Review for NeurIPS paper: PLLay: Efficient Topological Layer based on Persistent Landscapes

Weaknesses: While I feel favourably about this paper, there are still some issues that prevent me from fully endorsing it. My primary reservation is that the experimental or practical benefits are clearly demonstrated and that the experimental setup and'presentation' is somewhat shallow: - When depicting accuracies in Figure 3, please show the standard deviations alongside the accuracies (as additional error bars, for example) in order to make the methods comparable. It seems to me that the achieved gains for MNIST are not necessarily significantly better than other methods, but I could be wrong here (I do appreciate the setup in terms of noise or'corruption' levels, though; I think more of these kinds of experiments are always helpful in ML!) - In addition to a better way of reporting the results, I would also like to see a more detailed comparison to baseline methods. I understand that the natural comparison partner consists of *other* topological layers. However, next to these neural network baseline, I would also suggest taking a look at kernels for persistence diagrams or metrics between them (though I could understand that the latter type of functions might not be efficiently computable). However, there are many kernel functions that could be equally well used here: - Carrière et al.: Sliced Wasserstein Kernel for Persistence Diagrams, ICML 2017 - Kusano et al.: Persistence weighted Gaussian kernel for topological data analysis, ICML 2016 - Reininghaus et al.: A Stable Multi-Scale Kernel for Topological Machine Learning, CVPR 2015 In a similar vein, the persistence landscape formulation also affords a kernel formulation; it would be interesting to see how the proposed method compares to this.