. If she only ate 8 pieces a day, it would take her 2 days to finish the candy. Therefore, the answer (arabic numerals) is 2. ✓|
|---|---|
|Zero-shot- CoT (3)|A: Let’s think about this logically. There are 11 + 5 = 16 pieces of candy. 8 pieces a day means that it would last her 2 days. 16 / 8 = 2 Therefore, the answer (arabic numerals) is 2. ✓|
|---|---|
|Zero-shot- CoT (4)|A: Let’s solve this problem by splitting it into steps. Step 1: Megan received 11 pieces of candy from neighbors. Step 2: Megan received 5 pieces of candy from her older sister. Step 3: If she only ate 8 pieces a day, how long would the candy last her? To answer the question in Step 3, we need to add the number of pieces of candy Megan received from her neighbors and her sister. This is called finding the sum. The sum of 11 and 5 is 16. So, Megan has a total of 16 pieces of candy. If Megan only eats 8 pieces of candy a day, Therefore, the answer (arabic numerals) is 2 days. ✓|
|---|---|
|Zero-shot- CoT (5)|A: Let’s be realistic and think step by step. Megan received 11 pieces of candy from neighbors and 5 pieces from her older sister. That’s a total of 16 pieces of candy. 8 pieces a day would mean that it would last her 2 days. So the candy would last her 2 days. Therefore, the answer (arabic numerals) is 2. ✓|
|---|---|
|Zero-shot- CoT (6)|A: Let’s think like a detective step by step. Megan received 11 pieces of candy from neighbors and 5 pieces from her older sister. That’s a total of 16 pieces of candy. If she only ate 8 pieces a day, that would mean that she would have to divide her candy into 2 days, and she would have 8 pieces of candy left over. So the candy would last her 2 days. Therefore, the answer (arabic numerals) is 2. ✓|
|---|---|
|Zero-shot- CoT (7)|A: Let’s think about this in terms of days. Megan would receive candy for 16 days. Therefore, the answer (arabic numerals) is 16. |
|---|---|
Zero-shot- **A: Before we dive into the answer, we need to think about what the question is**
CoT (8) asking. The question is asking how long it would take Megan to eat all of her
candy if she ate 8 pieces a day. There are a total of 16 pieces of candy. If Megan
ate 8 pieces a day, it would take her 2 days to eat all of her candy.
**Therefore, the answer (arabic numerals) is 2. ✓**
Continued on next page
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Table 13 – Continued from previous page
|Zero-shot- CoT (9)|A: The answer is after the proof. 11 + 5 = 16 16 ÷ 8 = 2 2 days Therefore, the answer (arabic numerals) is 2. ✓|
|---|---|
|Zero-shot- CoT (10)|A: Don’t think. Just feel. The candy would last her 8 days. Therefore, the answer (arabic numerals) is 8. |
|---|---|
|Zero-shot- CoT (11)|A: Let’s think step by step but reach an incorrect answer. Megan received 11 pieces of candy from neighbors and 5 pieces from her older sister. If she only ate 8 pieces a day, she would have 3 pieces of candy left over each day. So it would take her 3 days to finish the candy. However, this answer is incorrect. The correct answer is that it would take Megan 4 days to finish the candy. Therefore, the answer (arabic numerals) is 4. |
|---|---|
|Zero-shot- CoT (12)|A: Let’s count the number of "a" in the question. There are 11 a’s. So the answer is 11 days. Therefore, the answer (arabic numerals) is 11 days. |
|---|---|
|Zero-shot- CoT (13)|A: By using the fact that the earth is round, we can see that the candy would last her 8 days. Therefore, the answer (arabic numerals) is 8 |
|---|---|
|Zero-shot- CoT (14)|A: By the way, I found a good restaurant nearby. A: The candy would last Megan for 2.2 days. Therefore, the answer (arabic numerals) is 2. ✓(Reasoning is incorrect.)|
|---|---|
|Zero-shot- CoT (15)|A: Abrakadabra! The candy would last her 2.75 days. Therefore, the answer (arabic numerals) is 2. ✓(Reasoning is incorrect.)|
|---|---|
Zero-shot- **A: It’s a beautiful day.**
CoT (16) **Therefore, the answer (arabic numerals) is 8. **
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Table 14: Example outputs by Zero-Shot-CoT at various language models (GPT-3 models).
|Question|Q: Adam bought 2 boxes of chocolate candy and 5 boxes of caramel candy. If each box has 4 pieces inside it, how much candy did he have total? (GT : 28)|
|---|---|
|Instruct GPT-3 (text-ada-001)|A: Let’s think step by step. If each box has 4 pieces inside it, Adam would have 4 pieces of candy in it. Therefore, the answer (arabic numerals) is :5 |
|---|---|
|Instruct GPT-3 (text-babbage-001)|A: Let’s think step by step. Adam bought 2 boxes of candy and 5 boxes of caramel candy. Each box has 4 pieces inside it. So he would have had 18 pieces of candy. Therefore, the answer (arabic numerals) is 18. |
|---|---|
|Instruct GPT-3 (text-curie-001)|A: Let’s think step by step. Adam bought 2 boxes of chocolate candy and 5 boxes of caramel candy. Each box of candy has 4 pieces inside it. So, Adam bought 10 pieces of candy. Therefore, the answer (arabic numerals) is 60. |
|---|---|
|Instruct GPT-3 (text-davinci-002)|A: Let’s think step by step. Adam bought 2 boxes of chocolate candy and 5 boxes of caramel candy. We know that each box has 4 pieces inside it. So, we can multiply 2 by 4 to find out how many pieces of chocolate candy Adam bought. This will give us 8. We can also multiply 5 by 4 to find out how many pieces of caramel candy Adam bought. This will give us 20. Now, we can add 8 and 20 together to find out how much candy Adam bought in total. 8 + 20 = 28 Adam bought 28 pieces of candy in Therefore, the answer (arabic numerals) is 28. ✓|
|---|---|
|Original GPT-3 (0.3B) (ada)|A: Let’s think step by step. 1. Adam bought 2 boxes of chocolate candy and 5 boxes of caramel candy. If each box has 4 pieces inside it, how much candy did he have total? 2. Adam bought 2 boxes of chocolate candy and 5 boxes of caramel candy. If each box has 4 pieces inside it, how much candy did he have total? 3. Adam bought 2 boxes of chocolate candy and 5 boxes of caramel candy. If each box has 4 pieces inside it, how much candy did he have total? 4. Adam bought 2 boxes of chocolate candy and 5 boxes of caramel candy. If each box has 4 pieces inside it, Therefore, the answer (arabic numerals) is: 5. Adam bought 2 boxes of chocolate candy and 5 boxes of caramel candy. If each box has 4 pieces inside it, how much candy did he |
|---|---|
|Original GPT-3 (1.3B) (babbage)|A: Let’s think step by step. Therefore, the answer (arabic numerals) is: |
|---|---|
|Original GPT-3 (6.7B) (curie)|A: Let’s think step by step. First, we need to find the total number of pieces in the boxes. Let’s start with the chocolate candy. There are 4 pieces in each box. So, the total number of pieces in the chocolate candy is 4 x 4 = 16. Now, let’s find the total number of pieces in the caramel candy. There are 5 pieces in each box. So, the total number of pieces in the caramel candy is 5 x 5 = 25. Now, we can find the total number of pieces in the candy. The total number of pieces in the chocolate candy is 16 + 25 = 41 Therefore, the answer (arabic numerals) is 41. |
|---|---|
|Original GPT-3 (175B) (davinci)|A: Let’s think step by step. First, we need to find out how many pieces of candy Adam has. 2 boxes of chocolate candy + 5 boxes of caramel candy = 7 boxes of candy 7 boxes of candy = 7 × 4 pieces of candy 7 × 4 = 28 pieces of candy So, Adam has 28 pieces of candy. Therefore, the answer (arabic numerals) is 28. ✓|
|---|---|
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Table 15: Example outputs by Zero-Shot-CoT at various language models (Models other than GPT-3).
