From: ICLR.cc/2023/Conference/Paper3567/Authors
title: Submission Withdrawn by the Authors

From: ICLR.cc/2023/Conference/Paper3567/Authors
title: On conclusions from our work
comment: Thank you for sharing your assessment and confirming the helpfulness of our rebuttal in clarifying the main points of our paper. We value all the reviewers’ comments and we believe that the rebuttal and the revised version of the paper address their concerns about clarity and potential for follow-up work. As we are in the midst of Discussion Stage 2 until December 12, if there are any remaining questions and comments, we’d be happy to address them. 

We would like to underscore that our conclusions are not solely based on empirical evidence. Instead, we provide detailed qualitative analyses for each dataset. Instead of merely stating “role of patterns is task-dependent”, we identify *the underlying causes for each observation*. For example, the patterns do not matter for maths and date reasoning **because** the task is clear even with wrong patterns in the prompt. That is not the case with SPORTS, in which wrong patterns change the reasoning construction.

From: ICLR.cc/2023/Conference/Paper3567/Reviewer_bAnm
title: Grateful for additional clarifications
comment: I appreciate all the additional clarifications and work the authors have provided - in particular "General Response (4/5)" was helpful.
Reading the co-reviewers opinion strengthen my double opinion that:

- the author are onto something potentially important on what makes prompts infuential
- the conclusions are presented in a confusing way and are not crisp enough to help other researchers to build upon

This last point is probably most striking with "Patterns", whose definition is task dependent and whose impact on the performance varies widly.

From: ICLR.cc/2023/Conference/Paper3567/Authors
title: Thanks for your feedback (2/3) 
comment: ### Definition of Patterns in SPORTS and No-Pattern Prompting

We apologize for any confusion about patterns in SPORTS. In the following, we clarify the definition of pattern in SPORTS and provide a rationale for No-Pattern prompting for this dataset.

- **(a) Patterns in SPORTS** We clarified the definition of the prompt components in the [General Response](https://openreview.net/forum?id=z9fXRC5XdT&noteId=3VU69Gx-MaC). The patterns in SPORTS are *not* `is`. As you mentioned in your review, the progression of information (sentence structure) in SPORTS is the pattern.

- **(b) No-Pattern Counterfactual Prompting** The premise of CoT prompting is as follows: given multiple input examples (e.g., 8 in SPORTS) with *similarly repeated* structures in the form of (Question, Thought, Answer) followed by an unanswered question, the model follows the provided structure in the prompts and generates the answer with a similar structure as prompts in the form of (Thought, Answer). Please refer to **Rev-Table-40-Page-67**, which shows the prompts used in [Chain of Thought Prompting Elicits Reasoning in Large Language Models](https://arxiv.org/abs/2201.11903). 

*Merely partially removing patterns is not sufficient* because if all the prompts have the same structure with partial patterns, the model may still be able to rely on these *similarly repeated* partial patterns to conclude an answer. This is not our objective in No-Pattern counterfactual prompting. Our approach instead is to break the *similarly repeated* patterns in the prompts. The rationale behind this approach is that the model can no longer rely on these *repeated patterns* to reach an answer. As such, we assemble different patterns (e.g., no fixed patterns) to simulate a No-Pattern counterfactual prompting (See **Rev-Table-63-Page-93** for the list of prompts used in no-pattern prompting). Consider the following two CoTp for SPORTS: the first is used in the standard CoT, and the second is our proposed No-Pattern CoTp. As you can see, the first one has a *fixed sentence structure* repeated across the thoughts. They are in the form of  `PERSON belongs to SPORT` followed by `ACTIVITY is SPORT`. This consistent sentence structure is the pattern in the prompt. 


