Analysing Mathematical Reasoning Abilities of Neural Models
Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation rules. In this paper, we present a new challenge for the evaluation (and eventually the design) of neural architectures and similar system, developing a task suite of mathematics problems involving sequential questions and answers in a free-form textual input/output format. The structured nature of the mathematics domain, covering arithmetic, algebra, probability and calculus, enables the construction of training and test spits designed to clearly illuminate the capabilities and failure-modes of different architectures, as well as evaluate their ability to compose and relate knowledge and learned processes. Having described the data generation process and its potential future expansions, we conduct a comprehensive analysis of models from two broad classes of the most powerful sequence-to-sequence architectures and find notable differences in their ability to resolve mathematical problems and generalize their knowledge.
 This paper presents a new synthetic dataset to evaluate the mathematical reasoning ability of sequence-to-sequence models. It consists of math problems in various categories such as algebra, arithmetic, calculus, etc. The dataset is designed carefully so that it is very unlikely there will be any duplicate between train/test split and the difficulty can be controlled. Several models including LSTM, LSTM + Attention, Transformer are evaluated on the proposed dataset. The result showed some interesting insights about the evaluated models. The evaluation of mathematical reasoning ability is an interesting perspective. However, the un-standard design of the LSTM models makes it unclear whether the comparisons are solid enough. The paper is relatively well-written, although the description of the neural models can be improved. The generation process of the dataset is well thought out. The insights from the analysis of the failure cases are intriguing, but it also points out that the neural networks models are not really performing mathematical reasoning since the generalization is very limited. One suggestion is that it might be useful to also release the structured (parsed) form besides the freeform inputs and outputs, for analysis and for evaluating structured neural network models like the graph networks. My main concerns are about the evaluation and comparison of standard neural models. The use of “blank inputs (referred to as “thinking steps”)” in “Simple LSTM” and “Attentional LSTM" doesn’t seem to be a standard approach. In the attentional LSTM, the use of “parse LSTM” is also not a standard approach in seq2seq models and doesn’t seem to work well in the experiment (similar result to “Simple LSTM"). I think these issues are against the goal of evaluating standard neural models on the benchmark and will raise doubts about the comparison between different models. With some improvements in the evaluation and comparison, I believe this paper will be more complete and much stronger. typo: page 3: “freefrom inputs and outputs” -> “freeform inputs and outputs”
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Analysing Mathematical Reasoning Abilities of Neural Models
Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation rules. In this paper, we present a new challenge for the evaluation (and eventually the design) of neural architectures and similar system, developing a task suite of mathematics problems involving sequential questions and answers in a free-form textual input/output format. The structured nature of the mathematics domain, covering arithmetic, algebra, probability and calculus, enables the construction of training and test spits designed to clearly illuminate the capabilities and failure-modes of different architectures, as well as evaluate their ability to compose and relate knowledge and learned processes. Having described the data generation process and its potential future expansions, we conduct a comprehensive analysis of models from two broad classes of the most powerful sequence-to-sequence architectures and find notable differences in their ability to resolve mathematical problems and generalize their knowledge.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 This paper presents a new synthetic dataset to evaluate the mathematical reasoning ability of sequence-to-sequence models. It consists of math problems in various categories such as algebra, arithmetic, calculus, etc. The dataset is designed carefully so that it is very unlikely there will be any duplicate between train/test split and the difficulty can be controlled. Several models including LSTM, LSTM + Attention, Transformer are evaluated on the proposed dataset. The result showed some interesting insights about the evaluated models. The evaluation of mathematical reasoning ability is an interesting perspective. However, the un-standard design of the LSTM models makes it unclear whether the comparisons are solid enough. The paper is relatively well-written, although the description of the neural models can be improved. The generation process of the dataset is well thought out. The insights from the analysis of the failure cases are intriguing, but it also points out that the neural networks models are not really performing mathematical reasoning since the generalization is very limited. One suggestion is that it might be useful to also release the structured (parsed) form besides the freeform inputs and outputs, for analysis and for evaluating structured neural network models like the graph networks. My main concerns are about the evaluation and comparison of standard neural models. The use of “blank inputs (referred to as “thinking steps”)” in “Simple LSTM” and “Attentional LSTM" doesn’t seem to be a standard approach. In the attentional LSTM, the use of “parse LSTM” is also not a standard approach in seq2seq models and doesn’t seem to work well in the experiment (similar result to “Simple LSTM"). I think these issues are against the goal of evaluating standard neural models on the benchmark and will raise doubts about the comparison between different models. With some improvements in the evaluation and comparison, I believe this paper will be more complete and much stronger. typo: page 3: “freefrom inputs and outputs” -> “freeform inputs and outputs”
assistant
 This paper presents a new synthetic dataset to evaluate the mathematical reasoning ability of sequence-to-sequence models. It consists of math problems in various categories such as algebra, arithmetic, calculus, etc. The dataset is designed carefully so that it is very unlikely there will be any duplicate between train/test split and the difficulty can be controlled. Several models including LSTM, LSTM + Attention, Transformer are evaluated on the proposed dataset. The result showed some interesting insights about the evaluated models. The evaluation of mathematical reasoning ability is an interesting perspective. However, the un-standard design of the LSTM models makes it unclear whether the comparisons are solid enough. The paper is relatively well-written, although the description of the neural models can be improved. The generation process of the dataset is well thought out. The insights from the analysis of the failure cases are intriguing, but it also points out that the neural networks models are not really performing mathematical reasoning since the generalization is very limited. One suggestion is that it might be useful to also release the structured (parsed) form besides the freeform inputs and outputs, for analysis and for evaluating structured neural network models like the graph networks. My main concerns are about the evaluation and comparison of standard neural models. The use of “blank inputs (referred to as “thinking steps”)” in “Simple LSTM” and “Attentional LSTM" doesn’t seem to be a standard approach. In the attentional LSTM, the use of “parse LSTM” is also not a standard approach in seq2seq models and doesn’t seem to work well in the experiment (similar result to “Simple LSTM"). I think these issues are against the goal of evaluating standard neural models on the benchmark and will raise doubts about the comparison between different models. With some improvements in the evaluation and comparison, I believe this paper will be more complete and much stronger. typo: page 3: “freefrom inputs and outputs” -> “freeform inputs and outputs”