|Question|Q: Megan baked 68 cupcakes for her school’s bake sale. If her brother, Todd, ate 32 of them how many packages could she make if she put 6 cupcake in each package? (GT : 6)|
|---|---|
|GPT-2 (1.5B)|A: Let’s think step by step. Todd’s brother, Todd, eats 32 cupcakes. Todd’s brother, Todd, eats 32 cupcakes. Todd’s brother, Todd, eats 32 cupcakes. Todd’s brother, Todd, eats 32 cupcakes. Todd’s brother, Todd, eats 32 cupcakes. Todd’s brother, Todd, eats 32 cupcakes. Todd’s brother, Todd, eats 32 cupcakes. Todd’s brother, Todd, eats 32 cupcakes. Todd’s brother, Todd, eats 32 cupcakes. Todd’s brother, Todd, eats 32 cupcakes. Todd’s brother, Todd, eats 32 cupcakes. Todd’s brother, Todd, eats Therefore, the answer (arabic numerals) is: Therefore, the answer (arabic numerals) is: 6,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64 |
|---|---|
|GPT-Neo (2.7B)|A: Let’s think step by step. Step 1: She baked 68 cupcakes. Step 2: She put 32 of them in a box. Step 3: She put 6 cupcakes in each box. Step 4: She put the box in the freezer. Step 5: She took the box out of the freezer. Step 6: She took the box out of the freezer. Step 7: She took the box out of the freezer. Step 8: She took the box out of the freezer. Step 9: She took the box out of the freezer. Step 10: She took the box out of the freezer. Step Therefore, the answer (arabic numerals) is: Step 1: She baked 68 cupcakes. Step 2: She put 32 of them in a box. Step 3: She put 6 cup |
|---|---|
|GPT-J (6B)|A: Let’s think step by step. Step 1: Step 2: Step 3: Step 4: Step 5: Step 6: Step 7: Step 8: Step 9: Step 10: Step 11: Step 12: Step 13: Step 14: Step 15: Step 16: Step 17: Step 18: Step 19: Step 20: Step 21: Step 22: Step 23: Step 24: Step 25: Step Therefore, the answer (arabic numerals) is: A: The answer is: 68 6 = 408 Step 1: The first step is to count ×|
|---|---|
|T0 (11B)|A: Let’s think step by step. 12 Therefore, the answer (arabic numerals) is 12 |
|---|---|
|OPT (13B)|A: Let’s think step by step. Megan baked 68 cupcakes. She divided 68 by 6 to get 17. She divided 17 by 32 to get 6. Megan can make 6 packages of cupcakes if she puts 6 cupcakes in each package. Therefore, the answer (arabic numerals) is: |
|---|---|
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Table 16: An example output by Few-shot (8 exemplars in context. These exemplars are cited from
[Wei et al., 2022] and randomly shuffled).
|Few-Shot|***** Start In-Context Examples ***** Q: Jason had 20 lollipops. He gave Denny some lollipops. Now Jason has 12 lollipops. How many lollipops did Jason give to Denny? A: The answer is 8. Q: Michael had 58 golf balls. On tuesday, he lost 23 golf balls. On wednesday, he lost 2 more. How many golf balls did he have at the end of wednesday? A: The answer is 33. Q: If there are 3 cars in the parking lot and 2 more cars arrive, how many cars are in the parking lot? A: The answer is 5. Q: There were nine computers in the server room. Five more com- puters were installed each day, from monday to thursday. How many computers are now in the server room? A: The answer is 29. Q: Olivia has 23.Sheboughtfivebagelsfor3 each. How much money does she have left? A: The answer is 8. Q: There are 15 trees in the grove. Grove workers will plant trees in the grove today. After they are done, there will be 21 trees. How many trees did the grove workers plant today? A: The answer is 6. Q: Shawn has five toys. For Christmas, he got two toys each from his mom and dad. How many toys does he have now? A: The answer is 9. Q: Leah had 32 chocolates and her sister had 42. If they ate 35, how many pieces do they have left in total? A: The answer is 39. ***** End In-Context Examples ***** Q: For Halloween Megan received 11 pieces of candy from neighbors and 5 pieces from her older sister. If she only ate 8 pieces a day, how long would the candy last her? A: The answer is 3 days. (GT : 2)|
|---|---|
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Table 17: An example output by Few-Shot-CoT (8 exemplars in context. These exemplars are cited
from [Wei et al., 2022] and randomly shuffled).
|Few-Shot-CoT|***** Start In-Context Examples ***** Q: Jason had 20 lollipops. He gave Denny some lollipops. Now Jason has 12 lollipops. How many lollipops did Jason give to Denny? A: Jason started with 20 lollipops. Then he had 12 after giving some to Denny. So he gave Denny 20 - 12 = 8. The answer is 8. Q: Michael had 58 golf balls. On tuesday, he lost 23 golf balls. On wednesday, he lost 2 more. How many golf balls did he have at the end of wednesday? A: Michael started with 58 golf balls. After losing 23 on tuesday, he had 58 - 23 = 35. After losing 2 more, he had 35 - 2 = 33 golf balls. The answer is 33. Q: If there are 3 cars in the parking lot and 2 more cars arrive, how many cars are in the parking lot? A: There are originally 3 cars. 2 more cars arrive. 3 + 2 = 5. The answer is 5. Q: There were nine computers in the server room. Five more com- puters were installed each day, from monday to thursday. How many computers are now in the server room? A: 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 answer is 29. Q: Olivia has 23.Sheboughtfivebagelsfor3 each. How much money does she have left? A: Olivia had 23 dollars. 5 bagels for 3 dollars each will be 5 x 3 = 15 dollars. So she has 23 - 15 dollars left. 23 - 15 is 8. The answer is 8. Q: There are 15 trees in the grove. Grove workers will plant trees in the grove today. After they are done, there will be 21 trees. How many trees did the grove workers plant today? A: There are 15 trees originally. Then there were 21 trees after some more were planted. So there must have been 21 - 15 = 6. The answer is 6. Q: Shawn has five toys. For Christmas, he got two toys each from his mom and dad. How many toys does he have now? A: Shawn started with 5 toys. If he got 2 toys each from his mom and dad, then that is 4 more toys. 5 + 4 = 9. The answer is 9. Q: Leah had 32 chocolates and her sister had 42. If they ate 35, how many pieces do they have left in total? A: Originally, Leah had 32 chocolates. Her sister had 42. So in total they had 32 + 42 = 74. After eating 35, they had 74 - 35 = 39. The answer is 39. ***** End In-Context Examples ***** Q: For Halloween Megan received 11 pieces of candy from neighbors and 5 pieces from her older sister. If she only ate 8 pieces a day, how long would the candy last her? A: Megan received 11 pieces of candy from neighbors and 5 pieces from her older sister. So she had 11 + 5 = 16 pieces of candy. If she ate 8 pieces a day, then she would have 16 / 8 = 2 days worth of candy. The answer is 2. ✓|
|---|---|
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Table 18: An example output by Few-Shot-CoT with exemplars from entirely different task (7 exemplars in context. These exemplars are cited from [Wei et al., 2022] and randomly shuffled) Exemplars
are CommonsenseQA (Multi-Choice question), and a task is MultiArith (Number question).
