Demystifying Prompts in Language Models via Perplexity Estimation
Authors: Hila Gonen
Srini Iyer
Terra Blevins
Noah A. Smith
Luke Zettlemoyer
Venue: EMNLP 2023 Findings (2023)
Keywords: LLM
perplexity
prompts
TL;DR: We show that lower perplexity of the prompt correlates well with better performance

Abstract: Language models can be prompted to perform a wide variety of tasks with zero- and few-shot in-context learning.
However, performance varies significantly with the choice of prompt, and we do not yet understand why this happens.
In this paper, we analyze the factors that contribute to this variance and establish a new empirical hypothesis: the performance of a prompt is predicted by the extent to which the model is familiar with the language it contains. Over a wide range of tasks, we show that the lower the perplexity of the prompt, the better it is able to perform the task, when considering reasonable prompts that are related to it. As part of our analysis, we also devise a method to automatically extend a small seed set of manually written prompts by paraphrasing with GPT3 and backtranslation. This larger set allows us to verify that perplexity is a strong predictor of the success of a prompt and we show that the lowest perplexity prompts are consistently effective.

Demystifying Prompts in Language Models via Perplexity Estimation
Hila Gonen 1.2
Srini Iyer*
Terra Blevins' Noah A. Smith Luke Zettlemoyer" 1.2
Paul G. Allen School of Computer Science & Engineering, University of Washington
Meta AI Research
AAllen Institute for Artificial Intelligence
hi hilagnn@gmail.cm com sviyerêmeta. ta com {blvns, nasmi 1sz @cs washington. wast
Abstract
Language models can be prompted to perform wide variety of tasks with zero- and few-shot in- context learning. However, performance varies significantly with the choice of prompt, and we not yet understand why this happens. In this paper, analyze the factors that contribute to this variance and establish new empirical hypothesis: the performance of prompt is predicted by the extent to which the model is familiar with the language it contains. Over wide range of tasks, we show that the lower the perplexity of the prompt, the better it is able to perform the task, when considering reason- able prompts that related to it. As part of our analysis, we also devise a method to auto- matically extend a small seed set of manually written prompts by paraphrasing with GPT3 and backtranslation. This larger set allows us verify that perplexity is strong predictor of the success of prompt and we show that the lowest perplexity prompts are consistently effective.
which newopoper would you exeect to Fnd this arficle?
0.6
Accuracy
whot' this news?
0.4
What's going on? What's goin or?
10
10"
10a
Perplexity
Figure 1: Accuracy perplexity for the AG News dataset with OPT 175B. The a axis is in log scale. Each point stands for different prompt.
on the task will be, when considering reasonable prompts that are related to the task. This is based on the intuition that the more frequently the prompt (or very similar phrases) appears the training data, the more the model is familiar with it and is able to perform the described task. We refrain from using the training data directly as it is often unavailable, expensive to search due to its size, and hard to use for approximate matching of similar prompts. Instead, we focus on the perplexity of the prompt as a proxy for its occurrences in the data.
1 Introduction
Language models can be prompted to perform a wide range of zero- and few-shot learning tasks (Brown et al., 2020; Schick and Schütze, 2020). However, there is significant variance in the performance of seemingly similar prompts (Chen al., 2022): for AG News (Zhang et al., 2015). we find an over point accuracy gap between differ- ent manually curated prompts (see Table 1) on OPT 175B (Zhang et al., 2022). Despite efforts to im- prove prompt engineering (Shin et al., 2020; Li and Liang, 2021; Gao et al., 2021), it is still challenging to develop high-quality prompts for new tasks, and little is known about why this phenomenon occurs.
To enable more complete analysis, we automati- cally expand the set of manually created prompts for the task by paraphrasing, resulting in much larger and diverse of prompts. We focus prompts in English that reasonably describe the task for two reasons: (a) our main motivation to understand what lies under the variance of perfor- mance in this type of prompt; (b) we aim to devise a useful method for creating prompts that are con- sistently effective, that could be easily adopted and interpreted by future, potentially non-expert users. We show empirically that our hypothesis holds across a diverse set of tasks (including classifi- cation and word prediction), models, and model
We interested in understanding what makes some prompts better than others. and using this un- derstanding to create better prompts for given tasks and models. We hypothesize that the lower the per- plexity of a prompt is, the better its performance

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We define the perplexity of the prompt as the perplexity of the full prompt sequence, including the input itself, and without the label, averaged over 1,000 examples (see Section 4 for details). The input is part of the prompt in the case of the word prediction tasks by design (e.g., "The opposite of the word good is"). Inclusion of the task input as part of the prompt for classification tasks as well is intentional: we want to ground the prompt to the task (without the input, we are testing the hypothesis that lower perplexity prompts across sizes, providing us some insights about the under- lying mechanism of prompting (see Figure 1). As a result, we devise a method, SPELL (Selecting Prompts by Estimating LM Likelihood), for cre- ating prompts in an informed manner. We show that using SPELL to choose prompts results in less variability in performance as well as in accuracy gains (1.8 accuracy points with OPT and 2.3 accu- racy points with Bloom on average). Importantly, our method does not require labels at all, only a small sample of inputs for the task.
roughly 366B tokens), and in addition, this training data is not always publicly available (e.g.. GPT3; Brown et al. 2020). Our initial attempts to estimate exact-match occurrences of prompts in the data resulted in very sparse counts, which led us to look for a softer formalization.
Instead of considering the training data directly, we propose to focus on the perplexity of the prompt as proxy for its occurrences in some form in the data - essentially indicating to what extent the model expects this prompt. This perplexity based framing helps to avoid the challenge of exact match in the data, and takes into account variations of the prompt that the model is also exposed to and might be influenced by. In addition, it helps overcome the challenges mentioned above as it requires neither access to the pretraining data (which is not always publicly available for LMs) nor matching over huge amounts of text.
Our contributions can be summarized as follows: (a) we formalize the notion that better familiarity of the model with the prompt correlates with better performance (Section 2); (b) we automatically elab- orate given set of seed prompts using paraphras- ing (Section 3); (c) establish experimentally the hypothesis that lower perplexity of the prompt cor- relates well with better performance (Section 5); (d) we devise a method to create a more consistent set of prompts, that also improve results even with no labels for the task (Section 7).
Hypothesis: lower perplexity correlates with bet- ter performance. We hypothesize that on aver- age, lower- pewre-perplexity prompts perform better. We are interested in establishing this hypothesis by experimentally showing a significant negative cor- relation between the perplexity of the prompt and its performance on the task, across a diverse set of tasks and models.
2 Why are prompts not all created equal?
Despite the popularity of prompting as a method for using language models (Shin et al., 2020; Li and Liang, 2021; Gao et al., 2021), the cause for the different behavior of various prompts remains unclear so far. Table 1 shows four example prompts for news topic classification task (AG News) and their respective accuracies when used to prompt OPT 175B (Zhang et al., 2022). The accuracy gap between the different prompts is not trivial and is not possible to predict from the prompts alone.
Prompl
Accuracy
What this piece of news regarding?
40.9
What this article about?
52.4
What the best way describe this article? What the most accurate label for this news article?
68.2
71.2
all tasks work better on every task). The label is not considered a part of the prompt and is not taken into consideration when computing the prompt. In practice this also results in a huge advantage of our method, SPELL (Section 7), which aims to find better prompts-it does not require any labels.
Table 1: Example prompts for the task AG News (news classification) that vary considerably in accuracy.
We propose that the more frequently a prompt appears in some variation in the data, the better it works for the task. The intuition behind this is that sequence that is more expected by the model is more likely to aid the model to extract the relevant information. However, this premise is hard to measure accurately: most language models use huge amounts of training data (c.g., OPT uses a corpus of roughly 180B tokens, and Bloom uses
For performance measures, we use the log- likelihood score assigned by the model to the cor- rect label given that prompt. We choose this metric
'We experimented with the task of AG News (see Sec- tion 4.1). and looked for all of its prompts (using exact match) in the OPT training data, Indeed, only 9/108 of the prompts appear in the training data. Such sparse counts do not allow for any useful or reliable analysis of prompt behaviour.