| **Standard CoTp with fixed sentence structure**                                                                                             |  | |
|-------|--------|--------|
| Question                                                                                             | Thought                                                                                         | Answer |
| Is the following sentence plausible? “Jamal Murray was perfect from the line.”                       | Jamal Murray is a basketball player. Being perfect from the line is part of basketball          | Yes    |
| Is the following sentence plausible? “Joao Moutinho caught the screen pass in the NFC championship.” | Joao Moutinho is a soccer player. The NFC championship is part of American football, not soccer | No     |
| Is the following sentence plausible? “Jonas Valanciunas beat the buzzer.”                            | Jonas Valanciunas is a basketball player. Beating the buzzer is part of basketball.             | Yes    |
| ...                                                                                                  | ...                                                                                             | ...    |
---

Alternatively, we can include the *same information* but phrase it differently with the goal of breaking the consistent sentence structure. The following table shows some inputs for No-Pattern CoTp. In this case, we remove the consistent sentence structure. We use the same strategy in crafting No-Pattern CoTp for other datasets. For example, **Rev-Table-62-Page-92** shows the inputs for No-Pattern CoTp for DATE.

| **No-Pattern CoTp with variable sentence structure (no repeated patterns)**                                                                                             |      | |
|-------|-----|----|
| Question     | Thought      | Answer |
| Is the following sentence plausible? “Jamal Murray was perfect from the line.”                       | Jamal Murray is a basketball player. Being perfect from the line is part of basketball          | Yes    |
| Is the following sentence plausible? “Joao Moutinho caught the screen pass in the NFC championship.” | Joao Moutinho and the NFC championship are not both part of American football. | No     |
| Is the following sentence plausible? “Jonas Valanciunas beat the buzzer.”                            | Beating the buzzer, Jonas Valanciunas, and basketball player are related.         | Yes    |
| ...                                                                                                  | ...                                                                                             | ...    |

From: ICLR.cc/2023/Conference/Paper3567/Authors
title: Thanks for your feedback (3/3) 
comment: ---

### Lower-Level Comments

**Text/Reference Format**

We fixed the issue on Page 3 with the content running into the margin. We just added a url for each reference to facilitate accessing the references for the readers. We are happy to unlink the references if that is what the reviewer is referring to.

---

**Related Work**

We apologize for the brevity of the related work in the main body. We have a detailed version of related work on **Page-20-21**. For clarity, we also included a pointer to the appendix for additional discussion at the beginning of the **Related Work** section.

---

**Figures/Attention Map**

We apologize for any inconvenience in viewing the figures. For **Figure-1**, we only wanted to emphasize the similar pattern between the two variants of CoT prompting. At the same time, the actual location of higher/lower attention scores is less relevant in this work.

---

**Number of Pages**

We included a table of contents in the appendix to make it clearer for the readers to find relevant information. All the content after **Page-67** is just the prompts we used in the paper for reproducibility. Our initial thought was that including all the prompts with proper referencing in the main body of the paper would make it easier for the readers to draw conclusions about them. We can move these prompts to GitHub in the final version to make the content more condensed.

From: ICLR.cc/2023/Conference/Paper3567/Authors
title: Thanks for your feedback (1/3)
comment: ### Choice of Components in Prompts

We apologize for the misunderstanding. To specifically answer your comment about $\mathrm{\textcolor{green}{Patterns}}$ in GSM, we would like to clarify that $\mathrm{\textcolor{green}{Patterns}}$ is *not* only at the end of the prompt. Any mathematical expression that modifies the symbols resides in this category. We clarified this in the [General Response](https://openreview.net/forum?id=z9fXRC5XdT&noteId=3VU69Gx-MaC). For example, the following table indicates that patterns may be present at different locations in a prompt.

| Thought   | $\mathrm{\textcolor{green}{Patterns}}$    |
|------|----|
| Emma  can  make  72  vlogs  per month.  She made 18 vlogs for the first week, 21 vlogs for the second week, and 15 vlogs for the third week. So she made 18 + 21 + 15 = 54 vlogs. 72 - 54 = 18. | $\mathrm{\textcolor{green}{18 + 21 + 15 = 54}}$ and $\mathrm{\textcolor{green}{72 - 54 = 18}}$ |
---

### Importance of Text and Patterns

The importance of the correctness of patterns and text is *task-dependent*. For GSM and DATE, wrong patterns do not hurt performance. Please refer to the [General Response (4/5) - Summary of Key Findings](https://openreview.net/forum?id=z9fXRC5XdT&noteId=M44WsAHFgj7) for details.