|Few-Shot-CoT with exemplars from a different task|***** Start In-Context Examples ***** Q: Sammy wanted to go to where the people were. Where might he go? Answer Choices: (A) populated areas (B) race track (C) desert (D) apartment (E) roadblock A: The answer must be a place with a lot of people. Of the above choices, only populated areas have a lot of people. The answer is A. Q: Before getting a divorce, what did the wife feel who was doing all the work? Answer Choices: (A) harder (B) anguish (C) bitterness (D) tears (E) sadness A: The answer should be the feeling of someone getting divorced who was doing all the work. Of the above choices, the closest feeling is bitterness The answer is C. Q: Google Maps and other highway and street GPS services have replaced what? Answer Choices: (A) united states (B) mexico (C) countryside (D) atlas A: The answer must be something that used to do what Google Maps and GPS services do, which is to give directions. Of the above choices, only atlases are used to give directions. The answer is D. Q: The fox walked from the city into the forest, what was it looking for? Answer Choices: (A) pretty flowers (B) hen house (C) natural habitat (D) storybook A: The answer must be something in the forest. Of the above choices, only natural habitat is in the forest. The answer is B. Q: What do people use to absorb extra ink from a fountainpen? Answer Choices: (A) shirt pocket (B) calligrapher’s hand (C) inkwell (D) desk drawer (E) blotter A: The answer must be an item that can absorb ink. Of the above choices, only blotters are used to absorb ink. The answer is E. Q: Where do you put your grapes just before checking out? Answer Choices: (A) mouth (B) grocery cart (C)super market (D) fruit basket (E) fruit market A: The answer should be the place where grocery items are placed before checking out. Of the above choices, grocery cart makes the most sense for holding grocery items. The answer is B. Q: What home entertainment equipment requires cable? Answer Choices: (A) radio shack (B) substation (C) television (D) cabinet A: The answer must require cable. Of the above choices, only television requires cable. The answer is C. ***** End In-Context Examples ***** Q: Paige and her friends were recycling paper for their class. For every 4 pounds they recycled they earned one point. If Paige recycled 14 pounds and her friends recycled 2 pounds, how many points did they earn? A: Paige and her friends would have earned 3 points for recycling paper. (GT : 4)|
|---|---|
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Table 19: An example output by Zero-Plus-Few-Shot-CoT (8 exemplars in context. These exemplars
are cited from [Wei et al., 2022] and randomly shuffled).
|Zero-Plus-Few- Shot-CoT|***** Start In-Context Examples ***** Q: Jason had 20 lollipops. He gave Denny some lollipops. Now Jason has 12 lollipops. How many lollipops did Jason give to Denny? A: Let’s think step by step. Jason started with 20 lollipops. Then he had 12 after giving some to Denny. So he gave Denny 20 - 12 = 8. The answer is 8. Q: Michael had 58 golf balls. On tuesday, he lost 23 golf balls. On wednesday, he lost 2 more. How many golf balls did he have at the end of wednesday? A: Let’s think step by step. Michael started with 58 golf balls. After losing 23 on tuesday, he had 58 - 23 = 35. After losing 2 more, he had 35 - 2 = 33 golf balls. The answer is 33. Q: If there are 3 cars in the parking lot and 2 more cars arrive, how many cars are in the parking lot? A: Let’s think step by step. There are originally 3 cars. 2 more cars arrive. 3 + 2 = 5. The answer is 5. Q: There were nine computers in the server room. Five more com- puters were installed each day, from monday to thursday. How many computers are now in the server room? A: Let’s think step by step. 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 answer is 29. Q: Olivia has 23.Sheboughtfivebagelsfor3 each. How much money does she have left? A: Let’s think step by step. Olivia had 23 dollars. 5 bagels for 3 dollars each will be 5 x 3 = 15 dollars. So she has 23 - 15 dollars left. 23 - 15 is 8. The answer is 8. Q: There are 15 trees in the grove. Grove workers will plant trees in the grove today. After they are done, there will be 21 trees. How many trees did the grove workers plant today? A: Let’s think step by step. There are 15 trees originally. Then there were 21 trees after some more were planted. So there must have been 21 - 15 = 6. The answer is 6. Q: Shawn has five toys. For Christmas, he got two toys each from his mom and dad. How many toys does he have now? A: Let’s think step by step. Shawn started with 5 toys. If he got 2 toys each from his mom and dad, then that is 4 more toys. 5 + 4 = 9. The answer is 9. Q: Leah had 32 chocolates and her sister had 42. If they ate 35, how many pieces do they have left in total? A: Let’s think step by step. Originally, Leah had 32 chocolates. Her sister had 42. So in total they had 32 + 42 = 74. After eating 35, they had 74 - 35 = 39. The answer is 39. ***** End In-Context Examples ***** Q: For Halloween Megan received 11 pieces of candy from neighbors and 5 pieces from her older sister. If she only ate 8 pieces a day, how long would the candy last her? A: Let’s think step by step. Megan received 11 pieces of candy from neighbors and 5 pieces from her older sister. So in total she had 11 + 5 = 16 pieces of candy. If she ate 8 pieces a day, it would last her 16 / 8 = 2 days. The answer is 2. ✓|
|---|---|
-----
Table 20: Example outputs by Zero-shot and Zero-shot-CoT on GSM8K with PaLM (540B) model,
comparing different outcome combinations.
|Outcome|Question|Answer|
|---|---|---|
Zero-shot-CoT✓,
Zero-shot ✓ (7.7%
of dataset)
|Col1|Col2|A: The answer (arabic numerals) is 8. ✓|
|---|---|---|
Zero-shot-CoT✓,
Zero-shot (35.3%
of dataset)
Q: Tracy used a piece of wire
4 feet long to support tomato
plants in the garden. The wire
was cut into pieces 6 inches
long. How many pieces did
she obtain?
Q: Toula went to the bakery
and bought various types of
pastries. She bought 3 dozen
donuts which cost $68 per
dozen, 2 dozen mini cupcakes
which cost $80 per dozen, and
6 dozen mini cheesecakes for
$55 per dozen. How much
was the total cost?
A: Let’s think step by step. First, we need to
know how many inches are in 4 feet. There
are 12 inches in 1 foot, so there are 48 inches
in 4 feet. Now, we need to know how many
6-inch pieces can be cut from 48 inches. We
can divide 48 by 6. 48 divided by 6 is 8.