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over accuracy as gives a more fine-grained dis- tinction between prompts and because accuracy can be unstable, as explained in more detail in Section 4. For classification tasks, we also report correlation with accuracy, which is the main evaluation metric for this type of task.
and close English, reduce the risk of noise. Since we aim get about 100 prompts per task, we add 8 additional languages² in the case where the basic 8 languages yielded too few alternatives. For word prediction tasks, we use the sequence of the created prompt up to the index of the label, not including the label, for example: The word "dog" in French is ". Depending on the task, we enforce the existence of specific words (e.g., the name of the language, and the souree word, in word-level translation) or enforce the prompt to be a question.
3 Automatic Expansion of Seed Prompts
We are interested in expanding our pool of prompts in order to: (a) have a more diverse set of prompts, making it more likely to find better prompt for our task, and (b) support better analysis to validate our prompt quality hypothesis. this section, we describe our method for automatically expanding a seed set of manually created prompts using para- phrasing.
Examples and Statisties Table 4 lists all 4 man- ually created prompts we use for the AG News task (news classification), alongside a few sampled prompts created automatically using our method. As was typically the case, we are able to get prompts that are rather different in phrasing and structure from those included in the seed set.
Step O: Creating a seed set of manually-written prompts We first write/collect small set of hu- man written prompts that describe the task. For classification tasks we assume that the input ap- pears before the prompt, with no choices appearing as part of the prompt (to help smooth paraphras- ing of the prompt itself).
The statistics of the prompts in the manually created seed set (Step 0) as well as the prompts after Step 1 and Step for each task (see Section 4.1 for details about the tasks) are detailed in Table 3.
4 Experimental Sctup
4.1 Models, Tasks and Datasets
Step 1: Paraphrasing with GPT3 We use the text-davinci-002 version of GPT3 (Brown et al., 2020) to generate paraphrases for each of the man- ual prompts in our seed set. We prompt it with a mela-prompt for paraphrasing to generate varia- tions of one of our seed prompts. An example of such a meta-prompt is: Write a paraphrase for the following sentence: <seed prompt> Paraphrase:. The 7 meta-prompts used in this step are listed in Table 2.
We study four auto-regressive models: OPT (Zhang et al., 2022) of different sizes (1.3B, 30B, 175B parameters), all trained mainly on English,* 4 and Bloom (176B parameters; Luccioni et al. 2022), which is trained on 46 natural languages and 13 programming languages. We experiment with two types of tasks: word prediction tasks and classifica- tion tasks, as detailed below.
Word Prediction Tasks The first task in this cat- egory is word-level translation. Given source word English and a target language, we expect the model to predict the correct translation. For this task we use NorthEuraLex (Dellert et al., 2019), lexical database providing translations of 1016 words into 107 languages. We experiment with 9 languages that use the Latin script. For Bloom, we use additional languages that do not use the
We choose GPT3 our paraphrasing model because of its well-documented generation abilities. This also to ensure that there is separation between the model we use to create the prompts and the models we use to rank them (OPT and Bloom, see Section 4 for details), to avoid confounding the experimental setup.
Paraphrasing using backtranslation Our second step takes as input the paraphrases from GPT3 (in addition to the seed set of prompts) and translates them into different languages and back into English get additional prompt paraphrases (Wieting et al., 2017). We use a set of languages available in the NLLB translation model (Costa- jussà et al., 2022) that are relatively high resource
Step 2:
Danish, German, Italian, French, Dutch, Portuguese,
Swedish, Spanish.
NNrwegian, Romanian, Catalan, Turkish, Ukrainian, Pol- ish, Russian, Arabic.
"As stated in the paper, the training corpora were previ- ously collected or filtered to contain predominantly English text, but a small amount non-English data is still present within the corpus via CommonCrawl.
3 httpp: meoorhheuuleee org/

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Meta prompts
Write a paraphrase for the following sentence: <seed- prompt> Paraphrase:
eseed-prompte Paraphrase:
Write a likely paraphrase of the text: <seed-prompt> Paraphrase:
Write a sentence similar to the following one: <seed-prompt> Paraphrase:
Paraphrase the following sentence: <seed-pi prred-promp>> Paraphrase:
Write a variation of this sentence: Eseed-prompp
How would you say the following sentence in a different way? <seed-prompl
Table Meta prompts used in Step of method for paraphrasing using GPT3.
Task
# Step 0
# Step 1
Step 2
tions; Saravia et al. 2018); (g) Tweet Offensive (classification to offensive vs. not offensive tweets; Barbieri et al. 2020). We use 1,000 random exam- plcs from each dataset.
Word-Level Translation
12
59
118
Antonyms
12
85
176
GLUE Cola
4
27
Newspop
13
43
119
The full set of manual prompts is listed in Sec- tion A in the Appendix. In these tasks, the prompt follows the input, and at the end of each prompt we add the choices of classes (i.e., we provide the possible labels explicitly in the prompt by listing the possible answers as defined by the dataset it- self.): "Choices: X, Y, Z. Answer:" as we find it helps in terms of accuracy. Defining the label space likely helps in our zero-shot setting because there are no previous demonstrations from which the model can learn the possible classes. Additionally, adding class options to the prompt helps to reduce the effect of the surface form competition (Holtz- man al., 2021). The option of generating the answer and comparing it with the gold label was not reasonable here, since we cannot expect the model to generate the exact label as the first choice often enough.
AG News
4
23
108
IMDB
10
45
178
DBpedia
8
23
103
Emotion
4
Tweet Offensive
5
41
119
Table 3: Number of prompts for the different tasks: prompts after step (creating prompts manually), prompts after step (GPT3 paraphrasing), and prompts after step 2 (backtranslation).
Latin script (since Bloom multilingual). Note that only 5 of the languages we experiment with are officially covered by Bloom.
We also consider antonym prediction where, given word, the model is expected to predict its antonym. For this task, we use data from Kaggle," which based on WordNet (Miller, 1995). We choose 1,000 word pairs at random.
4.2 Implementation Details
Classification Tasks We choose classification tasks from Huggingface Datasets, with an attempt to have a set of diverse tasks that use relatively short inputs, with some prompts available in Prompt- Source (Bach et al., 2022):9 (a) GLUE Cola (gram- maticality; Warstadt et al. 2018); (b) Newspop (news classification; Moniz and Torgo 2018); (c)
In all experiments we evaluate zero-shot perfor- mance. To avoid noise when computing perplexity, we instantiate the prompts with 1,000 examples of the dataset, compute the perplexity of the prompt with each example, and calculate the average across all instantiated prompts.
AG News (news classification; Zhang et al. 2015); (d) IMDB (movie review classification; Maas et al. 2011 I); (e) DBpedia (topic classification; Lehmann et al. 2015); (f) Emotion (classification to emo-
To estimate the performance of the prompt, we look at two measures: (a) the language model score (log probability) of the correct label, aver- aged across 1,000 examples; (b) the accuracy the task, computed over the 1,000 examples. To compute accuracy, for each example we score all classes and choose the highest ranking class as the prediction of the model. The score label multiple tokens is defined by the sum the token
BBsqqee, French, Portuguese, Spanish, and Arabic. Ptttps: //w::///wwww kaggle.
untonyms-wordne
"https://huggingfaa co//bocs/dattsses//neee 'nttps://iithul wttp./ccocciaaeceooeeeeeee...eea http/bigscieeee com/bigscienceeeeeeee wencewworsshop pramptsource