---

### Contributions of Patterns/Text to the Structure of Prompts

Patterns do not necessarily make up the majority of the structure of the prompt. For example, in GSM patterns are only the equations and mathematical expressions which are *not* the majority of prompts.

---

### Role of Patterns and Text in Prompts

Patterns and text have a complementary role in a prompt. For example, patterns in the SPORTS dataset are a way of structuring and communicating knowledge to the model. Therefore, even if we significantly manipulate the structure of a prompt (**Rev-Table-3-Page-6-Pattern-Only**), CoT performs reasonably well as long as we preserve the key information (74.13%). Furthermore, Pattern-Only prompting outperforms Pattern-Wrong prompting (74.13% vs. 46.02%) even though the former substantially changes the structure of the prompt.

These results show that the amount of changes to prompts/texts is not the **only** factor in determining the success of CoT. It is about identifying and discerning the role of each component in a prompt. 

Finally, we have supplemented these empirical findings with case analysis. We will be happy to share additional outputs and examples if required.

| Thought | Solve Rate |
|--------|--------------------------|
| **Pattern-Only** $\mapsto$ `Both are part of the same sport.`                                                 | 74.13% ($\Delta +28.11$) |
| **Pattern-Wrong** $\mapsto$ `Jamal Murray is a soccer player. Being perfect from the line is part of soccer.` | 46.02%  |

---

### Structure of Prompts in SPORTS

We agree with the reviewer’s observations about the importance of the sequence of information in the SPORTS dataset, and this is precisely what we define as patterns in this dataset. However, we would like to emphasize that each component has a unique role in different tasks, and there is no one-fit-all definition for $\mathrm{\textcolor{blue}{Symbols}}$/$\mathrm{\textcolor{green}{Patterns}}$/$\mathrm{\textcolor{black}{Text}}$ across all datasets. Instead, we chose a diverse set of tasks for which a clear and interesting distinction of these components is possible. We discussed this in detail in [General Response](https://openreview.net/forum?id=z9fXRC5XdT&noteId=3VU69Gx-MaC).

---

### Summary of Appendix

In our work, we found that every task reveals unique insights about CoT and prompting. Unfortunately, the empirical results are insufficient to always relay the necessary information, so we include a comprehensive qualitative analysis in the Appendix. Nevertheless, space constraints urged us to move some interesting insights to Appendix. We want to highlight a few of them that may be of interest to the reviewers:

 - **Rev-Tables-8-11-Page-29-30 (Appendix-F-1-Results on Codex, GPT-3, PALM-540B)**: Trends hold across all models. While we focus on PaLM-62B in the main draft, we conduct additional experiments on publicly available models  (GPT-3, CODEX) for reproducibility and find similar trends for all counterfactual prompts.


 - **Rev-Table-32-Page-60-63 (Appendix-J-2-Common Sense Extraction)**: 
We find that the average popularity (# google search results) of activities for which CoT exclusively yields correct answers is lower (52$\times$) compared to the ones for which the Pattern Only CoT exclusively lands correct answers. We conjecture that the well-formed structure of thoughts in SPORTS empowers the model to extract common sense knowledge about `<Activity>`, even when the activities are infrequently seen during training.

From: ICLR.cc/2023/Conference/Paper3567/Authors
title: Thanks for your feedback
comment: **Definition of Components in Prompts**

We have clarified these definitions in the [General Response](https://openreview.net/forum?id=z9fXRC5XdT&noteId=3VU69Gx-MaC). We hope it clarifies things, and we are looking forward to an engaging conversation with you.

