Extrapolation and learning equations
In classical machine learning, regression is treated as a black box process of identifying a suitable function from a hypothesis set without attempting to gain insight into the mechanism connecting inputs and outputs. In the natural sciences, however, finding an interpretable function for a phenomenon is the prime goal as it allows to understand and generalize results. This paper proposes a novel type of function learning network, called equation learner (EQL), that can learn analytical expressions and is able to extrapolate to unseen domains. It is implemented as an end-to-end differentiable feed-forward network and allows for efficient gradient based training. Due to sparsity regularization concise interpretable expressions can be obtained. Often the true underlying source expression is identified.
The authors attempt to extract analytical equations governing physical systems from observations - an important task. Being able to capture succinct and interpretable rules which a physical system follows is of great importance. However, the authors do this with simple and naive tools which will not scale to complex tasks, offering no new insights or advances to the field. The contribution of the paper (and the first four pages of the submission!) can be summarised in one sentence: *Learn the weights of a small network with cosine, sinusoid, and input elements products activation functions s.t. the weights are sparse (L1)*. The learnt network weights with its fixed structure are then presented as the learnt equation. This research uses tools from literature from the *90s (I haven*t seen the abbreviation ANN (page 3) for a long time) and does not build on modern techniques which have advanced a lot since then. I would encourage the authors to review modern literature and continue working on this important task.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Extrapolation and learning equations
In classical machine learning, regression is treated as a black box process of identifying a suitable function from a hypothesis set without attempting to gain insight into the mechanism connecting inputs and outputs. In the natural sciences, however, finding an interpretable function for a phenomenon is the prime goal as it allows to understand and generalize results. This paper proposes a novel type of function learning network, called equation learner (EQL), that can learn analytical expressions and is able to extrapolate to unseen domains. It is implemented as an end-to-end differentiable feed-forward network and allows for efficient gradient based training. Due to sparsity regularization concise interpretable expressions can be obtained. Often the true underlying source expression is identified.
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>



The authors attempt to extract analytical equations governing physical systems from observations - an important task. Being able to capture succinct and interpretable rules which a physical system follows is of great importance. However, the authors do this with simple and naive tools which will not scale to complex tasks, offering no new insights or advances to the field. The contribution of the paper (and the first four pages of the submission!) can be summarised in one sentence: *Learn the weights of a small network with cosine, sinusoid, and input elements products activation functions s.t. the weights are sparse (L1)*. The learnt network weights with its fixed structure are then presented as the learnt equation. This research uses tools from literature from the *90s (I haven*t seen the abbreviation ANN (page 3) for a long time) and does not build on modern techniques which have advanced a lot since then. I would encourage the authors to review modern literature and continue working on this important task.
assistant
The authors attempt to extract analytical equations governing physical systems from observations - an important task. Being able to capture succinct and interpretable rules which a physical system follows is of great importance. However, the authors do this with simple and naive tools which will not scale to complex tasks, offering no new insights or advances to the field. The contribution of the paper (and the first four pages of the submission!) can be summarised in one sentence: *Learn the weights of a small network with cosine, sinusoid, and input elements products activation functions s.t. the weights are sparse (L1)*. The learnt network weights with its fixed structure are then presented as the learnt equation. This research uses tools from literature from the *90s (I haven*t seen the abbreviation ANN (page 3) for a long time) and does not build on modern techniques which have advanced a lot since then. I would encourage the authors to review modern literature and continue working on this important task.