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All Mamually Created Prompts
Examples Similar Automatically Created Prompts
What label best describes this news article?
What's the most accurale label for this news article?
What is this piece of news regurding?
What does this piece of concern?
Which newspaper section would this article likely appear in?
In what section the newspaper could article published?
What lopic is this news article about?
What category does this article fall into?
Table 4: Prompts for the task AG News (news classification): the manually created prompts and a sample of
automatically created prompts using our method.
Model
Task
Perplexity-score corr.
Perplexity-ace corr.
Avg Acc
Acc 50 %
Pearson
Spearman
Pearson
Spearman
Antonyms
++.0.41
+*.0.53
GLUE Cola
-0.15
-0. 14
-0.04
-0.02
47.7
57.1
Newspop
*-0.24
* #+.0.26
*-0.20
-0.18
66.4
72.9
AG News
**.00.63
*+.00.88
**.0.77
#4.0.81
57.5
68.7
OPT 175B
IMDB
**0,35
+*0.40
0.14
#0.20
86.2
91.0
DBpedia
*+..0.50
++4.0.44
##.0.51
#4.0.42
46.7
55.2
Emotion
-0.14
-0.19
* 0.30
#*.0.32
16.4
23.0
Tweet Offensive
#-0.19
0.07
0.18
+0.23
51.3
55.8
Antonyms
#93.0.37
+..0.23
GLUE Cola
0.07
0.11
.*20.
#+.0.26
55.5
65.6
Newspop
#9.0.50
++-0.42
**-0.59
#4.0.51
78.9
87.8
AG News
#*.0062
+ ++50..54
**-0.44
**.0.44
50.3
59.4
Bloom 176B
IMDB
0.04
0.09
-0.08
-0.14
89.3
92.2
DBpedia
#*.0.47
*-0.27
#*30.35
*-0.21
27.2
33.4
Emotion
**3.0.33
++2.0.42
**-0.48
*4.0.55
29.3
31.7
Tweet Offensive
0.14
#0.24
*-0.20
-0.03
41.6
46.2
Antonyms
** 0..0
** **.0.70
GLUE Cola
-0.05
0.03
-0.13
0.02
32.2
35.5
Newspop
*-0.23
*.0.25
*-0.18
-0.12
60.3
66.6
OPT 30B
AG News
***.0.66
++.00.11
#*.0.81 0.81
#+.0.80
49.3
60.7
IMDB
-0,06
#0.17
0.04
*+0.22
81.6
86.1
DBpedia
*+9.0.41
++.0..34
0.21
*.0.25
35.9
42.4
Emotion
0.00
-0,03
0.18
0.13
12.3
16.2
Tweet Offensive
**.00.44
+9.00.9
-0.11
-0.05
54.6
60.2
Antonyms
*+.0.45
++.0.33
GLUE Cola
+*30.39
-0.3
-0.09
+4).19
60.3
65.9
Newspop
*00.3
*0.21
-0.07
-0.07
37.6
40.3
OPT 1.3B
AG News
+*.00.3
++.0.29
.+-0).56
++4).49
31.9
37.6
IMDB
-0.11
-0.07
*,0224
+0222
86.0
89.1
DBpedia
-0.16
-0.14
-0.02
-0.01
8.7
9.2
Emotion
0.08
0.08
.0.2
+..30
7.0
9.1
Tweet Offensive
++.0).2
++.0).35
e ++-0.5
++.0.38
58.6
62.6
Table Correlation results the different tasks, with OPT (different sizes) and Bloom. Correlations with p < 0.05 marked with #, Correlations with 0.00625 (according to Bonferroni correction for multiple hypotheses) are marked with Dark and light blue colored cells stand for negative correlations < -0.2 and >> -0.2, respectively. Dark and light orange colored cells stand for positive correlations 0.2 and 0.2, respectively. Average accuracy across all prompts and average accuracy of best 50% prompts are also reported for reference (Avg Ace and Acc 50%, respectively).
scores.
tasks in our setting (the chances the model will gen- erate exact match of the label are low). Hence, the score of the correct label gives better estimate of the actual performance of the model.
For the word prediction tasks we only report scores, since accuracy in general is less stable, suf- fers more from the surface form competition (Holtz- man et al., 2021), and is usually quite low for these

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OPT 175B
Bloom 176B
general the trend appears be the same in the smaller models as well: however, the correlations seem to be slightly weaker. We hypothesize that this might be due to the overall lower performance of these smaller models, making the performance results we use for correlation less stable and reli- able. For word-level translation, however, all corre- lations with the 30B and 1.3B models are similar to those with the 175B model, and are all statisti- cally significant (also after Bonferroni correction for multiple hypotheses).
Lang
Pearson
Spear:
Pearson
Spear.
ita
-0.44
-0.57
-0.37
-0.63
spa
-0.47
-0.61
-0.51
-0.66
cat
-0.47
-0.58
-0.24
-0.31
fra
-0.48
-0.57
-0.48
-0.64
deu
-0.44
-0.60
-0.46
-0.65
fin
-0.44
-0.62
-0.34
-0.56
por -0.45
-0.62
-0.46
-0.61
eus
-0.47
-0.61
-0.45
tur
-0.44
-0.62
-0,33
-0.62
ppn
-0.33
-0.26
arb
-0.36
-0.47
rus
-0.54
-0.69
kor
-0,42
-0.58
Analysis
ell
-0.40
-0.51
Next, we further explore the observed relationship between model perplexity and prompt performance. Despite the consistently high correlation between these two factors, the structure of this relationship varies across tasks (Section 6.1). Additionally, we find that the automatically added prompts are high- quality and not significant source of noise (Sec- tion 6.2), and that the best prompts selected by our approach vary across models (Section 6.3).
Table 6: Correlation results for word-level translation, with OPT 175B and Bloom 176B. All correlations are statistically significant also according to Bonferroni cor- rection for multiple hypotheses for OPT 0.0055). Same for Bloom (p < 0.00357), except for Catalan (Pearson) and Japanese (Spearman).
5 Results
Classification Tasks and Antonym Prediction Table 5 depicts the Pearson and Spearman corre- lation results on the classification tasks and the antonym task, with both OPT 175B and Bloom (two upper blocks). We that most correlations are negative and statistically significant, we pect. This validates our hypothesis and shows that the majority of tasks we indeed get a strong cor- relation between low perplexity of the prompt and better performance on the task." 10 For each task we also report the average accuracy.
6.1 Visualizing the Relationship between Perplexity and Performance
To visualize the correlations we get between the per- plexity and the performance of the prompts across the different settings, we plot a few examples for different tasks and languages. Figures I and 2 show some of the results for selected tasks, as detailed in the captions. The negative trend of the corre-
lation is clearly visible in all plots. Interestingly, the structure of the plots for word-level translation are very similar across all the language pairs, sug- gesting that prompts get consistent perplexity and performance across languages (possibly at different scales). Indeed, the intersection of the 10 lowest perplexity prompts between any two different lan- guages is 8.6 and 8.4 on average (for OPT 175B and Bloom, respectively), which is extremely high. This is very surprising since we know that the only differences between the prompts in the differ- ent languages are the names of the target languages (e.g., The word for "dog" in French *). Addition- ally, the intersection of 10 prompts with the highest label score between any two different languages is 7 and 6.5 on average (for OPT 175B and Bloom. respectively).
Word-Level Translation The results of the word- level translation task are reported in Table 6. Here the correlations are extremely consistent across all languages and across models, with statistical sig- nificance for all languages except for Catalan and Japanese (in Bloom).
Results across Different Model Sizes We repeat the same experiment with the OPT models of sizes 1.3B and 30B, to investigate whether these corre- lations are also consistent across model sizes or should expect
whether this is phenomenon only in large language models. Table (two lower blocks) shows these results for all classification tasks and antonym prediction. We do see that in
A notable finding that appears in the word-level translation plots is the clear separation between prompts that include or do not include quotation
10 Reppating the experiments with the length of the prompt instead of perplexity yields weak positive correlations, almost all of which are not statistically significant.