**Per-Task Results**

The only common thread in our work is that $\mathrm{\textcolor{blue}{Symbols}}$ and $\mathrm{\textcolor{green}{Patterns}}$ have a complementary role in the success of CoTp. The exact impact they have is indeed *task-dependent*. Please refer to the [General Response (3/5)-Is it possible that there can be other definitions of these components?](https://openreview.net/forum?id=z9fXRC5XdT&noteId=9UAmUgFIEi) for additional context. Further, we have attempted to supplement all empirical findings with qualitative examples and case analysis. We will be happy to share additional outputs and examples if required.

**How does CCoT work?**

We have clarified the methodology for creating CCoT prompts in the [General Response (5/5)-CCoT Prompting](https://openreview.net/forum?id=z9fXRC5XdT&noteId=vynQDdvrBNc). Briefly, our findings demonstrate the unique role that text and patterns play for each dataset.

**Section 2 clarity/Direct vs. CoT/pat_wrong results in the Table**

We have clarified content in **Section 2**, and have addressed comments regarding direct vs. CoT labels and pat_wrong results in the revision.

From: ICLR.cc/2023/Conference/Paper3567/Authors
title: Thanks for your feedback
comment: **Constructing CCoT**

CCoT is not the main contribution of our paper. It is merely a case study to show how a better understanding of CoTp could help us to build effective prompts by only keeping the consequential components. Please refer to the [General Response (5/5)](https://openreview.net/forum?id=z9fXRC5XdT&noteId=vynQDdvrBNc) for additional details.


**Non-conclusive Results on Patterns and Text**

As noted by the reviewer, the results for the role of Patterns and Text are indeed *task-dependent*. This work does not aim to make any universal conclusions about the importance of each of these components across all the possible tasks. For example, compared to no patterns prompting, prompting with wrong patterns degrades model accuracy significantly (79.01% $\mapsto$ 46.02%) in SPORTS, whereas in GSM, wrong patterns prompting has no adverse impact on model performance (21.46% $\mapsto$ 24.39%). These results indicate that the contribution of each component to the success of CoT is heavily task-dependent. In our analysis, we have attempted to go beyond empirical numbers and supply each number with qualitative analysis. 

Please refer to the [General Response (3/5)-Is it possible that there can be other definitions of these components?](https://openreview.net/forum?id=z9fXRC5XdT&noteId=9UAmUgFIEi) for additional context. 


**Model Architecture**

We apologize for the confusion about the statement on model architecture. We have revised the text in **Section-2-Page-2**.

**Hypothesis Box**

Per the reviewer's suggestion, we dropped the hypothesis box.


### Style and ICLR Template

**Table Captions**

We have updated the style of captions (not **bold** anymore). However, based on the ICLR formatting guideline, the captions of tables are permitted to be at the top.

From: ICLR.cc/2023/Conference/Paper3567/Reviewer_bAnm
confidence: 3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
summary_of_the_paper: This paper relates to the analysis of "Chain of Thought" (CoT) to prompt Larege Language Models.
Its proposes to dissect a prompt into 3 parts: symbols, patterns and text; and to analyze the relative impact of each part in the final result. Based on those findings, the authors then propose a more compressed version of chain of thoughts which requires less number of tokens
strength_and_weaknesses: STRENGTH:
- CoT is still very poorly understood, but behind lots of excitement in the domain (arguably, the most hype aspect of LLM, which arguably is the most hype area of NLP or even ML). Any analysis into that is welcome and timely. In particular, this papers questions the real importance of the content of the prompt, in a similar vein than [1] did for in-context learning. 
- The results of the (non) importance of numbers is striking, and will certainly spurn follow-up work
- compression Chain of Thoughts is a very useful technique to leverage LLM as they are today: beyond their energy consumption, that reduction could allow to provide more input into the fixed-size window

WEAKNESS
- Clarity: it is not clear at all how CCOT are actually obtained, and the results on that are very scarce. I appreciate the lack of space, but if this is a separate idea it might merit a separate paper.
- The results on text and pattern are non-conclusive (dependent on the dataset) and hard to distangle. In words of the authors "texts and patterns are intertwined". This makes one of the main contributions (the dissection of possible influencers into 3 groups) less striking.