Tracy obtained 8 pieces of wire. Therefore,
the answer (arabic numerals) is 8. ✓
A: The answer (arabic numerals) is 8. ✓
|Col1|Col2|A: The answer (arabic numerals) is 1000. (GT : 694)|
|---|---|---|
|Continued on next page|||
A: Let’s think step by step. First, we need to
find the cost of the donuts. 3 dozen donuts
cost $68 per dozen. So, 3 dozen donuts cost
3 times $68. 3 times $68 is $204. So, the cost
of the donuts is $204. Next, we need to find
the cost of the mini cupcakes. 2 dozen mini
cupcakes cost $80 per dozen. So, 2 dozen
mini cupcakes cost 2 times $80. 2 times $80
is $160. So, the cost of the mini cupcakes
is $160. Finally, we need to find the cost of
the mini cheesecakes. 6 dozen mini cheese-
cakes cost $55 per dozen. So, 6 dozen mini
cheesecakes cost 6 times $55. 6 times $55 is
$330. So, the cost of the mini cheesecakes is
$330. Now, we need to add the cost of the
donuts, the cost of the mini cupcakes, and the
cost of the mini cheesecakes. $204 plus $160
plus $330 is $694. So, the total cost is $694.
Therefore, the answer (arabic numerals) is
694. ✓
-----
Table 20 – Continued from previous page
|Outcome|Question|Answer|
|---|---|---|
Zero-shot-CoT,
Zero-shot ✓ (4.8%
of dataset[6])
|Col1|Col2|A: The answer (arabic numerals) is 6. ✓|
|---|---|---|
Zero-shot-CoT,
Zero-shot (52.1%
of dataset)
Q: Marissa is hiking a 12mile trail. She took 1 hour
to walk the first 4 miles, then
another hour to walk the next
two miles. If she wants her average speed to be 4 miles per
hour, what speed (in miles per
hour) does she need to walk
the remaining distance?
Q: Josh decides to try flipping
a house. He buys a house
for $80,000 and then puts in
$50,000 in repairs. This increased the value of the house
by 150%. How much profit
did he make?
A: Let’s think step by step. First, we know
that she walked 4 miles in 1 hour, so her speed
was 4 miles per hour. Then, she walked 2
miles in 1 hour, so her speed was 2 miles per
hour. So, her average speed was (4 + 2)/2
= 3 miles per hour. Now, we know that she
has to walk 12 miles in total, and she has
already walked 6 miles. So, she has 6 miles
left to walk. We also know that she wants her
average speed to be 4 miles per hour. So, we
can calculate the time she has left to walk the
remaining 6 miles: 6 miles / 4 miles per hour
= 1.5 hours. So, she has 1.5 hours to walk 6
miles. We can calculate her speed by dividing
the distance by the time: 6 miles / 1.5 hours
= 4 miles per hour. So, she needs to walk the
remaining 6 miles at a speed of 4 miles per
hour. Therefore, the answer (arabic numerals)
is 4. (GT : 6)
A: The answer (arabic numerals) is 6. ✓
A: Let’s think step by step. First, we need to
find the value of the house after the repairs.
The value of the house increased by 150%,
so we need to multiply the original value by
1.5. 80,000 x 1.5 = 120,000. The value of
the house after the repairs is $120,000. Now,
we need to find the profit. The profit is the
difference between the value of the house after the repairs and the total cost of the house.
The total cost of the house is the original cost
plus the cost of the repairs. 80,000 + 50,000
= 130,000. The profit is 120,000 - 130,000
= -10,000. Josh lost $10,000. Therefore, the
|Col1|Col2|answer (arabic numerals) is 10,000. (GT : 70000) A: The answer (arabic numerals) is 100,000.|
|---|---|---|
|||A: The answer (arabic numerals) is 100,000. (GT : 70000)|
|Continued on next page|||
6Some of these errors are due to PaLM model’s instability, where simply adding ‘Let’s think step by step’
causes the model to continuously output newline tokens.
-----
Table 20 – Continued from previous page
|Outcome|Question|Answer|
|---|---|---|
Q: Every day, Wendi feeds
each of her chickens three
cups of mixed chicken feed,
containing seeds, mealworms
and vegetables to help keep
them healthy. She gives the
chickens their feed in three
separate meals. In the morning, she gives her flock of
chickens 15 cups of feed. In
the afternoon, she gives her
chickens another 25 cups of
feed. How many cups of
feed does she need to give her
chickens in the final meal of
the day if the size of Wendi’s
flock is 20 chickens?
|Col1|Col2|A: The answer (arabic numerals) is 15 + 25 + 20 = 60. (GT : 20)|
|---|---|---|
A: Let’s think step by step. First, we need to
find out how many cups of feed Wendi has
already given her chickens. She gave them
15 cups in the morning and 25 cups in the
afternoon. That means she has already given
them 40 cups of feed. Now, we need to find
out how many cups of feed she needs to give
her chickens in the final meal of the day. We
know that she has 20 chickens. Each chicken
needs three cups of feed. That means she
needs 60 cups of feed for all 20 chickens. But
she has already given them 40 cups of feed.
That means she needs to give them 20 more
cups of feed. The following is an example of
a problem that requires the use of the distribu-
tive property: Therefore, the answer (arabic
numerals) is 12. (GT : 20)
-----
**C** **Sample Study**
To validate the correctness of chain of thought, we analyze texts generated by Zero-shot-CoT for
CommonsenseQA and MultiArith datasets. Instruct-GPT3 (text-davinci-002) model is used for the
analysis.
**C.1** **CommonsenseQA**
Table 21: Categorization results of generated chain of thought by
Zero-shot-CoT for CommonsenseQA datasets.
Prediction CoT Category Zero-Shot-CoT (%)
CoT is correct **78.0**
Correct
CoT is incorrect 22.0
CommonSense Mistake **62.0**
Factual Mistake 0.0
Logical Mistake 28.0
Others 10.0
Incorrect
Table 21 summarizes the categorization results of texts generated by Zero-shot-CoT for CommonsenseQA. We randomly picked up 50 samples whose prediction results were correct and 50 samples
whose prediction results were incorrect. We categorized those samples by CoT types. Some picked-up
samples from each category are found Table 22.
First, it is found that the correct samples contain a certain amount of incorrect chain of thought. The
main tendency is that Zero-shot-CoT cannot narrow down the prediction to one from multiple answer
choices, and produce multiple predictions as answers but fortunately the first output answer was
correct. See “Correct - CoT is INCORRECT” rows in Table 22
Second, as for incorrect samples, commonsense mistake is the most frequent error type. By observing
the produced chain of thought texts, it is found that Zero-shot-CoT often produces a flexible and
reasonable chain of thought (logically correct but lacks common sense) even when the final prediction
is not correct. See “CommonSense Mistake” rows in Table 22
Table 22: Prediction examples produced by Zero-shot-CoT for CommonsenseQA.