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marks for the label (usually aligns with whether the prompt uses quotation marks for the source word) - three example prompts appear on the plot. Prompts with quotation marks for the words tend to have both lower perplexity and better performance, consistently. We further analyze the results for OPT 175B within clusters (with/without quotations marks). In the cluster with quotation marks, we get negative correlations (in the range -022 to -0.38) that are statistically significant for almost all languages. The correlations within the other cluster are weaker and less significant (this is expected given the overall lower performance of that cluster).
prompt
ppl
Is this example correct English usage?
25.79
this example using English correctly?
25.46
this example correct English? Is this the example in correct English?
25.33
25.00
English in this example correct?
24.90
Table Example of the 5 highest perplexity prompts for GLUE Cola, using OPT 175B.
Before filtering
After filtering
Task
Lang
Pearson
Spearman
Pearson
Spearman
AG News
.0.63
-0.68
-0.62
-0.54
Ita -0.44
-0.58
-0.44
-0.57
00.7
-0.61
-0.47
-0.61
cal
-0.45
-0.57
-0.47
-0.58
fra
-0.47
-0.57
-0.48
-0.57
French
WLT
deu
-0.43
-0.60
-0.44
-0.60
'som The word for 'doy' in Finnnhh
-0.60
-0.62
por -0.43
-0.61
-0.45
-0.62
-0.45
-0.60
-0.47
-0.61
-8-
-0.43
-0.61
-0.44
-0.62
day' Fiench For
-10-
Table 8: Correlations before and after filtering out noisy prompts, with AG News and Word-Level Translation (WLT).
-12
-14
-16-
dog is French for
-20
As a sanity check, we choose two tasks: word- level translation and AG News, manually filter out the noisy prompts, and compute the correlations again. The annotation is done by external anno- tators (NLP researchers) that were presented with the tasks and asked label whether the prompt is reasonable use for the task. The new correlations with OPT 175B are reported in Table We find that all correlations remain strong and statistically significant when noise is manually removed from the analysis. We get the same trends with Bloom as well.
10a
10a
Perpiexity
Figure 2: Score of correct label vs. perplexity for the word-level translation task in French with OPT 175B. The r axis in log scale. The blue points stand for prompts with quotation marks for the words, while the yellow points are of prompts without quotation marks.
6.2 Effect of Noisy Prompts
We expect our automatic method for expand- ing the set of prompts to also introduce some noise. Though our focus is on the lower perplexity prompts, since we want to benefit from this anal- ysis and be able to devise method for creating better prompts, we do want to make sure that this potential noise is not the cause for the strong cor- relations get. In other words, one might claim that some noisy prompts have particularly high per- plexity and also perform badly, thus, supporting our hypothesis in an undesirable and uncontrolled manner.
6.3 Best Performing Prompts
Table 9 lists the 5 lowest perplexity prompts for the task of antonym prediction, an example. Similar lists for the rest of the tasks are listed in Section B in the Appendix.
A closer look the lowest perplexity prompts reveals that the intersection of 10 lowest perplex-
prompt
ppl
We turn inspect the 10% highest perplex- ity prompts in the different tasks and find subjec- tively that they are noisy, and are usually valid prompts for the tasks. The 5 highest perplexity prompts for the GLUE Cola task are listed in Ta- ble 7 as an example.
The following two The antonym of the word "good" The word that has the opposite meaning of the word "good" is
antonyms: "good"
10.24
10.32
10.43
The word "good"" is antithesis of the word The word "good" opposite the word""
10.85
11.15
Table 9: Lowest perplexity prompts for the antonym prediction task, using OPT 175B.

---

ity prompts between OPT 175B and Bloom 7.1 on average, across the classification tasks. When looking at the 10 highest accuracy prompts across models we get an average intersection of 3.1 across the classification tasks.
OPT
Bloom
Task
low ppl
manual
low ppl
mamual
GLUE Cola
51.7
48.5
3.1
64.5
60.9
3.6
Newspop
80.6
70.4
10.2
90.0
80.0
10.0
AG News
68.4
61.9
6.5
51.0
63.5
-12.5
IMDB
90.4
88.9
91.3
88.8
2.5
DBpedia
46.0
31,2
30.2
Emotion
21.6
22.6
-1.1
35,8
32.1
3.6
7 SPELL: Selecting Prompts by Estimating LM Likelihood
Tweet Offensive
48.4
50.6
-2.3
48.6
40.8
7.8
Table 10: The average accuracy with the manual prompts (manual) compared the average accuracy with the lowest-perplexity prompts (low-ppl), for both OPT 175B and Bloom, across tasks.
The primary contribution of this work is the analy- sis of the relationship between prompt perplexity and downstream task performance (Section 5). As one potential application of our findings, we also present a new method, SPELL, for generating and selecting consistently effective prompts.
points with Bloom, demonstrating the effectiveness of our method.
Assuming a fixed computational budget for find- ing effective prompts for given task, and that the search space might be quite large, we devise the following straightforward procedure:
The variability in accuracy of the 3 lowest per- plexity prompts is also much lower than that of the manually created prompts: with OPT 175B, the average standard deviation within the 3 lowest perplexity prompts (across tasks) is 5.07, vs. 6.86 for the manual prompts, and with Bloom the gap is much bigger, with an average of 2.6 for the 3 lowest perplexity prompts vs. 7.47 for the manual ones." This further shows that SPELL is more stable and reliable compared to using an arbitrary set of man- ually created prompts. SPELL sets the stage for further development in this direction, and serves as initial indication of the benefits of involving perplexity estimation in the process of generating effective prompts.
1. Obtain a small set of manually created prompts for the task.
2. Expand the set of prompts with automatic paraphrasing using a LM (e.g.. GPT3) and backtranslation (see Section 3).
3. Rank the list of prompts by perplexity (aver- aged on representative sample of task inputs, e.g., 1,000).
4. Choose the t (e.g.. 3) lowest perplexity prompts.
Related Work
Using this algorithm, we show empirically that it is best to prioritize experimenting with the lowest perplexity prompts, they are more stable (exhibit less variation in performance) and perform better than manual prompts average. This method also does not require any labels for the task, and is applicable to any task, also by non-experts, given example inputs only.
Relation between performance and training data Previous work looking directly into the rela- tion between the training data and the performance is limited. Razeghi et al. (2022) study numeric deduction tasks, and examine the correlations be- tween the model performance on specific test in- stances and the frequency of terms from those in- stances in the pretraining data. They find that the models more accurate instances whose terms more prevalent in the training data. Addition- ally, Han and Tsvetkov (2022) propose method effectively identify a very small subset of pretrain- ing data that directly supports the model in perform- ing specific task. Elazar et al. (2022) use causal inference to measure the effect of pretraining data statistics on factual knowledge performance, and
7.1 Empirical Validation of SPELL
To show the effectiveness our method, we report the results we get using SPELL across the different tasks. In Table 10 we report the average accuracy with the manual prompts compared to the average accuracy with the 3 lowest-perplexity prompts, for both OPT 175B and Bloom. Indeed, in most cases, the average accuracy using the 3 lowest perplex- ity prompts outperforms the average accuracy of the manual prompts, with an average of 1.8 accu- racy points across tasks with OPT and 2.3 accuracy
WWe also calculate the standard deviation when using the same amount of low-perplexity prompts as in the manual prompts set for each task and get averages of 6,32 and 3.78 for OPT 175B and Bloom, respectively.