- On writing: it is a bit grandiose by times, although this might be just me. However, the following parts might need some re-writing
> "Nonetheless, we do not make any assumptions about the underlying model architecture"
Not really. Those are all Transformer architecture that the authors benchmark

The Hypothesis boxes appear to be there to give the paper (more) aura of scientific credibility (which it does not need, imo). However, they do not seem to be framed before the experimental study (otherwise this would contradict the often-used phrase of "surprising" and "counterintuitive"), and the wording is quite ambiguous. I would recommend to either drop those altogether, and replace them with "Key Finding" or similar; or at least make the wording more concrete.

Also, on style: caption of tables should be below the table itself I believe, and certainly not bold (the type-setting of the paper is quite dense as it is).



[1] Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?
https://arxiv.org/abs/2202.12837
clarity,_quality,_novelty_and_reproducibility: Clarity; as mentioned, this is rather low

Quality: the claims with respect to and work around smybols will be impactful; the ones on text & pattern less so. Unfortunately, there is not enough information to assess the importance on the compression

Novelty: new

Reprodubility: the main results are reported on PLAM (irreproducible), but the authors also benchmarked GPT3 and Codex
summary_of_the_review: Interesting insights in the (non-) importance of sybmols for chain-of-thought. Less clear results on other aspects.
correctness: 2: Several of the paper’s claims are incorrect or not well-supported.
technical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
empirical_novelty_and_significance: 4: The contributions are significant, and do not exist in prior works.
flag_for_ethics_review: NO.
recommendation: 5: marginally below the acceptance threshold

From: ICLR.cc/2023/Conference/Paper3567/Reviewer_7wQJ
confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
summary_of_the_paper: This paper presents an analysis of various manipulations on prompts to try to understand the conditions under which chain of thought prompting is effective.  It also presents a technique for 'concise chain of thought' that uses fewer prompt tokens and actually performs quite a bit better than standard chain of thought.
strength_and_weaknesses: Strengths

This paper explores an interesting problem space and performs evaluations with a number of models, and includes an extensive appendix with details.  Many of the individual experimental measurements are interesting and give some insight into how CoT works.

Weaknesses

This paper is hampered by being very unclear, and I also felt like the components (text, patterns, symbols) of the analysis were ill-defined, and while the individual experimental results were interesting in some cases, the paper needs more work to tie those measurements together into a coherent story.

I still don’t really understand the differences between the symbol, pattern, and text components of the analysis.  The definitions in Section 3.1, and some of the examples like the textual phrase “being perfect from the line” being a *symbol* in the analysis or the statement “person is a sport,” I was not really able to comprehend.  I would not be able to determine which parts of a prompt in some other problem should be deemed patterns, symbols, or text as in this paper.  I think there might be some important and meaningful distinctions the authors are drawing here, but they were not explained sufficiently for me to understand them.

Then, some of the results send a mixed message about the importance of some of the components.  For example, I would characterize the conclusions in Table 2 as inconclusive.  Symb_ood for sports and symb_abs for date do drop performance of CoT significantly.  Given this and the fact that the conclusions are stated in terms of components (text, symbols, patterns) whose meaning I don't actually understand, it is hard for me to draw general insights from the experiments.  The individual experiments themselves (e.g. replacing dates with the word DATE and seeing how well CoT works) are interesting, but the more general conclusions (e.g. symbiotic relationship between text and patterns argued at the end of the paper) were not understandable to me.