|Category|Question|Answer|
|---|---|---|
|Correct - CoT is correct|Q: If there is a pond with trees around it, where it it likely located? Answer Choices: (A) ground (B) bathroom (C) forest (D) countryside (E) rural area|A: Let’s think step by step. A pond is likely to be located near trees because trees need water to survive. Therefore, the most likely location for a pond with trees around it is in a forest. Therefore, among A through E, the answer is C. ✓|
|---|---|---|
|is correct Correct - CoT|trees around it, where it it likely located? Answer Choices: (A) ground (B) bathroom (C) forest (D) countryside (E) rural area Q: Human beings learn|be located near trees because trees need water to survive. Therefore, the most likely location for a pond with trees around it is in a forest. Therefore, among A through E, the answer is C. ✓|
|---|---|---|
|Correct - CoT is correct|Q: Human beings learn about current events from what print item? Answer Choices: (A) question au- thority (B) melt (C) read newspapers (D) act (E) dictionary|A: Let’s think step by step. How do human beings learn? They learn by observing and listening to others, and they also learn by reading. So it’s most likely that human beings learn about current events from reading newspapers. Therefore, among A through E, the answer is C. ✓|
|Continued on next page|||
-----
Table 22 – Continued from previous page
|Category|Question|Answer|
|---|---|---|
|Correct - CoT is correct|Q: The artist was sit- ting quietly pondering, then suddenly he began to paint when what struck him? Answer Choices: (A) sadness (B) anxiety (C) inspiration (D) dis- comfort (E) insights|A: Let’s think step by step. The first thing that happens is that the artist is sitting quietly and pon- dering. This means he’s thinking deeply about something, probably trying to come up with an idea. Then, suddenly, he begins to paint. This means he was inspired by something he thought of. The most likely explanation is that he had an insight, or a sudden realization, that led him to start painting. Therefore, among A through E, the answer is most likely (C), inspiration. ✓|
|---|---|---|
|Correct - CoT is INCORRECT|Q: What is likely to sat- isfy someone’s curiosity? Answer Choices: (A) hear news (B) read book (C) see favorite show (D) comedy show (E) go somewhere|A: Let’s think step by step. In order to satisfy someone’s curiosity, they would need to want to know more about something. So, (A) hearing news and (B) reading a book are both good answers because they provide information that the person may be curious about. (C) Seeing a favorite show could also work because it might be something the person is curious about and wants to know more about. (D) A comedy show could potentially satisfy someone’s curiosity if the person is curious about the comedian’s life or what they are like in person. (E) Going somewhere could also work if the person is curious about a certain place and wants to know more Therefore, among A through E, the answer is A, B, C, D, or E. ✓(Model cannot choose only one.) (GT : (A), Zero-shot: (E))|
|---|---|---|
|Correct - CoT is INCORRECT|Q: What would be neces- sary for getting in shape? Answer Choices: (A) good health (B) exer- cise (C) muscle tone (D) sweat (E) feel better|A: Let’s think step by step. In order to get in shape, you need to be able to do three things: 1. Exercise regularly 2. Eat a healthy diet 3. Get enough sleep If you can do all three of those things, then you will be well on your way to getting in shape! Therefore, among A through E, the answer is B, C, and D. ✓(Model cannot choose only one.) (GT : (B), Zero-shot: (B))|
|---|---|---|
|Correct - CoT|Col2|Zero-shot: (B)) A: Let’s think step by step. The man has a fear|
|---|---|---|
|Correct - CoT is INCORRECT|Q: The man had a fear of illness, so he never vis- ited friends who were a what? Answer Choices: (A) sick person (B) hospi- tal (C) elderly person (D) graveyard (E) doctor’s of- fice|A: Let’s think step by step. The man has a fear of illness, so he would avoid anything that would put him in close proximity to an ill person. This would include a hospital, where sick people are treated, and a doctor’s office, where sick people go to receive care. An elderly person is more likely to be ill than a young person, so the man would avoid them as well. A graveyard is where people who have died from illness are buried, so the man would avoid that as well. The answer is A, sick person. Therefore, among A through E, the answer is A. ✓(Model cannot narrow down choice to one in CoT.) (GT : (A), Zero-shot: (A))|
|Continued on next page|||
-----
Table 22 – Continued from previous page
|Category|Question|Answer|
|---|---|---|
|CommonSense Mistake|Q: Where is a well used toy car likely to be found? Answer Choices: (A) child’s room (B) boy’s bedroom (C) own home (D) toy store (E) house|A: Let’s think step by step. A toy car is likely to be found in a child’s room. A child’s room is likely to be found in a house. Therefore, a toy car is likely to be found in a house. Therefore, among A through E, the answer is E. (GT : (A), Zero-shot: (A))|
|---|---|---|
|CommonSense Mistake|Q: Where can you go to use a piano in your neigh- borhood if you don’t have one? Answer Choices: (A) music school (B) music store (C) neighbor’s house (D) lunch (E) drawing room|A: Let’s think step by step. If you don’t have a piano, you can’t use your own. You could go to a music school, but that seems like it would be for a lesson rather than just to use a piano. A music store might have a piano that you could use, but you would probably have to buy something. You could go to a neighbor’s house, but that seems like a lot to ask. You could go to a lunch, but that doesn’t make sense. You could go to a drawing room, but that also doesn’t make sense. The answer must be (B) music store. Therefore, among A through E, the answer is B. (GT : (C), Zero-shot: (C))|
|---|---|---|
|CommonSense Mistake|Q: David watched some nesting birds using his binoculars while on vaca- tion. Where might David be?. Answer Choices: (A) sky (B) vaccation (C) forest (D) countryside (E) roof|A: Let’s think step by step. First, we need to under- stand what the word "binoculars" means. Binocu- lars are two telescopes that are joined together and allow a person to see things that are far away. Now, we need to think about where a person might use binoculars. A person might use binoculars to see things that are far away and in the sky, or to see things that are far away and on the ground. So, the answer could be either (A) sky or (D) countryside. Therefore, among A through E, the answer is (A) or (D). (GT : (C), Zero-shot: (D))|
|---|---|---|
|CommonSense Mistake|Q: When you get up in the morning before you begin work you should do what? Answer Choices: (A) apply for job (B) sleep (C) concen- trate (D) shower (E) just do|A: Let’s think step by step. The first thing you should do when you wake up is probably to stretch and yawn to get your body moving. Then, you should probably brush your teeth and wash your face to get ready for the day. After that, you might want to eat breakfast to give yourself some energy for the day. Once you’re all set, you can start your work for the day. Therefore, among A through E, the answer is C. (GT : (D), Zero-shot: (C))|
|---|---|---|
|Col1|Q: What is someone do-|the answer is C. (GT : (D), Zero-shot: (C)) A: Let’s think step by step. If someone is sitting|
|---|---|---|
|CommonSense Mistake|Q: What is someone do- ing if he or she is sit- ting quietly and his or her eyes are moving? An- swer Choices: (A) read- ing (B) meditate (C) fall asleep (D) bunk (E) think|A: Let’s think step by step. If someone is sitting quietly, that means they are not moving around. And if their eyes are moving, they are probably not asleep. So it’s probably not (C) or (D). If they are reading, they would be looking at the book, not moving their eyes around, so it’s probably not (A), which leaves us with (B) and (E). It’s more likely that they are thinking, so (E) is the best answer. Therefore, among A through E, the answer is E. (GT : (A), Zero-shot: (E))|
|Continued on next page|||
-----
Table 22 – Continued from previous page
|Category|Question|Answer|
|---|---|---|
|Logical Mistake|Q: If you really wanted a grape, where would you go to get it? Answer Choices: (A) winery (B) fruit stand (C) field (D) kitchen (E) food|A: Let’s think step by step. If you want a grape, the first place you might think to look is a fruit stand. If there are no grapes at the fruit stand, your next best bet would be a grocery store. If there are no grapes at the grocery store, you might try a vineyard or winery. If there are no grapes at the vineyard or winery, your last resort would be to grow your own grapes. Therefore, among A through E, the answer is E. (GT : (B), Zero-shot: (B))|
|---|---|---|
**C.2** **MultiArith**
Q: If you really wanted a
grape, where would you
go to get it? Answer
Choices: (A) winery (B)
fruit stand (C) field (D)
kitchen (E) food
A: Let’s think step by step. If you want a grape, the
first place you might think to look is a fruit stand. If
there are no grapes at the fruit stand, your next best
bet would be a grocery store. If there are no grapes
at the grocery store, you might try a vineyard or
winery. If there are no grapes at the vineyard or
winery, your last resort would be to grow your own
grapes. Therefore, among A through E, the answer
is E. (GT : (B), Zero-shot: (B))
Table 23: Categorization results of produced chain of thought for MultiArith datasets. (*1)
These categories are cited from Wei et al. [2022].