---

Kandpal et al. (2022) show correlational and causal relationships between aceuracy and relevant docu- ment count (from training data) for QA datasets.
Limitations
Searching for human-readable prompts We limit our search space to human-readable prompts that are fluent and accurately describe the task at hand, as standing why some relevant prompts work better than others. We do this by using manually cre- ated prompts and their automatically created para- phrases. Our findings may not hold when the possi- ble prompt space is expanded to include any token sequence; we leave this direction to future work.
Prompt tuning and analysis There is very rich line of work trying to find prompts automatically, Shin et al. (2020) present an automated method to create discrete prompts for a diverse set of tasks, based on a gradient- guided search, and they demon- strate their method on masked LMs. Other work also focuses on discrete prompts, aiming to im- prove zero-shot performance (Gao et al., 2021; Le Scao and Rush, 2021; Deng al., 2022: Shi et al., 2022), or trains continuous prompts (Li and Liang, 2021; Lester et al., 2021; Qin and Eisner, 2021).
primarily motivated in under-
Generality of our analysis and of the SPELL method We perform our analysis on and build our method around specific models, namely OPT and Bloom. Additionally, our study is limited to the specific tasks we experiment with and to English. It is possible that our analysis and SPELL. method do not generalize to other pretrained models tasks; however, consider models of various sizes and from different sources, and a wide range of tasks to mitigate this risk.
On top of works that suggest a variety of meth- ods for creating better prompts, some work also analyzes those prompts to try and get some insights about them: Khashabi et al. (2022a) find that model performance is highly sensitive to small changes in wordings and Khashabi et al. (2022b) point to surprising disconnect between continuous and discrete prompts.
Acknowledgements
We thank Alisa Liu and Orevaoghene Ahia for their help in annotating noisy prompts. We also thank the reviewers for their valuable comments on the paper.
9 Conclusion
We investigate the phenomenon where some prompts perform better than others despite appear- ing similar to the human users of LMs. Specifically, we hypothesize that the perplexity of prompt un- der a given LM is closely tied to its task perfor- mance. We test this theory on a large number of tasks and autoregressive LMs, and the resulting correlation study validates our hypothesis. Further analysis of this relationship demonstrates that the best prompts differ across models, highlighting the importance of model-specific analysis, and that the underlying structure of the relationship between perplexity and performance varies across tasks.
References
Stephen H. Bach, Victor Sanh, Zheng-Xin Yong, Albert Webson, Colin Raffel, Nihal V. Nayak, Abheesht Sharma, Taewoon Kim, M Saiful Bari, Thibault Fevry, Zaid Alyafcai, Manan Dey, Andrea San- tilli, Zhiqing Sun, Srulik Ben-David, Canwen Xu. Gunjan Chhablani, Han Wang, Jason Alan Fries, Maged S. Al-shaibani, Shanya Sharma, Urmish Thakker, Khalid Almubarak, Xiangru Tang, Xian- gru Tang. Mike Tian-Jian Jiang, and Alexander M. Rush. 2022. Promptsource: An integrated develop- ment environment and repository for natural language prompts.
In light of these findings, we then propose a method, SPELL,, to help users find well- performing prompts for new tasks. Empirical validation of the proposed procedure shows that SPELL generates effective prompts with low vari- ability in performance, and produces small gains of 1.8 (2.3) accuracy points with OPT (Bloom) over manual prompts. We therefore conclude that SPELL provides general and interpretable ap- proach for applying LMs to new tasks while requir- ing minimal human effort, and no labels.
Francesco Barbieri, Jose Camacho-Collados, Luis Espinosa-Anke, and Leonardo Neves. 2020. TweetE- Vnl:Unified Benchmark and Comparative Evaluation Tweet Classification. Proceedings of Findings of EMNLP.
Tom Brown, Benjamin Mann, Nick Ryder, Melanic Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, al. 2020. Language models are few-shot learners. Advances neural information processing systems, 33: 19711

