Paper:
Published as a conference paper at ICLR 2018 DETECTING STATISTICAL INTERACTIONS FROM NEURAL NETWORK WEIGHTS
Interpreting neural networks is a crucial and challenging task in machine learning. In this paper, we develop a novel framework for detecting statistical interactions captured by a feedforward multilayer neural network by directly interpreting its learned weights. Depending on the desired interactions, our method can achieve significantly better or similar interaction detection performance compared to the state-of-the-art without searching an exponential solution space of possible interactions. We obtain this accuracy and efficiency by observing that interactions between input features are created by the non-additive effect of nonlinear activation functions, and that interacting paths are encoded in weight matrices. We demonstrate the performance of our method and the importance of discovered interactions via experimental results on both synthetic datasets and real-world application datasets.

Review:
Based on a hierarchical hereditary assumption, this paper identifies pairwise and high-order feature interactions by re-interpreting neural network weights, assuming higher-order interactions exist only if all its induced lower-order interactions exist. Using a multiplication of the absolute values of all neural network weight matrices on top of the first hidden layer, this paper defines the aggregated strength z_r of each hidden unit r contributing to the final target output y. Multiplying z_r by some statistics of weights connecting a subset of input features to r and summing over r results in final interaction strength of each feature interaction subsets, with feature interaction order equal to the size of each feature subset. 
Main issues:
1. Aggregating neural network weights to identify feature interactions is very interesting. However, completely ignoring 
activation functions makes the method quite crude. 
2. High-order interacting features must share some common hidden unit somewhere in a hidden layer within a deep neural network. Restricting to the first hidden layer in Algorithm 1 inevitably misses some important feature interactions.
3. The neural network weights heavily depends on the l1-regularized neural network training, but a group lasso penalty makes much more sense. See Group Sparse Regularization for Deep Neural Networks (https://arxiv.org/pdf/1607.00485.pdf).
4. The experiments are only conducted on some synthetic datasets with very small feature dimensionality p. Large-scale experiments are needed.
5. There are some important references missing. For example, RuleFit is a good baseline method for identifying feature interactions based on random forest and l1-logistic regression (Friedman and Popescu, 2005, Predictive learning via rule ensembles); Relaxing strict hierarchical hereditary constraints, high-order l1-logistic regression based on tree-structured feature expansion identifies pairwise and high-order multiplicative feature interactions (Min et al. 2014, Interpretable Sparse High-Order Boltzmann Machines); Without any hereditary constraint, feature interaction matrix factorization with l1 regularization identifies pairwise feature interactions on datasets with high-dimensional features (Purushotham et al. 2014, Factorized Sparse Learning Models with Interpretable High Order Feature Interactions). 
6. At least, RuleFit (Random Forest regression for getting rules + l1-regularized regression) should be used as a baseline in the experiments.
Minor issues:
Ranking of feature interactions in Algorithm 1 should be explained in more details.
On page 3: b^{(l)} \in R^{p_l}, l should be from 1, .., L. You have b^y.
In summary, the idea of using neural networks for screening pairwise and high-order feature interactions is novel, significant, and interesting.  However, I strongly encourage the authors to perform additional experiments with careful experiment design to address some common concerns in the reviews/comments for the acceptance of this paper.
 
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The additional experimental results are convincing, so I updated my rating score.