DL2: Training and Querying Neural Networks with Logic
We present DL2, a system for training and querying neural networks with logical constraints. The key idea is to translate these constraints into a differentiable loss with desirable mathematical properties and to then either train with this loss in an iterative manner or to use the loss for querying the network for inputs subject to the constraints. We empirically demonstrate that DL2 is effective in both training and querying scenarios, across a range of constraints and data sets.
 The paper tackles the interesting problem of combining logical approaches with neural networks in the form of translating a logical formula into a non-negative loss function for a neural network. The approach is novel and more general than previous approaches and the math is sound. However, I feel that the method is not well presented. Sadly the introduction does not set the method into context or give a motivation. The abstract is very short and misses key information. Indeed, even the more technical parts sometimes lack clarity and assume familiarity with a wide range of methods. The experiments are well thought out and show the promise of the method when encoding performance measures such as entropy into the constraints. It would have been interesting to additionally see other kinds of constraints such as purely logical formulas that do not have a specific aim (robustness or performance or otherwise) but simply state preconditions that should be fulfilled. It would furthermore be interesting to inspect the corner cases of the proposed method such as what happens if two constraints are nearly opposing each other and so on. To conclude, the presented method is clearly novel and provides an interesting solution to a challenging problem. However the paper in the current form does not fully adhere to the standards of conferences such as ICLR. I suggest rewriting especially the abstract and the introduction and then submitting to a different venue as the approach itself seems promising. Additionally, as only very limited comparison experiments can be performed the method itself should be more thoroughly inspected by performing, for example, edge-case or time/number of constraints inspections. Minor remarks: Hyperparameters such as batch size not reported Spelling mistake in line 2, page 2 “Lipschitz condition” When mentioning “prior work” in the introduction a citation is needed.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
DL2: Training and Querying Neural Networks with Logic
We present DL2, a system for training and querying neural networks with logical constraints. The key idea is to translate these constraints into a differentiable loss with desirable mathematical properties and to then either train with this loss in an iterative manner or to use the loss for querying the network for inputs subject to the constraints. We empirically demonstrate that DL2 is effective in both training and querying scenarios, across a range of constraints and data sets.
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 paper tackles the interesting problem of combining logical approaches with neural networks in the form of translating a logical formula into a non-negative loss function for a neural network. The approach is novel and more general than previous approaches and the math is sound. However, I feel that the method is not well presented. Sadly the introduction does not set the method into context or give a motivation. The abstract is very short and misses key information. Indeed, even the more technical parts sometimes lack clarity and assume familiarity with a wide range of methods. The experiments are well thought out and show the promise of the method when encoding performance measures such as entropy into the constraints. It would have been interesting to additionally see other kinds of constraints such as purely logical formulas that do not have a specific aim (robustness or performance or otherwise) but simply state preconditions that should be fulfilled. It would furthermore be interesting to inspect the corner cases of the proposed method such as what happens if two constraints are nearly opposing each other and so on. To conclude, the presented method is clearly novel and provides an interesting solution to a challenging problem. However the paper in the current form does not fully adhere to the standards of conferences such as ICLR. I suggest rewriting especially the abstract and the introduction and then submitting to a different venue as the approach itself seems promising. Additionally, as only very limited comparison experiments can be performed the method itself should be more thoroughly inspected by performing, for example, edge-case or time/number of constraints inspections. Minor remarks: Hyperparameters such as batch size not reported Spelling mistake in line 2, page 2 “Lipschitz condition” When mentioning “prior work” in the introduction a citation is needed.
assistant
 The paper tackles the interesting problem of combining logical approaches with neural networks in the form of translating a logical formula into a non-negative loss function for a neural network. The approach is novel and more general than previous approaches and the math is sound. However, I feel that the method is not well presented. Sadly the introduction does not set the method into context or give a motivation. The abstract is very short and misses key information. Indeed, even the more technical parts sometimes lack clarity and assume familiarity with a wide range of methods. The experiments are well thought out and show the promise of the method when encoding performance measures such as entropy into the constraints. It would have been interesting to additionally see other kinds of constraints such as purely logical formulas that do not have a specific aim (robustness or performance or otherwise) but simply state preconditions that should be fulfilled. It would furthermore be interesting to inspect the corner cases of the proposed method such as what happens if two constraints are nearly opposing each other and so on. To conclude, the presented method is clearly novel and provides an interesting solution to a challenging problem. However the paper in the current form does not fully adhere to the standards of conferences such as ICLR. I suggest rewriting especially the abstract and the introduction and then submitting to a different venue as the approach itself seems promising. Additionally, as only very limited comparison experiments can be performed the method itself should be more thoroughly inspected by performing, for example, edge-case or time/number of constraints inspections. Minor remarks: Hyperparameters such as batch size not reported Spelling mistake in line 2, page 2 “Lipschitz condition” When mentioning “prior work” in the introduction a citation is needed.