---

Yanda Chen, Chen Zhao. Zhou Yu, Kathleen McKeown, and He He. 2022. On the relation between sensitivity and accuracy in in-context learning. arXiv e-prints, pages arXiv-2209.
Singh, and Yejin Choi 2022b. Prompt wayward- ness: The curious case of discretized interpretation of continuous prompts. In Proceedings of the 2022 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies.
Marta R Costa-jussà, James Cross, Onur Çelebi, Maha Elbayad, Kenneth Heafield, Kevin Heffernan, Elahe Kalbassi, Janice Lam. Daniel Licht, Jean Maillard, al. 2022. No language left behind: Scaling human-centered machine translation. arXiv preprint arXiv:2207.04672.
Teven Le Scao and Alexander Rush. 2021. How many data points is a prompt worth? In Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Hu- man Language Technologies. Association for Com- putational Linguistics.
Johannes Dellert, Thora Daneyko, Alla Münch, Alina Ladygina, Armin Buch, Natalie Clarius, Iia Grigor- jew, Mohamed Balabel, Hizniye Isabella Boga, Za- lina Baysarova, et al. 2019. Northeuralex: wide- coverage lexical database of northern eurasia. Lan- guage Resources and Evaluation, pages 1-29.
Jens Lehmann, Robert Isele, Max Jakob, Anja Jentzsch, Dimitris Kontokostas, Pablo N Mendes, Sebastian Hellmann, Mohamed Morsey, Patrick Van Kleef, Sören Auer, et al. 2015. Dbpedia-a large-scale, mul- tilingual knowledge base extracted from wikipedia. Semantic web, 6(2):167-195.
Mingkai Deng, Jianyu Wang, Cheng-Ping Hsieh, Yihan Wang, Han Guo, Tianmin Shu, Meng Song, Eric P Xing, and Zhiting Hu. 2022. Riprompt: Optimizing discrete text prompts with reinforcement learning. arXiv preprint arXiv:2205. 12548.
Brian Lester, Rami AI-Rfou, and Noah Constant. 2021. The power of scale for parameter-efficient prompt tuning. In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing. pages 3045-3059.
Yanai Blazar, Nora Kassner, Shauli Ravfogel, Amir Feder, Abhilasha Ravichander, Marius Mosbach, Yonatan Belinkov, Hinrich Schütze, and Yoav Gold- berg. 2022. Measuring causal effects of data statis- tics on language model's model'sfactual ppreciccierssos..... arXiv preprint arXiv:2207. 142.51
Xiang Lisa Li and Percy Liang. 2021. Prefix- tunnig: Optimizing continuous prompts for generation. In Proceedings of the 59th Annual Meeting of the Asso- ciation for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers), pages 4582- 4597.
Tianyu Gao, Adam Fisch, and Danqi Chen. 2021. Making pre-trained language models better few-shot learners. In Proceedings of the 59th Annual Meet- ing of the Association for Computational Linguistics and the 1 1ihh International Joint Conference on Natu- ral Language Processing (Volume I: Long Papers), pages 3816-3830.
Alexandra Sasha Luccioni, Sylvain Viguier, and Anne- Laure Ligozat. 2022. Estimating the carbon footprint of bloom, 176b parameter language model. arXiv preprint 2.0000221.00001.
Xiaochuang Han and Yulia Tsvetkov, 2022. Orca: In- terpreting prompted language models via locating supporting data evidence in the ocean of pretraining data. arXiv preprint arXiv:2205. 12600.
Andrew L. Maas, Raymond E. Daly, Peter T. Pham, Dan Huang, Andrew Y. Ng. and Christopher Potts. 201 I. Learning word vectors for sentiment analysis. In Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies, pages 142-150, Portland, Oregon, USA. Association for Computational Lin- guistics.
Ari Holtzman, Peter West, Vered Shwartz, Yejin Choi, and Luke Zettlemoyer. 2021. Surface form competi- tion:
Why the highest probability answer isn't 't always right. In Proceedings of the 2021 Conference on Ea- pirical Methods in Natural Language Processing, pages 7038 1051-7051.
George A Miller. 1995. Wordnet: a lexical database for english. Communications of the ACM, 38(11 (1111))39941) 41.
Nikhil Kandpal, Haikang Deng, Adam Roberts, Eric Wallace, and Colin Raffel. 2022. Large language models struggle to learn long-tail knowledge, arXiv preprint 2rXiv:2211.084111
N. Moniz and L. Torgo. 2018. Multi-source social feed- back of online news feeds. ArXiv, abs/1801.00 180107055.
Guanghui Qin and Jason Eisner. 2021. Learning how to ask: Querying Ims with mixtures of soft prompts. In Proceedings of the 2021 Conference of the North American Chapter of the Association for Computa- tional Linguistics: Human Language Technologies. pages 5203-5212.
Daniel Khashabi, Chitta Baral, Yejin Choi, and Han- naneh Hajishirzi. 2022a. Reframing instructional prompts to gptk's language. In Findings of the As- sociation for Computational Linguistics: ACL 2022, pages 612.
Yasaman Razeghi, Robert I. Logan IV, Matt Gardner, and Sameer Singh. 2022. Impact of pretraining term frequencies on sho-shot reasoning. arXiv preprint arXiv:2202.07206.
Daniel Khashabi, Xinxi Lyu, Sewon Min, Lianhui Qin, Kyle Richardson, Sean Welleck, Hannaneh Ha- jishirzi, Tushar Khot, Ashish Sabharwal, Sameer

---

Elvis Saravia, Hsien-Chi Toby Liu, Yen-Hao Huang. Junlin Wu, and Yi-Shin Chen. 2018. CARER: Con- textualized affect representations for emotion recog- nition. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, pages 3687-3697, Brussels, Belgium. Association for Computational Linguistics.
Timo Schick and Hinrich Schütze. 2020. It's not just size that matters: Small language models are also few-shot leamnrrs arXiv preprint ar 2009::2000
Weijia Shi, Xiaochuang Han, Hila Gonen, Ari Holtzman, Yulia Tsvetkov, and Luke Zettlemoyer. 2022. Toward human readable prompt tuning: Kubrick's s the shining is good movie, and good prompt too? arXiv preprint arXiv:2212.15339
Taylor Shin, Yasaman Razeghi, Robert L. Logan IV, Eric Wallace, and Sameer Singh. 2020. Autoprompt: Eliciting knowledge from language models with automatically generated prompts. arXiv preprint arXiv:2010. 15980.
Alex Warstadt, Amanpreet Singh, and Samuel R Bow- 2018. Neural network acceptability judgments. arXiv preprint arXiv: 12471.
John Wieting, Jonathan Mallinson, and Kevin Gimpel. 2017. Learning paraphrastic sentence embeddings from back- translated bitext. In Proceedings the 2017 Conference on Empirical Methods in Natural Language Processing, pages 274-285.
Susan Zhang, Stephen Roller, Naman Goyal, Mikel Artetxe, Moya Chen, Shuohui Chen, Christopher De- wan, Mona Diab, Xian Li, Xi Victoria Lin, et al. 2022, Opt: Open pre-trained transformer language models. arXiv preprint arXiv:2205.01668
Xiang Zhang, Junbo Jake Zhao, and Yann LeCun. 2015. Character-lever convolutional networks for text clas- sification. In NIPS.
A Manually Created Prompts
Table lists the manually created prompts we use for the different tasks. We manually add, remove and edit prompts for some these tasks, to make them fit for our setting. For example, the following prompt for AG News, taken from Promptsource. does not fit our setting: Would you recommend the following article to a politician, athlete, busi- ness executive, or a scientist?
Lowest Perplexity Prompts
Table 12 lists the 5 lowest perplexity prompts for each task, using OPT 175B.

---

Task
Manual Prompts
The antonym of the word "good" is"
The opposite meaning the word "good"
"Good" the opposite
"Good" is the negation of"
The following are opposites of each other: "good" and "goad" contradicts The antonym of the word good
word
Antonyms
The opposite meaning of the word good is the opposite Good the negation of
The following opposites of each other: good and The word good contradicts the word
Does this sentence make sense and use correct English?
Is this example grammotically correct and sensible?
GLUB Cola
Does this sentence make sense and is it grammatically corret?
Does this example use correct English?
What is the article about?
What this about?
What is the topie this news piece?
What does article discuss?
topic
sentence?
What category does the article belong to?
Newspop
Pick one category for this news piece. fits the text. The article refers which category? ?
Pick the calegory
What topic does the article helong to?
What category fits this article?
news piece helong Choose the correct category for this article.
topic
What lahel best descrihes this news article? likely uppear in?
What is this piece of news regarding?
AG News
Which newspaper
would
What topic this article about?
This movic review expresses what sentiment?
Did the reviower find this movie good or bad? Is review positive negative?
How does the viewer feel about the movie?
What sentiment does the writer express for the movie?
IMDB
What sentiment is expressed for the movie?
sentiment expressed Did the reviewer enjoy the movie?
text?
What is the sontiment expressed by the reviewer for the movie?
How does the reviewer about the movic?
category
paragraph belong
Pick one category for the text.
Pick the calegory that fits the texl.
refers which category?
DBpedia
What category does the title belong to?
What category fits this text!
What topic does text belong to?
Choose
category
What the emotion expressed this message?
What emotion does this message express?
Emotion
How will you feel about the message? emotion does the
express for message?
Is this tweet offensive?
Can the tweet be removed for heing offensive?
Tweet Offensive
Is the author's 's tweet offensive?
Identify Is this offeusive tweet?
offensive.
The translation of the word "dog" to French is The translation of the word dog to French is "dog" French
"dog" (In French:
Translate the ward dog into French:
The translation of dog to French
Word Level Translation
"dug" (French..
The word dog in French is Translate the word "dag" into French: dog
dog (French:
The translation of "dog" to French is
Table 11: The set of manually created prompts for each task.

