Out-Of-Distribution Detection With Smooth Training

Q1: What are the intuitions/interpretations of $\sqrt(C/n)$ in Equ(4), and the equations of equations of theorem 1 and 2? The connection between the equations and the implications is not clear.

A1: We apologize for the confusion. $n$ is the number of training samples and $C$ is a uniform constant. When the number of the training samples is large enough, this term tends to 0 such that the risk of empirical predictor $\mathbf{f}_{\boldsymbol{\theta}_S}$ can approximate to the optimal risk. Theorem 1 states that under the right conditions, the model is likely to be overconfident in the ID data. Theorem 2 states that when the model is overconfident in the ID data, it will also be overconfident in the OOD data which have a small distribution discrepancy with ID data. We'll go into more detail in the revised version.

Q2: Can SMOT use the updated model trained on the fly to get the mask for perturbation?

A2: Thanks for your kind suggestion, we perform the experiment you described. We still train 300 epochs, in the first 100 epochs we perform the standard training and then we use the model in training to obtain the CAM to perform the SMOT training. The results are as follows:

It is shown what you described works well! Thanks again for your insightful comments. We will add these results and discussions to our revision.

We sincerely thank you for your constructive comments! Please find our responses below.

Q1: The conclusion of Theorem 1 is "given a sufficient amount of training data and a small optimal risk, ..., the issue of over-confidence for ID data is highly probable to arise". However, the equation is only related to "over-confidence" (which I assume refers to excessive maximum softmax probability according to Eq. 2) when the loss is exactly cross-entropy loss. If we use label smoothing as the loss (although it is later empirically shown not to work), then there won't be over-confidence by looking at Eq. 4.

A1: Thanks for your valuable comments. Theorem 1 states that networks trained on ERM principle are likely to be overconfident in ID data. We do not discuss the vanilla label smoothing here. We agree that label smoothing can alleviate the problem of overconfidence in neural networks. However, this is more of a conclusion drawn from experimental results. It is hard to follow the your conclusion "If we use label smoothing as the loss, then there won't be over-confidence by looking at Eq. 4". In fact, label smoothing is not widely used in OOD detection. Our experimental results also demonstrate that vanilla label smoothing does not improve the model's OOD detection performance. We intuitively believe that this may be due to the fact that label smoothing is applied to raw ID samples, which is contrary to the goal of OOD detection.

Q2: I can't see how exactly the "over-confidence in OOD data" is reflected in Theorem 2. More elaboration and clarification is necessary.

A2: We apologize for the misunderstanding. Theorem 2 states that for any OOD sample $x$, the upper bound of the risk that the well-trained model $\mathbf{f}_{\boldsymbol{\theta}_S}$ misassigns it to the label space of the ID samples is the right-hand term of the inequality in Theorem 2 (I'm sorry, but openreview doesn't seem to be able to compile that equation).

Q3: The concluding paragraph under Theorem 2 makes me lost again. Why we want to "access real OOD data to reduce the distribution discrepancy during training"? What does it mean to "reduce the distribution discrepancy" (the $d(\theta)$ in Theorem 2?) between ID and OOD? Meanwhile, why suddenly "limited training ID data", "overfitting", and "the failure of ID classification" become issues for OOD detection?

A3: Thanks for your insightful comments.

In the OE approach, we are allowed to use surrogate OOD data to regularize the model, i.e., to allow the model to have low confidence on this data. However, it is clear that the surrogate OOD data has distributional differences from the real OOD data encountered during testing. Here REDUCE the distribution discrepancy refers to reducing the distribution discrepancy between the surrogate OOD data and the real OOD data.

Q4: Lastly, where are the proofs of the Theorems (or where are the references if they were proved by existing works)?

A4: The proofs are in APPENDIX A. We will highlight it in our revision. Thanks for your kind suggestion.

Q5: Eq. 9 seems a little arbitrary. Why using a temperature-scaled exponential function? What's the intuition behind it? Why (t - 255)? What is the value range of t?

A5: Thanks for pointing out this potentially confusing problem. We design the smoothing parameter function based on the following three principles：

• The smoothing parameter should be a monotonically decreasing function of the masking threshold, because the more regions are masked, the smoother its label should be.
• When no region is masked, the smoothing parameter should be (or close to) 0.
• When all regions are masked, the smoothing parameter should be (or close to) 1.

The designed temperature-scaled exponential function satisfies the above rules and can simply adjust the steepness of the function by one parameter $T$. Of course, other more complex functions or learnable functions can be considered, and this is our future work. $t$ is the masking threshold, ranging from 0 to 255, corresponding to the values in the generated heat map. We set $(t-255)$ because when the masking threshold $t$ is 255, the image will not be masked, and we should use hard label, i.e., $\epsilon = 0$.

We sincerely thank you for your constructive comments! Please find our responses below.

Q1: It is a little bit expensive to use CAM for identifying those label-correlated regions. I would like to see the OOD detection performance with the randomly generated masks. For example, randomly masking 30%-70% of the image for smoothing training.

A1: Thanks to your kind suggestion. Following your constructive comments, we have added the experiment, with the randomly generated masks. More detailed results and disucssions can be found in A3 to Reviewer H2kX.

