Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 9: Very Strong Accept: Technically flawless paper with groundbreaking impact on at least one area of AI/ML and excellent impact on multiple areas of AI/ML, with flawless evaluation, resources, and reproducibility, and no unaddressed ethical considerations.
review_content: summary: This work proposes a large language model *Minerva* to solve scientific and mathematical questions in natural language and generate step-by-step solutions using correct  Latex notation. This model is trained on a high-quality data collection composed of scientific and mathematical information. This model got impressive results across a wide variety of quantitative reasoning tasks, including Precalculus, Geometry, and many more.


strengths_and_weaknesses: * This paper provides a well-documented analysis of results and the reason behind the usage of metrics.
* The work will be a founding stone in making AI for tutoring. This can have a significant impact on students with fewer resources.
* The authors also addressed the issues of False positives and Memorization with a detailed investigation.

questions: 1. Any reason behind the incorrect answers for the solutions that were short?
2. Can it derive math expressions instead of numbers as the final answer like solving an indefinite integral?
limitations: There is currently no automated mechanism to check the correctness of the model's answers, and the authors also acknowledge it. This work has no major negative societal impact, but people may use it to cheat on some STEM tests.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper introduces a large language model and new training and evaluation dataset for quantitative reasoning problems. It first overviews existing methods and resources for quantitative reasoning, then discusses the datasets collected for training and evaluation, and finally provides comprehensive results and analysis of a model that is finetuned on the collected training data, finding that in comparison to existing models, the proposed large language model performs well.
strengths_and_weaknesses: Strengths:

* Good overview on challenges associated with quantitative reasoning
* Very comprehensive error analysis (and examples in appendix)
* Great analysis of the model robustness wrt. memorization

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Weaknesses:

* The main contribution here is collecting (scraping and filtering) a dataset, and fine-tuning a large model on it. By itself, I am not sure this is a huge contribution. However, the analysis in the latter half of the paper is quite comprehensive.
* I was confused about the majn@k format in Fig 1 and 2.3 until section 2.5. Would help to clarify in the Fig 1 caption and 2.3 that it's majority voting on the final answer, not the whole generated text (how does this work for something like a proof, though, that's inherently a chain of reasoning?).
* I'd like to see more discussion on the limitations of existing quantitative benchmarks. I was expecting this in the related work section but couldn't find anything (just briefly mentioned on L86).
questions: * Clarification question: Table 1 lists tokens in the entire dataset, right? Not the amount sampled for the technical training dataset? Otherwise the proportions don't make sense. 
* Is the general NL data for the technical dataset sampled randomly from the full general NL dataset?
* Why truncate inputs from the left? Besides fitting in the limited transformer input. How often does this happen?
* What does it look like for reasoning to be wrong but the answer to be right? It's a bit surprising that the false positive rate is 30% in difficulty 5 examples -- without knowing what those examples look like, I find it very surprising that there are so many false positives.
* How many times each are the 20 examples in 5.2 modified to test memorization? 
limitations: I'm wondering about copyright/consent issues when it comes to scraping/re-releasing data from math webpages and ArXiv. Are you planning to release the training data?

Similarly, details on the contract work used to clean the dataset -- typically crowdsourcing contributions will have (at least in the appendix) details on compensation, etc. but I couldn't find that.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: State-of-the-art language models have generally struggled with tasks that require quantitative reasoning, such as solving mathematics, science, and engineering problems at the college level. This paper introduced Minerva, a large language model pretrained on general natural language data and further trained on technical content. The authors conducted experiments in a few-shot setting across a range of tasks that require quantitative/numerical/symbolic reasoning, including one they manually collected for better evaluation (OCWCourses). The results demonstrated that it achieved strong performance on all the datasets and set state-of-the-art
 performance on the MATH dataset. Through an error analysis, they also found the two most common cases in which their model made wrong predictions are *Incorrect reasoning* and *Incorrect calculation*.



strengths_and_weaknesses: - Originality: The idea of further training a pretrained language model on a math-heavy corpus is quite straightforward yet effective (as can be seen from the results).

- Quality: The proposed approach is technically sound and the experimental results showed that it outperformed the previous language model on MATH and OCWCourses by a large margin. However, I don't think there are many insights I can draw from this paper. My main takeaway about this paper is that we can achieve much better performance on quantitative/numerical/symbolic reasoning by further training a pretrained language model on high-quality corpus containing equations and diagrams. What if we just train a language model from scratch using the same corpus? What is the role of the general language data played here? I think answering such questions could make this paper stronger.

- Clarity: This paper is well-organized and easy to follow. 

- Significance: This paper achieved strong results across a range of different datasets and the reasoning skill demonstrated by the model is amazing. As pointed out by the authors that one of the main challenges is to automatically verify the correctness of the generated reasoning chains/answers, I believe this work would prosper the work in such directions.

questions: n/a
limitations: The authors have sufficiently addressed the limitations in the paper.
review_title: null

final_score: rating: 2: Strong Reject: For instance, a paper with major technical flaws, and/or poor evaluation, limited impact, poor reproducibility and mostly unaddressed ethical considerations.
review_content: summary: The authors fine-tune large PLMs (pre-trained on a corpus of scientific and mathematical text) on a new quantitative reasoning dataset, evaluating on existing benchmarks and a new, custom benchmark. The main contribution is the formulation of these datasets, which allows for sota on MATH and strong performance on other benchmark. Notably, this approach relies exclusively on a language model, which has no outside access to libraries, calculators, or other tools in performing the task.
strengths_and_weaknesses: Strengths
- The most obvious strength of the paper is the considerable improvement over SOTA scores, although I'm quite surprised at how low such scores are, especially when GPT-3 also so exceeds them. 
- I think the majority voting idea is really cool, since sampling obviously provides a limited view of the branching probability tree characterizing the language model's processing of the original prompt, and majority rule arguably offers a more fulsome picture of the outputs. The obvious problem with it is that cost scales linearly.
- Checking the answers using sympy is a clever way to bin different expressions of answers.