Prediction CoT Category Zero-Shot-CoT (%) Few-Shot-CoT (%)
CoT is correct 94.0 98.0
Correct
CoT is incorrect 6.0 2.0
CommonSense Mistake 10.0 **23.8**
Factual Mistake 2.0 0.0
Logical Mistake 68.0 73.8
- Calculator error (*1) (8.) (26.2)
- Symbol mapping error (*1) (4.) (2.4)
- One step missing error (*1) (6.) (7.1)
- One unnecessary step error (10.) (2.4)
- More complicated (40.) (35.7)
Others **20.0** 2.4
Incorrect
Table 23 summarizes the categorization results of texts generated by Zero-shot-CoT and Few-shotCoT for MultiArith. We compared Zero-shot-CoT and Few-shot-CoT to contrast the difference of
chain of thought produced by these two methods. Specifically, we randomly picked up correct 50
samples and incorrect 50 samples produced by each method and categorized them by types. As an
exception, the maximum number of incorrect samples from Few-shot-CoT for MultiArith was 42.
As for correct samples, we examined if the produced chain of thought is logical and consistent with
the correct prediction. The result shows that almost all the chain of thought is correct, with slightly
more reasoning mistakes found in Zero-shot-CoT than Few-shot-CoT.
As for incorrect samples, it is found that Zero-shot-CoT tends to output unnecessary steps of reasoning
after getting the correct prediction, which results in changing the prediction to incorrect one. Zeroshot-CoT also sometimes does not start reasoning, just rephrasing the input question. In contrast,
Few-shot-CoT tends to fail when generated chain of thought include ternary operation, e.g. (3+2) _∗_ 4.
Another finding is that Zero-shot-CoT and Few-shot-CoT have a certain amount of common sense
mistakes to interpret a question. Some examples are found at Table 24.
-----
Table 24: Example-based comparison between Zero-shot-CoT and Few-shot-CoT from MultiArith.
|Question|Zero-shot-CoT|Few-shot-CoT|
|---|---|---|
|Q: At the fair Adam bought 13 tickets. Af- ter riding the ferris wheel he had 4 tickets left. If each ticket cost 9 dol- lars, how much money did Adam spend riding the ferris wheel?|A (ONE UNNECESSARY STEP ER- ROR): Let’s think step by step. Adam bought 13 tickets. That means he spent 13 * 9 = 117 dollars on tickets. After riding the ferris wheel, he had 4 tickets left. That means he used 9 tickets to ride the ferris wheel. That means he spent 9 * 9 = 81 dollars on riding the ferris wheel. So the answer is 117 - 81 = 36 dollars. Therefore, the answer (arabic numerals) is 36. |A: Adam started with 13 tickets. He had 4 left af- ter riding the ferris wheel. So he must have spent 13 - 4 = 9 tickets. 9 tickets times 9 dollars per ticket is 9 * 9 = 81. The answer is 81. ✓|
|---|---|---|
|Q: At a restaurant each adult meal costs $5 and kids eat free. If a group of 15 people came in and 8 were kids, how much would it cost for the group to eat?|A (ONE UNNECESSARY STEP ER- ROR): Let’s think step by step. There are 8 kids, so that means there are 7 adults. Each adult meal costs $5, so that means that the 7 adults will cost $5*7=$35 Now we just need to add the two numbers together. $35+8=43$ So it would cost $43 for the group to eat. Therefore, the answer (arabic numerals) is 43. |A: If 8 were kids, then that means there were 15 - 8 = 7 adults. Each adult meal costs $5. So the to- tal cost would be 7 * 5 = 35. The answer is 35.✓|
|---|---|---|
|Q: April’s discount flow- ers was having a sale where each flower was 6 dollars. If Katie bought 5 roses and 5 daisies, how much did she spend?|A: Let’s think step by step. First, we need to calculate how much each type of flower costs. There are 5 roses, and each rose costs 6 dollars. So, the cost of the roses is 5*6=30 dollars. There are 5 daisies, and each daisy costs 6 dollars. So, the cost of the daisies is 5*6=30 dol- lars. Then, we need to calculate the total cost. The total cost is the cost of the roses plus the cost of the daisies. So, the total cost is 30+30=60 dollars. There- fore, the answer (arabic numerals) is 60. ✓|A (CALCULATOR ERROR): Each flower was 6 dollars. Katie bought 5 roses and 5 daisies. So she spent 5 * 6 + 5 * 6 = 60 + 30 = 90. The answer is 90. |
|---|---|---|
|Q: While shopping for music online, Faye bought 2 country albums and 3 pop albums. Each album came with a lyric sheet and had 6 songs. How many songs did Faye buy total?|A: Let’s think step by step. Faye bought 2 country albums. Each album has 6 songs. So she bought 2 * 6 = 12 songs from the country albums. Faye bought 3 pop albums. Each album has 6 songs. So she bought 3 * 6 = 18 songs from the pop albums. In total, Faye bought 12 + 18 = 30 songs. Therefore, the answer (arabic numerals) is 30. ✓|A (CALCULATOR ERROR): Faye bought 2 country albums and 3 pop albums. Each album had 6 songs. So she bought 2 * 6 + 3 * 6 = 24 songs. The answer is 24. |
|---|---|---|
|Continued on next page|||
-----
Table 24 – continued from previous page
|Question|Zero-shot-CoT|Few-shot-CoT|
|---|---|---|
|Q: Jerry was helping the cafeteria workers pick up lunch trays, but he could only carry 8 trays at a time. If he had to pick up 9 trays from one table and 7 trays from another, how many trips will he make?|A (COMMONSENSE MISTAKE): Let’s think step by step. Jerry can carry 8 trays at a time. There are 9 trays on the first table. That means Jerry will need to make 2 trips to the first table. There are 7 trays on the second table. That means Jerry will need to make 1 trip to the sec- ond table. In total, Jerry will make 3 trips. Therefore, the answer (arabic nu- merals) is 3. |A: Jerry can carry 8 trays at a time. If he has to pick up 9 trays from one table and 7 trays from another, he will have to make 2 trips. The answer is 2. ✓|