---

Task
Lowest Perplexity Prompts
Perplexity
The following words antonyms: "good" and
10.24
The antonym the word "good"
10.32
Antonyms
The word that has the opposite meaning of the word "good" is The word "good" is the antithesis of the word
10.43
10.85
The "good" is opposite
word
11.15
Is this example of the proper use of the English language? Does sentence make sense does follow the rules of grammar? Is this sentence an example of the correct use of the English language? Does this sentence make sense and it grammatically correct? Is this
11.63
11.76
GLUE Cola
12.10
12.15
grammatically correct and does make sense?
12.68
What is the main subject of the article?
10.01
What the main topic of the article?
10.01
Newspop
What is the subject matter the article?
10.17
What is the subject of the article?
10.21
What is the main idea of this article?
10.21
In what section of the newspaper would you expect to find this article? In which section of the newspaper would you expect find this article?
7.51
7.52
News
In which section In what section of the newspaper do you expect to find this article? In what section of the newspuper would this article most likely appear?
newspaper would this article be most likely appear?
7.80
7.87
What is the opinion of the review? Is positive or negative? Is this positive or negative review? What you think the movie? What you think the film? Is that positive or negative?
7.19
7.31
IMDB
7.33
7.35
7.35
What is the category which the text refers?
8.99
What is the subject of the text?
9.15
DBpedia
What category does the title belong to?
9.18
Which category does
refer
9.19
What is the subject of this text?
9.20
How do you feel when you hear message?
12.72
What is the writer's emotional reaction to this news?
13.18
Emotion
What is the emotion expressed in this message?
13.20
How does this message make you fee!?
13.32
How do you feel about this message?
13.50
If somcone said this you, would you be offended? If someone that to you, would you be offended?
13.00
13.10
Tweet Offensive
Would you be offended if someone said that to you? Would offend you if someone said that you? someone you that, would you offended?
13.73
14.79
14.93
The word for "dog" in French is The French word "dog" is
7.73
8.16
Word-Level Translation
The French translation of the word "dog" is The translation of the word "dog" in French is The translation of the word "dog" French is
8.24
8.35
8.91
Table 12; The lowest perplexity prompts for each task, using OPT 175B.