Q2: The proposed SMOT utilizes data augmentation for OOD detection. Therefore, the author should introduce and compare more related methods that investigate the effectiveness of data augmentation in OOD detection. I believe there have been many papers that exploring data augmentation for Calibration or OOD detection.

A2: Thank you for your kind suggestion.

For the first paper RankMixup[1] you mentioned, it does have similarities to our work at the top level of thought. It argues that mixed samples should have lower confidence and that the higher the mixing, the lower the confidence. In our work, we think that the less complete the sample, the lower the confidence. We take inspiration from the human perspective and design our algorithm accordingly. We believe that our approach more closely aligns with how humans perceive the world However, since RankMixup is a relatively new piece of work, the authors have not published its code for the time being and we have not compared it with SMOT. As for the other mentioned work DOE[2], it uses a min-max learning scheme-searching to synthesize OOD data that leads to worst judgments and learning from such OOD data for uniform performance in OOD detection. The biggest difference between us and them is that we make a smooth excess between ID data and OOD data. We compare DOE and SMOT on CIFAR10. The result is as follows:

As can be seen from the experimental results, SMOT is not as good as DOE. However, this is not a fair comparison. DOE belongs to the Outlier Exposure (OE) framework and requires surrogate OOD data. while SMOT does not require any additional data. We will add a discussion of these outstanding works in the revised version.

Q3: The SMOT framework is similar to the Outlier Exposure (OE) framework, the author should also compare the proposal with other Outlier exposure (OE) based methods, and discuss the advantages compared with the OE framework.

A3: We agree with your point. Our approach is indeed similar to OE. Masked samples can be viewed as OOD samples.

We would like to highlight the differences between ours and OE. Specificaly, we do smoothing between ID samples and OOD samples. The more ID samples are masked, the more it is considered an OOD sample. This makes the transition between ID and OOD smoother. Also, our OOD samples are created by simply masking ID samples without the need for an external dataset. We compared our method with some OE methods with the following results:

As can be seen from the experimental results, SMOT is not as good as OE and MixOE. We would like to note that it's not a fair comparison.

Thanks agin for your constructive comments. We will add the results and discussions to the revised paper.

[1]: RankMixup: Ranking-Based Mixup Training for Network Calibration

[2]: OUT-OF-DISTRIBUTION DETECTION WITH IMPLICIT OUTLIER TRANSFORMATION

[3]:Deep anomaly detection with outlier exposure

[4]:Mixture Outlier Exposure: Towards Out-of-Distribution Detection in Fine-grained Environments

Q3: Further analysis could be devoted to how the results are sensitive to variations in hyperparameter settings. For instance, how essential is the use of a CAM heatmap to guide masking? What's the optimal way to establish the relationship between mask size and label smoothing hyperparameter?

A3: We apologize that we missed the important experiment of comparing with random masking.

As suggested by you and other reviewers, we add this experiment on CIFAR10. Since the images in CIFAR10 is of 32*32, we divide the image into 64 small 4*4 squares, and in each loop, we sample a probability $p$ from the distribution of $Beat(\alpha, \beta)$, let each small square be masked with probability $p$, and then smooth the label. The smoothing parameter is designed as $\epsilon(p) = (exp(p/T) - 1)/(exp(1/T)-1)$. We conducted experiments with different $\alpha, \beta$ and T. Results are as follows(The numbers in the table are the average AUROC/the average FPR95.):

As can be seen from the experimental results, when CAM is not used to guide masking, it does not work well and in many cases has lower performance than using simple cross-entropy loss. This is because masking randomly does not necessarily result in a change in the label of the image. It doesn't make sense to soften the label when we mask the background

As for how to establish a relationship between the masking size and label smoothing hyperparameter, this is really a major drawback of SMOT at the moment. In our paper, we simply use a temperature-scaled exponential function with a adjustable temperature. A better approach might be to get the relation between masking size and smoothing hyperparameter from priori knowledge or to learn one such relation. This is our future research direction.

We sincerely thank you for your constructive comments! Please find our responses below.

Q1: Although smooth training enhances Out-Of-Distribution (OOD) detection, there's a minor decrease in in-distribution accuracy compared to conventional training. An in-depth exploration of this trade-off could be beneficial.

A2: Thanks for your suggestion.

Smooth training does lead to a minor decrease (from 95.12% to 94.54%) in classification accuracy of ID samples. Following your suggestion, we further explore the trade-off between OOD detection performance and ID classification performance on CIFAR-10. We do this by varying the values of the hyperparameters $\lambda$. The experimental results are as follows:

The experimental results show that the ID ACC of models trained with SMOT is lower than that of models trained with normal cross-entropy loss, and that larger $\lambda$ usually leads to lower ID ACC, but not necessarily to higher AUROC. In practice, we need to choose an appropriate $\lambda$ so that the model maintains both high ID classification ability and good OOD detection ability.

Q2: The authors employ class activation maps to pinpoint label-relevant regions for masking, necessitating a pre-trained model. Studying other perturbation techniques that don't require a pre-trained model could expand the method's applicability.

A2: Thank you for your kind suggestion.

In addition to using masking as perturbation function, we also use adding gaussian noise to inputs as perturbation function, which does not require additional pre-trained models. We report the experimental results in Table 9 in the Appendix:

It is shown that adding noise can also improve the OOD detection performance of the model.