Finally, while the results in Table 5 actually seem to be fairly strong compared to the CoT prior art, how the concise prompts worked or how they draw from the analysis earlier in the paper was never explained.  So ultimately that contribution is hard to evaluate.
clarity,_quality,_novelty_and_reproducibility: The clarity of the paper has substantial room for improvement.  The intro of the paper is hard to understand and needs to be more explicit and transparent.  The intro does not make it clear what the paper is about—it says it is aimed at understanding “why, when, and how” CoT operates, but this is very vague and it is not clear what specific questions this paper will answer.  The intro also states its results in terms of “symbols, patterns, and text,” but doesn’t define those things (except to say that symbols can be numbers or greek symbols), so it is hard for us to understand what the paper is about (what’s the difference between patterns and text, is what I wondered here—it was impossible for me to appreciate the conclusions of the paper with these terms being undefined throughout the intro).
 
Section 2 starts by introducing a half dozen mathematical symbols and not defining any of them.  With some unnecessary work I was able to deduce what they meant from context.

In Table 2, it’s not explicitly defined what “direct” and “CoT” mean and how can they be compared to solve rate, although I was eventually able to understand this.  It should be defined explicitly.

The pat_wrong results are missing from Table 3.

On the other hand, these measurements are novel as far as I know and the specific experiments here seem likely reproducible given the details provided.
summary_of_the_review: This paper presents some interesting experiments, but needs dramatic improvements in clarity and more development in tying the results together into insights.
correctness: 3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.
technical_novelty_and_significance: 2: The contributions are only marginally significant or novel.
empirical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
flag_for_ethics_review: NO.
recommendation: 3: reject, not good enough

From: ICLR.cc/2023/Conference/Paper3567/Reviewer_Ep7J
confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
summary_of_the_paper: This paper tests performance of large pre-trained LMs with chain-of-thought prompting, testing sensitivity to different manipulations of the prompts. They divide the components that they manipulate into categories of "symbols", "patterns", and "text", and have a couple of types of manipulations of each of these components. They report effects of the results from PaLM-62B, complemented by GPT-3 and CODEX results in the appendix. Their main finding is that replacing "symbols" in the prompts does not affect CoT performance, but replacing -- and especially removing -- "patterns" or "text" does greatly affect CoT performance.
strength_and_weaknesses: Strengths: I found this paper for the most part interesting, clearly written, and natural to read, all of which I appreciated. The problem of better understanding models' sensitivity in chain-of-thought-prompting is relevant and timely, and I think the authors are trying to make  sensible steps toward investigating these phenomena. The goals and takeaways are mostly clearly articulated, and at least on a surface level it feels like the conclusions here are straightforward and informative.

Weaknesses: I think the biggest issue with this paper is that the "components" that the authors have identified and manipulated are not very well-defined. This is particularly true for "patterns" and "text", but even "symbols" really isn't a very solid concept, with the provided definition for "Symbols" being "sequences of tokens in the prompt, about which the model reasons to solve a task". This definition sounds like it could apply to every word in the prompt, so it mostly seems that the authors have chosen as "Symbols" the salient content words depending on the nature of the prompt (i.e. numbers for math and number sorting tasks, players and activities for prompts talking about sports players and activities, dates and times for tasks involving manipulating dates and times). 

The definitions for the other two component are similarly vague. "Patterns" are "either composition of symbols and operators or a structure of a prompt that reinforces task understanding" and "Text" is "tokens that are neither symbols, nor part of patterns". None of these are adequate definitions to actually know in a generalizable way what the authors are referring to with these concepts, and the major consequences include the following: 

1) The choice of what exactly to manipulate turns out to be unclear. In the math CoT prompts, the authors decide that the "patterns" component is just the equation at the end of the prompt, and so they try removing that or keeping only that. For the Sports prompts, they decide the patterns are "is" and the [SPORT/ACTIVITY] that comes after "is". For the Sports prompts, using the convoluted reasoning that "merely partially removing patterns is not sufficient" (why would you partially remove the patterns in the first place?) they settle on "crafting a prompt in which several variations of thoughts are mixed". Concretely this turns out to correspond (in the sports prompt) to converting the two-sentence chain of reasoning into a merged single sentence conveying roughly the same thing. This feels arbitrary and ad hoc, and in the other types of prompts the "pattern" identification and choices of manipulation feel equally arbitrary / ad hoc.