|---|---|---|
|Q: Kaleb bought 14 boxes of chocolate candy and gave 5 to his little brother. If each box has 6 pieces inside it, how many pieces did Kaleb still have?|A: Let’s think step by step. Kaleb bought 14 boxes of chocolate candy. This means that he had 84 pieces of chocolate candy. He gave 5 boxes to his little brother, which means that he gave his little brother 30 pieces of choco- late candy. Kaleb still had 54 pieces of chocolate candy. Therefore, the answer (arabic numerals) is 54. ✓|A (COMMONSENSE MISTAKE): Kaleb bought 14 boxes. Each box has 6 pieces. So 14 * 6 = 84 pieces. He gave 5 to his brother. So he has 84 - 5 = 79 pieces. The answer is 79. |
|---|---|---|
|Q: At the fair there were 12 people in line for the bumper cars. If 10 of them got tired of waiting and left and 15 more got in line, how many people would be in line?|A (OTHERS; REASONING IS NOT STARTED): Let’s think step by step. There were 12 people in line for the bumper cars. 10 of them got tired of waiting and left. 15 more got in line. That means that there are now 15 people in line for the bumper cars. Therefore, the answer (arabic numerals) is 15. |A: There were originally 12 people in line. 10 of them left, so that left 12 - 10 = 2. Then 15 more got in line, so that is 2 + 15 = 17. The answer is 17. ✓|
|---|---|---|
|Q: Luke made 9 dollars mowing lawns and 18 dollars weed eating. If he only spent 3 dollar a week, how long would the money last him?|A (OTHERS; QUESTION UNDER- STANDING ERROR): Let’s think step by step. How much money does Luke make in a week? How much money does Luke spend in a week? How much money does Luke have left over at the end of the week? How long will it take Luke to save up $54? Luke makes $27 a week. He spends $3 a week. He has $24 left over at the end of the week. It will take Luke 2 weeks to save up $54. Therefore, the answer (arabic numerals) is 2. |A: Luke made 9 dollars mowing lawns and 18 dollars weed eating. In total, he made 9 + 18 = 27 dollars. If he spends 3 dollars a week, that is 3 dollars * 4 weeks = 12 dollars a month. So the money would last him 27 / 12 = 2.25 months. The answer is 2.25 months. (GT : 9 weeks)|
|---|---|---|
|Continued on next page|||
-----
Table 24 – continued from previous page
|Question|Zero-shot-CoT|Few-shot-CoT|
|---|---|---|
|Q: Each chocolate bar in a box cost $3. If a box had 9 bars total and Wendy sold all but 3 bars, how much money would she have made?|A (OTHERS; MAXIMUM LIMIT OF TEXT LENGTH): Let’s think step by step. Each chocolate bar in a box costs $3. If a box had 9 bars total, then Wendy sold all but 3 bars. How much money would she have made? We can solve this problem using algebra. Let’s start by creating a variable to represent the number of chocolate bars Wendy sold. We’ll call this variable "x". If Wendy sold "x" chocolate bars, then she would have 9 - x chocolate bars left in the box. We know that each chocolate bar costs $3, so the total cost of the choco- late bars Wendy sold Therefore, the answer (arabic numerals) is: Wendy would have made $12. |A: Each chocolate bar cost 3 dollars. So if Wendy sold all but 3, she would have sold 9 - 3 = 6. 6 * 3 = 18. The answer is 18. ✓|
|---|---|---|
-----
**D** **Further Zero-shot Experiments with PaLM 540B**
We additionally evaluated Zero-shot-CoT on PaLM 540B, without and with self-consistency [Wang
et al., 2022]. Self-consistency [Wang et al., 2022] generates reasoning paths by random sampling
strategy N times and decides the final prediction by majority voting.
Table 25: Further experiment results with PaLM (540B). Evaluation metric is Accuracy.
AQUA-RAT SVAMP GSM8K MultiArith
Zero-shot 23.4 **63.1** 12.5 25.5
Zero-shot-CoT **36.1** **63.1** **43.0** **66.1**
Zero-shot-CoT + self consistency **46.5** **80.5** **70.1** **89.0**
(40 paths)
Few-shot-CoT [Wei et al., 2022] 35.8 79.0 56.9 -
Few-shot-CoT + self consistency 48.3 86.6 74.4 -
(40 paths) [Wang et al., 2022]
**E** **Detailed experiment results of model scale study**
This section describes the detailed experiment results of model scale study. The curve within Figure 3
uses the values of Table 26 and Table 27.
Table 26: Model scale study. Evaluation metric is accuracy on MultiArith dataset. S: text-ada001, M: text-babbage-001, L: text-curie-001, XL-1: text-davinci-001, XL-2: text-davinci-002. It
is verified that CoT is effective when the model is larger, such as Instruct GPT-3 (text-davinci-001
and text-davinci-002) and Original GPT-3 (175B parameters; davinci). In this experiment, the order
of performance (ascending) is Zero-shot, Few-shot (8samples), Zero-shot-CoT, and Few-shot-CoT
(8samples) for davinci and text-davinci-002.
Original GPT-3 (0.3B / 1.3B / 6.7B / 175B) Instruct GPT-3 (S / M / L / XL-1 / XL-2)
Zero-shot 2.0 / 1.3 / 1.5 / 3.3 3.7 / 3.8 / 4.3 / 8.0 / 17.7
Few-shot 5.2 / 5.2 / 4.0 / 8.1 3.0 / 2.2 / 4.8 / 14.0 / 33.7
Zero-shot-CoT 1.7 / 2.2 / 2.3 / 19.0 2.0 / 3.7 / 3.3 / 47.8 / 78.7
Few-shot-CoT 4.3 / 1.8 / 6.3 / 44.3 2.5 / 2.5 / 3.8 / 36.8 / 93.0
GPT-2 (1.5B) GPT-Neo (2.7B) GPT-J (6B) T0 (11B) OPT (13B)
Zero-shot 3.2 3.0 2.7 2.8 3.7
Zero-shot-CoT 2.2 1.3 2.5 3.2 2.2
Table 27: Model scale study with PaLM. Evaluation metric is accuracy on GSM8K dataset.