Reviews:
[{"review_id": "IRDlCkQGT3", "reviewer": "Reviewer_ZmV4", "summary": "", "questions": "", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks a lot for your positive feedback!\n\n1. Correlations of classification tasks vs. word-level translation: \nIndeed, the correlations we get for the word-level translation task tend to be higher. Note however that this is true also for the antonyms task, which is not multilingual. We do not attribute the gap to the multilinguality of the translation task, but to the nature of it - both the word level translation and the antonyms tasks are somewhat easier for a language model (in that they are word predictions and therefore closer to the objective of an LM), and we believe that this is what’s causing the correlations to be stronger for this type of task.\n\n2. Performance with smaller models: \nWe agree that smaller models struggle with the tasks we experiment with, and it’s a known fact that larger models do much better in general, and specifically in zero-shot settings. We expect the 175B models to be more reliable for our set of experiments, and we added the smaller models mainly as a sanity check for lower scale as well.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "1. The proposed perplexity estimation approach demonstrates wide applicability in reducing the variance of zero-shot learning performance, particularly in multilingual tasks, as evidenced by the strong correlation between perplexity estimation scores and task performance.\n2. The authors introduced a framework that enables automatic rephrasing and adjustment of the seed prompt to enhance compatibility with language models, resulting in improved performance.\n3. Through the authors' perplexity estimation method, it is revealed that certain prompts, despite having similar semantics and appearing acceptable to humans, can lead to poor performance. These prompts can be identified using the perplexity estimation approach, providing valuable insights for prompt learning debugging without reliance on external knowledge.", "reasons_to_reject": "1. While the authors assert that perplexity estimation has the potential for broad application across various tasks, its significance is primarily evident in multilingual tasks. However, the correlation in classification tasks provides less support for this hypothesis.\n\n2. The authors concentrate on zero-shot settings across all tasks, which can pose challenges for smaller language models (such as 1.3B and 30B models) in specific tasks like CoLA and Tweet Offensive. Notably, in these challenging tasks, the performance and correlation may not exhibit a consistent pattern, indicating potential limitations of perplexity estimation.", "questions_to_authors": "", "paper_topic_and_main_contributions": "The sensitivity of prompt-based learning to varying templates often results in a wide range of performance levels. This study seeks to understand why certain prompts outperform others by examining the concept of \"familiarity\". The authors use perplexity estimation to express this concept, ultimately finding that prompts with lower perplexity tend to yield better results. To build upon this discovery, they introduce a methodology for automatically adjusting the initial prompt template, and subsequently choose the most efficient template using perplexity estimation. Through empirical testing and evaluation, it is demonstrated that this approach of perplexity estimation is straightforward yet potent for enhancing zero-shot learning performance.", "excitement": 4, "reproducibility": 5, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "UF1jFJHpAd", "reviewer": "Reviewer_feBz", "summary": "", "questions": "* Question A: How do you prove it is perplexity but not other factors that influence the performance? In Table 1, it seems that the best prompt describes the task target the most precisely. What if we construct some prompts with higher perplexities but containing more accurate task descriptions? Let us say: Among all prompts that obtain high perplexity, we manually choose the ones that give accurate task descriptions. How do they perform on downstream tasks then?\n\n* Question B: For classification tasks, did you explicitly provide label words? How do you choose label words then?", "limitations": "", "rating": 3, "confidence": 3, "soundness": 4, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks a lot for your positive feedback!\n\n1. Other possible factors (QA): \nOur main finding is that perplexity is a predictive signal for the quality of a prompt (rather than a causal factor). We definitely agree that there are other potential factors that likely affect the success of prompts, and that perplexity does not explain all of the variability we see among different prompts. Here we focus specifically on perplexity, and as we show experimentally across 9 tasks and 4 models, it is an important predictive factor and is strongly correlated with the performance of the prompt.\nAs for testing the effect of prompt relevance: we only consider prompts that are presumably related to the task (hand written), and those that are paraphrased out of them. The more fine-grained definition of relevance suggested may affect performance, but these distinctions are subjective and difficult to quantify. \n\n2. Variety of tasks: \nIn this paper we try, for the first time, to explore the correlation between the perplexity of the prompt and its performance. When designing the experiments, we wanted to keep the setting basic, in order to not introduce confounding factors into our analysis. Using a zero-shot setting, with somewhat shorter prompts and a well defined set of tasks, helped us achieve this goal. Nonetheless, we do experiment with 4 different models across 9 different tasks.\n\n3. SPELL: \nAs stated in the paper, we want to highlight again that while we believe that the SPELL method is a simple and effective one for getting improved performance by generating and choosing better prompts, this is not the main contribution of our work. Our key findings are the analysis of the differences between different prompts, and our new characterization of what makes a good prompt. This analysis allows us to establish correlations of the effectiveness of a prompt with its perplexity, which in turn allows us to introduce a simple new method to find better prompts. Additionally, an important outcome of SPELL is not only improved performance but also prompts that are less variable in their performance.\n\nQB: \nwe do provide label words in the prompt - we simply list the possible answers as defined by the dataset itself (e.g. Sports, Science and technology, World politics, Business for the dataset of ag_news). We will make this clearer in the paper.\n\nWe will make changes to Tab 1 and Fig 2 as suggested, thank you!", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "* This work presents an analysis of the correlation between LM's perplexity with prompts and downstream performances. The analysis has some merits for future research.\n\n* The proposed SPELL shows performance gains on some datasets, especially for Newspop (+10 accuracy points across two LMs).", "reasons_to_reject": "* The problem setting is not well-established. As this paper focuses on perplexity, there are other factors other than perplexity that could influence downstream performances. These factors should also be discussed in the paper; otherwise, the authors cannot ensure that it is perplexity really matters. More details are in Question A in the next section.\n\n* This paper conduct experiments on word translation and text classification. The two tasks somehow have limited coverage. It would be better if more tasks could be adopted, especially some more complex tasks like planning and reasoning. With more complex tasks, the differences among prompts would be more significant, providing more generalizable experimental conclusions.\n\n* The performance gains of SPELL are not consistent across datasets and LMs, raising concern about whether the proposed method could work in a broader scope.", "questions_to_authors": "* Question A: How do you prove it is perplexity but not other factors that influence the performance? In Table 1, it seems that the best prompt describes the task target the most precisely. What if we construct some prompts with higher perplexities but containing more accurate task descriptions? Let us say: Among all prompts that obtain high perplexity, we manually choose the ones that give accurate task descriptions. How do they perform on downstream tasks then?\n\n* Question B: For classification tasks, did you explicitly provide label words? How do you choose label words then?", "paper_topic_and_main_contributions": "1. This paper investigates the research question that why some prompts perform better than others. The authors hypothesize that the performance of a prompt is negatively correlated with LM's perplexity on that prompt. \n\n2. To verify the above hypothesis, the authors design experiments with GPT-3, BLOOM, and OPT on word translation and text classification tasks. Experimental results show that negative correlations do exist.\n\n3. Based on the preliminary experiments, the authors propose SPELL, which generate-then-rerank prompts according to perplexity. Experimental results show that the proposed method sometimes outperforms the manual prompt baseline.", "excitement": 3, "reproducibility": 4, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"Typos_Grammar_Style_and_Presentation_Improvements": "Presentation Improvements:\n  * Table 1 and Figure 2, would be better if on top of the page."}, "extra_text": {}}, {"review_id": "gtbPX4YJmm", "reviewer": "Reviewer_nmvT", "summary": "", "questions": "- While I assumed that correlations with score could be more significant compared to correlations with accuracy (but in the same direction), this seems not to be the case in Table 3. Can you provide more explanation and comparison between the two?\n- The overall accuracy of the models on the tasks chosen is quite low. I wonder how much of these results extend to models fine-tuned with instructions, which seems to be the de-facto standard these days, do the authors have any opinion on this?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 4, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks a lot for your positive feedback!\n\n1. Relevance of the prompt: \nNote that the space of prompts we are dealing with has only prompts that are presumably related to the task (hand written), and those that are paraphrased out of them. So except for noise, with which we also deal later - all prompts are relevant to the task. A more fine grained definition of relevance could be explored here, but these distinctions are subjective and difficult to quantify. We do believe that other factors than perplexity can be predictive of the variability among prompts.\n\n2. Variability in accuracy: \nThanks for raising this point. We did see consistently good performance also among 5 and 10 lowest-ppl prompts (not only 3). To make sure that the samples are of the same size, we will choose the same amount of prompts for each task and add those results to the final version as well. \n\n3. Emotion task: \nWe believe that when the delta is negative, it is due to hand written prompts that happened to work well. This is directly related to one of the points we make in the paper: with hand-written prompts we are not always guaranteed to get good performance, and whether this is the case for a particular prompt is very difficult to predict from the text of the prompt. \n\nQA:\nCorrelation with accuracy vs score: Indeed, there is no clear “winner” between the two, though both show consistent correlations with the performance. A possible explanation for the difference could be the variability of the scores of the different labels, for example: if the scores vary a lot, you could get a weaker correlation even if the rankings are relatively good (high accuracy). This may also be related to the inherent difference between the two metrics, accuracy being brittle and discrete vs. LM scores that are continuous. We see this as a very interesting point for future work. \n \nQB:\nInstruction-tuned models: We agree that extending our experiments to instruction-tuned models would be very interesting! We expect to see similar trends there as well, but it’s an empirical question.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "- Understanding why some prompts might work better than others and finding systematic ways to find better prompts is in fact a very important research direction, especially since prompting (in-context learning) is becoming the de-facto standard for adapting LMs to downstream tasks. This paper addresses exactly this research question.\n- The experiments and analysis are carefully designed while controlling for confounders. \n- The paper is generally well-written and easily understandable.", "reasons_to_reject": "- From line 126 onwards, the authors state that lower perplexity correlated with better performance. A possible confounder here could be the relevance of the prompts. While in section 6.2 the authors investigate the effect of noisy prompts, I wonder if the relevance of the prompts to the task can be factored in systematically earlier in experiments in section 5 (like Table 3 results).\n- Lines 480-482 compare the variability in accuracy between the two settings, however, the number of prompts assessed in these two settings are not equal, doesn't it introduce some bias?\n- In Table 8, for the Emotion task, we see that the delta is negative, this is true while in Table 3 and for the same OPT model and Emotion task, the correlation was negative. I wonder how this could be the case.", "questions_to_authors": "- While I assumed that correlations with score could be more significant compared to correlations with accuracy (but in the same direction), this seems not to be the case in Table 3. Can you provide more explanation and comparison between the two?\n- The overall accuracy of the models on the tasks chosen is quite low. I wonder how much of these results extend to models fine-tuned with instructions, which seems to be the de-facto standard these days, do the authors have any opinion on this?", "paper_topic_and_main_contributions": "This paper puts the following hypothesis to the test: the performance of a prompt is predicted by the extent to which the model is familiar with the language it contains. The authors use perplexity as the proxy measure of familiarity of the LM with the prompt language. Based on the empirical findings, lower perplexity does correlate with better performance. Furthermore, the authors use this insight to propose a prompt selection method based on the perplexity measure. ", "excitement": 4, "reproducibility": 4, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: This work proposes and investigates the hypothesis that the likelihood assigned by a language model to a task-specifying prompt is a useful predictor of the performance of that model on the task that the prompt specifies, such that among intuitively similar prompts, one can/should pick the highest-likelihood prompt under the model to maximize performance in expectation. The reviewers were overall positive, despite some concerns about the scope of experiments (no instruction tuned / RLHF’d models) as well as uncertainty about how far the hypothesis can hold true (as perplexity alone certainly isn’t the only factor.) Overall, it seems that the claims of the authors are interesting enough and backed up enough by their experiments for a good empirical takeaway.

The reviewers collectively had concerns as to the seemingly causal claims, or at least rather strong correlational claims, that lower prompt perplexity implies better few-shot performance, whereas certainly this is only true within a certain (even if just intuitive) bound of task-relevance or task-descriptive quality; one can likely always find prompts with increasingly high probability under the model with increasingly little to do of the task of interest, which would not work. This is an important nuance that I encourage the authors to engage more seriously with, starting in the abstract. Another related nuance that deserves mention is that this work deals exclusively with the perplexity of the prompt under the model of interest, which is related to the particularities of how the model has learned (or failed to learn) and is distinct, e.g., from the “true” probability/perplexity of the prompt under the training distribution (which is mentioned in the motivation).

Thanks for doing Bonferroni correction, authors!
Decision: Accept-Findings