2) It is unclear what we should actually conclude from the authors' findings that "patterns" and "text" are both important while "symbols" can be replaced. In terms of the finding that patterns and text are important, it feels a bit like the authors have mostly just found that if the text is mangled/truncated very substantially, it affects model performance, since the patterns/text make up the majority of the structure of the prompt, while the symbols are (sort of) individual content tokens. I think there's a very good chance that there are interesting and potentially important insights that can be gained from the results of the manipulations the authors did, but because their way of characterizing those manipulations is so vague, it's difficult at this point to tell what those insights might be. I think to derive insights from these experiments, it would be better to zoom in on each individual manipulation for each individual prompt type, characterize more precisely what exactly was done, and then comment on what this says about what lexical/structural/world knowledge information the models are relying on to do successful CoT prompting. For instance, "converting from a chain of two sentences in the sports prompt to a single sentence summarizing the reasoning in those sentences hurts the model performance, suggesting it is relying on the progression of information in the two sentences / the separation of information into separate units, in order to guide successful CoT performance". Ultimately, it would be better to actually identify properties of the prompts that are more concrete, like in my hypothetical description there, and then guide manipulations accordingly.

The one thing that does feel comparatively more interpretable, and reasonably interesting, is the finding about replacing "Symbols" with more abstract placeholders or out-of-distribution symbols. This seems potentially surprising and insightful. Once again, though, the authors' vague characterization of these concepts and manipulations makes it harder to interpret the exact takeaways from this. I think the basic takeaway is that the models when generating from the prompts are able to take the templates from the prompts and insert actual concrete numbers/concepts, and then use those sequences to produce actual answers (e.g., having seen only abstract symbols within an equation template, they can insert actual numbers and get a correct answer for the corresponding arithmetic, roughly as often as when actual numbers were in the prompts). This is interesting, but we need more concrete observations like this, rather than the vaguer description currently provided.

Lower-level things:

The text does not seem to adhere to the standard format/template. I can't tell precisely, but the text size/font seems slightly off, and the References are listed in non-standard format. There is also content on p3 that runs into the margins.

The Related Work section is extremely brief. There is a reasonable amount of work included there, but there really needs to be more detailed and precise discussion of how this work relates to existing work.

Section 8 seems like a nice application, but on closer inspection it doesn't obviously seem to actually use insights from the analysis in the rest of the paper -- it's sounds like it's just making the prompts more concise while keeping the meaning.

Figure text, attention map in Fig 1, etc, are unreasonably small. 

clarity,_quality,_novelty_and_reproducibility: I think this paper does a good job of making the questions and motivations clear, and the methods are reasonably clear -- though relegating so much content to the (hundred pages of!) appendix makes it feel like methodological information is not quite sufficient for confidently reproduce the results. The authors also don't seem to specify exactly how they measure accuracy. It's also harder to gauge novelty with the extremely brief Related Work section. Quality is reduced by various issues I've pointed out above, and I think the paper quality can/should be improved by addressing these issues, and in particular by improving the characterization of phenomena being manipulated.
summary_of_the_review: I think this paper is promising -- it's tackling an important problem, and the basic method of introducing minimal manipulations and testing how they affect model performance seems like a good one. However, currently the paper is characterizing relevant components of the prompts in a very vague way that leads to ad hoc instantiation of the described manipulations, and substantial lack of clarity about what we should concretely conclude from the findings. The paper also doesn't sufficiently discuss related work, and it seems to be squeezing content in in a strange way that involves non-standard formatting and an extremely long appendix. 
correctness: 2: Several of the paper’s claims are incorrect or not well-supported.
technical_novelty_and_significance: 2: The contributions are only marginally significant or novel.
empirical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
flag_for_ethics_review: NO.
recommendation: 5: marginally below the acceptance threshold