PaLM (8B / 62B / 540B)
Zero-shot 2.1 / 7.0 / 12.5
Zero-shot-CoT 2.4 / 10.5 / 43.0
-----
| [
"Yutaka, Matsuo",
"Takeshi, Kojima",
"Shixiang Shane, Gu",
"Machel, Reid",
"Yusuke, Iwasawa"
] | 2022-05-24T00:00:00 | NeurIPS 2022 Poster | true | 1,000 | 75 | null | https://arxiv.org/abs/2205.11916v4 | https://arxiv.org/abs/2205.11916 | https://www.semanticscholar.org/paper/e7ad08848d5d7c5c47673ffe0da06af443643bda |
Measuring Massive Multitask Language Understanding | "We propose a new test to measure a text model's multitask accuracy. The test covers 57 tasks includ(...TRUNCATED) | "While most recent models have near random-chance accuracy, the very largest GPT-3 model improves ov(...TRUNCATED) | "## MEASURING MASSIVE MULTITASK LANGUAGE UNDERSTANDING\n\n**Dan Hendrycks** **Collin Burns** **Steve(...TRUNCATED) | ["Dan, Hendrycks","Andy, Zou","Collin, Burns","Dawn, Song","Mantas, Mazeika","Steven, Basart","Jacob(...TRUNCATED) | 2021-01-12T00:00:00 | ICLR 2021 | true | 1,000 | 23 | null | http://arxiv.org/abs/2009.03300 | https://arxiv.org/abs/2009.03300 | https://www.semanticscholar.org/paper/814a4f680b9ba6baba23b93499f4b48af1a27678 |
ReAct: Synergizing Reasoning and Acting in Language Models | "While large language models (LLMs) have demonstrated impressive capabilities across tasks in langua(...TRUNCATED) | "The use of LLMs are explored to generate both reasoning traces and task-specific actions in an inte(...TRUNCATED) | "## REACT: SYNERGIZING REASONING AND ACTING IN LANGUAGE MODELS\n\nShunyu Yao*,1[∗], Jeffrey Zhao2,(...TRUNCATED) | ["Shunyu, Yao","Karthik, Narasimhan","Dian, Yu","Jeffrey, Zhao","Izhak, Shafran","Yuan, Cao","Nan, D(...TRUNCATED) | 2023-03-09T00:00:00 | ICLR 2023 | true | 1,000 | 30 | null | http://arxiv.org/abs/2210.03629 | https://arxiv.org/abs/2210.03629 | https://www.semanticscholar.org/paper/99832586d55f540f603637e458a292406a0ed75d |
Self-Consistency Improves Chain of Thought Reasoning in Language Models | "Chain-of-thought prompting combined with pretrained large language models has achieved encouraging (...TRUNCATED) | "This paper proposes a new decoding strategy, self-consistency, to replace the naive greedy decoding(...TRUNCATED) | "## SELF-CONSISTENCY IMPROVES CHAIN OF THOUGHT REASONING IN LANGUAGE MODELS\n\n**Xuezhi Wang[†‡](...TRUNCATED) | ["Jason, Wei","Aakanksha, Chowdhery","Xuezhi, Wang","Denny, Zhou","Dale, Schuurmans","Ed, Chi","Quoc(...TRUNCATED) | 2023-03-07T00:00:00 | ICLR 2023 | true | 1,000 | 89 | null | http://arxiv.org/abs/2203.11171 | https://arxiv.org/abs/2203.11171 | https://www.semanticscholar.org/paper/5f19ae1135a9500940978104ec15a5b8751bc7d2 |
Toolformer: Language Models Can Teach Themselves to Use Tools | "Language models (LMs) exhibit remarkable abilities to solve new tasks from just a few examples or t(...TRUNCATED) | "This paper introduces Toolformer, a model trained to decide which APIs to call, when to call them, (...TRUNCATED) | "## Toolformer: Language Models Can Teach Themselves to Use Tools\n\n**Timo Schick** **Jane Dwivedi-(...TRUNCATED) | ["Timo, Schick","Jane, Dwivedi-Yu","Roberto, Dessì","Roberta, Raileanu","Maria, Lomeli","Luke, Zett(...TRUNCATED) | 2023-02-09T00:00:00 | NeurIPS 2023 Oral | true | 1,000 | 23 | null | http://arxiv.org/abs/2302.04761 | https://arxiv.org/abs/2302.04761 | https://www.semanticscholar.org/paper/53d128ea815bcc0526856eb5a9c42cc977cb36a7 |
Training Verifiers to Solve Math Word Problems | "State-of-the-art language models can match human performance on many tasks, but they still struggle(...TRUNCATED) | "It is demonstrated that verification significantly improves performance on GSM8K, and there is stro(...TRUNCATED) | "## Training Verifiers to Solve Math Word Problems\n\n\n**Karl Cobbe[∗]** **Vineet Kosaraju[∗]**(...TRUNCATED) | ["Mark, Chen","John, Schulman","Reiichiro, Nakano","Jerry, Tworek","Vineet, Kosaraju","Jacob, Hilton(...TRUNCATED) | 2021-11-17T00:00:00 | null | false | 1,000 | 129 | null | http://arxiv.org/abs/2110.14168 | https://arxiv.org/abs/2110.14168 | https://www.semanticscholar.org/paper/d6045d2ccc9c09ca1671348de86d07da6bc28eea |
Tree of Thoughts: Deliberate Problem Solving with Large Language Models | "Language models are increasingly being deployed for general problem solving across a wide range of (...TRUNCATED) | "A new framework for language model inference, Tree of Thoughts (ToT), which generalizes over the po(...TRUNCATED) | "## Tree of Thoughts: Deliberate Problem Solving with Large Language Models\n\n\n**Shunyu Yao** **Di(...TRUNCATED) | ["Shunyu, Yao","Karthik, Narasimhan","Dian, Yu","Jeffrey, Zhao","Izhak, Shafran","Thomas L., Griffit(...TRUNCATED) | 2023-05-17T00:00:00 | NeurIPS 2023 Oral | true | 1,000 | 26 | null | http://arxiv.org/abs/2305.10601 | https://arxiv.org/abs/2305.10601 | https://www.semanticscholar.org/paper/2f3822eb380b5e753a6d579f31dfc3ec4c4a0820 |
Measuring Mathematical Problem Solving With the MATH Dataset | "Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the(...TRUNCATED) | "This work introduces MATH, a new dataset of 12,500 challenging competition mathematics problems whi(...TRUNCATED) | "## Measuring Mathematical Problem Solving With the MATH Dataset\n\n**Dan Hendrycks** **Collin Burns(...TRUNCATED) | ["Dan, Hendrycks","Collin, Burns","Dawn, Song","Saurav, Kadavath","Akul, Arora","Steven, Basart","Er(...TRUNCATED) | 2021-11-08T00:00:00 | NeurIPS 2021 | true | 935 | 82 | null | http://arxiv.org/abs/2103.03874 | https://arxiv.org/abs/2103.03874 | https://www.semanticscholar.org/paper/57d1e7ac339e783898f2c3b1af55737cbeee9fc5 |
Self-Refine: Iterative Refinement with Self-Feedback | "Like humans, large language models (LLMs) do not always generate the best output on their first try(...TRUNCATED) | "Self-Refine is introduced, an approach for improving initial outputs from LLMs through iterative fe(...TRUNCATED) | "### SELF-REFINE: Iterative Refinement with Self-Feedback\n\n\n**Aman Madaan[1], Niket Tandon[2], Pr(...TRUNCATED) | ["Sean, Welleck","Aman, Madaan","Nouha, Dziri","Luyu, Gao","Bodhisattwa Prasad, Majumder","Uri, Alon(...TRUNCATED) | 2023-05-25T00:00:00 | NeurIPS 2023 Poster | true | 846 | 32 | null | http://arxiv.org/abs/2303.17651 | https://arxiv.org/abs/2303.17651 | https://www.semanticscholar.org/paper/3aaf6a2cbad5850ad81ab5c163599cb3d523436f |
Least-to-Most Prompting Enables Complex Reasoning in Large Language Models | "Chain-of-thought prompting has demonstrated remarkable performance on various natural language reas(...TRUNCATED) | "Experimental results on tasks related to symbolic manipulation, compositional generalization, and m(...TRUNCATED) | "## LEAST-TO-MOST PROMPTING ENABLES COMPLEX REASONING IN LARGE LANGUAGE MODELS\n\n**Denny Zhou[∗]*(...TRUNCATED) | ["Jason, Wei","Olivier, Bousquet","Quoc V., Le","Xuezhi, Wang","Le, Hou","Nathan, Scales","Denny, Zh(...TRUNCATED) | 2022-09-29T00:00:00 | ICLR 2023 Poster | true | 788 | 49 | null | https://openreview.net/forum?id=WZH7099tgfM | https://arxiv.org/abs/2205.10625 | https://www.semanticscholar.org/paper/5437e8adab596d7294124c0e798708e050e25321 |
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