Weaknesses
- The main problem with the paper, in my view, is that the training data is the main contribution of the paper, but I cannot tell what it is like. Basically the only thing I can tell is that it contains mathematical expressions. Fig. 1 and Fig. 2 show the evaluation data, which is already outlined in other work, and I wonder why that space wasn't used to explain this paper's training corpus. At one point, the authors mention "equations and diagrams" juxtaposed with natural language, but how would a language model process diagrams, or how would they be converted to text? I have many more questions, and they might be answered in the appendix, which wasn't available to me, but this lack of clarity seems to me to preclude the publication of this paper at NeurIPS.
- The benchmark introduced may be too small to be meaningful, and I don't think the paper makes it clear how representative it is. Furthermore, I worry, when it includes questions from "‘solid-state chemistry’, ‘information and entropy’, ‘differential equations’, and ‘special relativity'", that quantitative reasoning is not what we are testing, but specific scientific knowledge that makes use of quantitative reasoning. 
- Doesn't reference EQUATE (Ravichander et al. 2019), one such recent, decently-cited quantitative reasoning benchmark.
- The authors say in L51 that "existing benchmarks are limited with respect to quantitative reasoning", and I'd like to know what they mean by that. I couldn't find any corresponding discussion.
questions: - The claim in L175-177 seems unfounded to me. Why wouldn't you be sure you haven't found a local minimum with the fine-tuned model by training on the wrong dataset, whereas you haven't with the base model?
- In L57-58, I cannot parse "Prompting language models... unseen problems". Do you mean to say "apply" instead of "output"?
- I cannot tell whether the pre-trained model, on which Minerva is based, is a contribution of this paper or another paper?
- I don't understand the need for the OCW benchmark introduced, in addition to MATH, GSM8k, and others. Which part of the new dataset do these more established benchmarks lack?

limitations: The authors rightly identify 3 limitations of their method. There is nothing set in stone, however, about these limitations (one could engineer a dataset to give specific capabilities to a model, or use a model that had access to outside tools, etc), and the authors do not discuss why they chose the model, data, etc. that they did __with respect to__ these limitations.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: The paper focuses on the problem of quantitative reasoning in large language models, and introduces Minerva, a large language model that is pretrained on general language data and then further trained on a dataset containing scientific and mathematical data. 

The training data is collected from arXiv and web pages that were preprocessed to conserve mathematical content. The authors then use this data to finetune pretrained decoder-only transformer LMs (8B and 62B parameter models) using an autoregressive objective. During inference time, the paper suggests sampling k > 1 solutions and selecting one using majority voting. The authors show empirically that this approach considerably outperforms greedy decoding. 

The authors compare their models against previous works on the MATH, GSM8k, and MMLU-STEM datasets, and also build a dataset (OCWCourses) of 272 undergraduate questions in science and mathematics to evaluate the model's quantitative reasoning abilities in a chain-of-thought context. The authors report that the Minerva 62B significantly outperforms state-of-the-art results on the MATH dataset, and achieves similar performance on MMLU-STEM. Furthermore, the authors conduct analyses to understand the types of mistakes the models make, the effect of false positives (cases where the answer is correct but the chain of reasoning is not), and whether the model is memorizing the answers. They find that most of the errors are incorrect reasoning and incorrect calculations, that false positive rate increases with difficulty level (with an estimated average of 8% on the MATH dataset), and that there is little evidence that the model's performance can be attributed to memorization. 




strengths_and_weaknesses: **Strengths**

The topic of quantitative reasoning with large language models is of interest to the research community. By finetuning pretrained LMs on large math and science datasets and comparing against models that were not trained with such data, the paper highlights the importance of data quality for achieving quantitative reasoning abilities. Furthermore, the authors build a new dataset for evaluating quantitative reasoning, and conduct thorough evaluation of the type of mistakes the models make, highlighting the issue with false positives, and investigating the impact of memorization on performance.

**Weaknesses**

Although the authors mention that the dataset is the main novelty of their paper (line 45), there isn't sufficient discussion of it in the paper and appendix. Will this approach scale to more complex math and science problems? Are further gains expected with larger models? Furthermore, what is the breakdown of papers by area/topic? How are diagrams (as mentioned in the intro) processed? What are the examples of heuristics used to process the pages as mentioned in the appendix? etc.

questions: 1- Are the "BaseModel" models used publicly available? Appendix B does not contain sufficient information for reproducibility.
2- Table 4 only reports the distribution of failure modes of the 8B model, and the text only mentions the dominating failure modes for the 62B model. What is the distribution for the 62B model, where the 8B model solved correctly and the 62B model did not? Is there a further breakdown of incorrect reasoning?
limitations: The authors discuss the limitations and potential societal impact of their work.
review_title: null

Meta-review: metareview: This is a very strong solid work that extracts equations from scientific papers and show strong performance in mathematical reasoning. 
confidence: Certain
Decision: Accept