Paper:
Discriminatively trained neural classifiers can be trusted, only when the input data comes from the training distribution (in-distribution). Therefore, detecting outof-distribution (OOD) samples is very important to avoid classification errors. In the context of OOD detection for image classification, one of the recent approaches proposes training a classifier called "confident-classifier" by minimizing the standard cross-entropy loss on in-distribution samples and minimizing the KL divergence between the predictive distribution of OOD samples in the low-density "boundary" of in-distribution and the uniform distribution (maximizing the entropy of the outputs). Thus, the samples could be detected as OOD if they have low confidence or high entropy. In this paper, we analyze this setting both theoretically and experimentally. We also propose a novel algorithm to generate the "boundary" OOD samples to train a classifier with an explicit "reject" class for OOD samples. We compare our approach against several recent classifier-based OOD detectors including the confident-classifiers on MNIST and Fashion-MNIST datasets. Overall the proposed approach consistently performs better than others across most of the experiments.

Review:
** post rebuttal start **
After reading reviews and authors' response, I decided not to change my score.
I recommend to strengthen their theoretical justification or make their method scalable to improve their work.
Detailed comments:
2. "Moreover, their results on some of the gray-scale experiments are significantly worse compared to ours."
-> If you are talking about the comparison in MNIST-variants, please note that experimental results on MNIST cannot be seriously taken unless there is a strong theoretical background; especially, MNIST-variants are too small to talk about the scalability of the method. It is hard to convince readers only with results in MNIST-variants, unless the method has a strong theoretical justification.
However, if your claim is true for general gray-scale images, e.g., preprocessing CIFAR to be in gray scale, then you may add supporting experiments about it.
4. Again, if the method is only applicable to MNIST-variants due to its computational complexity while it has no strong theoretical justification, I can't find benefits from it.
** post rebuttal end **
- Summary:
This paper proposes to improve confident-classifiers for OOD detection by introducing an explicit "reject" class. Although this auxiliary reject class strategy has been explored in the literature and empirically observed that it is not better than the conventional confidence-based detection, the authors provide both theoretical and empirical justification that introducing an auxiliary reject class is indeed more effective.
- Decision and supporting arguments:
Weak reject.
1. Though the analysis is interesting, it is not applicable to both benchmark datasets and real-world cases. Including the benchmark datasets they experimented, the input to the model is in general bounded, e.g., natural images are in RGB format, which is typically normalized to be bounded in [0,1]. Therefore, the polytopes would not be stretched to the infinity in most cases.
On the other hand, note that softmax classifiers produce a high confidence if the input vector and the weight vector of a certain class are in the same direction (of course feature/weight norm also matters, but let's skip it for simplicity). Therefore, if there is an auxiliary reject class, only data in the same direction will be detected as OOD; in other words, OOD is "modeled" to be in the same direction with the weight vector of the auxiliary reject class. However, the conventional confidence-based detection does not model OOD explicitly. Since OOD is widely distributed over the data space by definition, modeling such a wide distribution would be difficult. Thus, the conventional approach makes more sense to me.
2. The experiment is conducted only on MNIST variations, so it is unclear whether their claim is true on large-scale datasets and real-world scenario.
Why don't you provide some experimental results on other datasets commonly used in other OOD detection papers, such as CIFAR, SVHN, TinyImageNet, and so on?
- Comments:
1. In section 4, the authors conjectured the reason why the performance of reject class in Lee et al. (2018a) was worse is that the generated OOD samples do not follow the in-distribution boundaries well. I think Appendix E in the Lee et al.'s paper corresponds to this reasoning, but Lee et al. actually didn't generate OOD samples but simply optimized the confidence loss with a "seen OOD." Lee et al. didn't experiment on MNIST variations but many natural image datasets. So, it is possible that the auxiliary reject class strategy is only effective in MNIST variations. I suggest the authors to do more experiments on larger datasets to avoid this criticism.