Diversity Modeling for Semantic Shift Detection

1. Motivation

   1. Semantic shift detection: Users hope DNNs to reliably reject predictions when facing data beyond its training distribution, rather than providing incorrect results with high confidence. Semantic shift detection is similar to common OOD detection, except that we neither explicitly emphasize ID classification nor use class labels. We believe this setting is general and practical in real-world scenarios thus worth studying.
   2. Modeling diversity-agnostic non-semantic patterns:
      • Modeling non-semantic patterns: As mentioned in Sec. 3.1, memory models are used to prevent reconstruction-based methods from reconstructing OODs. But discrete prototypes may discard non-semantic patterns and suppress diverse IDs simultaneously. The solution is to restore non-semantic diversity of prototypes in a well-constrained way. That is, modeling non-semantic patterns aims to solve the trade-off dilemma between reconstructing diverse IDs and suppressing undesired OODs.
      • Diversity-agnostic: Existing methods (e.g. DMAD) leverage strong diversity priors to deal with specific non-semantic patterns. They are not general enough for natural images and cause worse performance in semantic shift detection. Therefore, we need to model more general and regularized diversity without prior assumptions about the type of diversity patterns.

2. Different types of shifts: We assume ``different types of semantic shifts'' refers to non-semantic attribute/diversity (because semantic shifts could only be explained as the changes of semantic label which has no different types). If we understand correctly, BiRDM could implicitly handle all different types of non-semantic shifts. An qualitative example in Fig. 3 shows BiRDM handles view, size, and 3 colors changes without specifying a specific pattern in advance.

3. Hyper-parameter & sensitiveness:

   1. We report the main hyperparameters tuning in Tab. 2. Other hyperparameters are (1) set to 1, e.g. regularization weight except the second term in Eq. 11; (2) set to common values, e.g. $\beta$ = 0.25 for all VQVAE-related method; (3) selected by pseudo validation set with rotation/blurring as OODs, e.g. $\alpha_{1}$...$\alpha_{3}$ in Eq. 12.

   2. Number of modulation stages: We test our model on dSprite and find the results is not sensitive to modulation stages as long as it is not too limited.

      $\sharp$ Stages	AUC(%)
      0	57.6
      1	97.5
      2	99.0
      3	99.9
      4	100.

   3. Regularization weights: We set most regularization weights to 1, because they are not adversarial to the reconstruction objective. The only exception is the weight of $L_{mod}$, but it is not sensitive as shown in the table below:

      $\gamma$	CIFAR10-OC	FMNIST-OC
      0.1	90.4	96.4
      0.25	90.9	96.3
      0.5	91.0	96.4
      0.75	91.2	96.3
      1	91.3	96.2
      baseline	86.0	95.4

Dear Reviewer oBBb,

As the rebuttal period is ending soon, we kindly wonder if our responses answer your questions and address your concerns. Please let us know if there are any further questions.

1. Spatial transformation vs. common data augmentation: We assume you are referring to replace spatial transformation with image space augmentation. The problems are as follow:
   1. It is difficult to figure out how explicit data augmentations can be implemented, since most of them are non-differentiable and difficult to train end-to-end. This causes another issue that the model cannot be diversity-agnostic.
   2. Limited hand-crafted augmentation cannot span a representation space covering all ID diversity. For IDs, this means most diversity beyond rotating or flipping cannot be reconstructed well. For OODs, this means there are still a lot of untrained regions in the representation space which may fail to suppress OODs.
   3. We cannot assume that the augmented results still stay on ID manifold, e.g. image after MixUp is not a real ID image any more and may becomes OOD in the interpolation path (see [1] for more details).
   4. Actually, Fig. 2 does not mean that BiRDM can be regarded as a kind of simple data augmentation like rotation. It captures diversity-agnostic non-semantic factors of natural images restrictly beyond rotation, flipping, clipping, etc. and restores them with prototypical ID features.
2. Hyper-parameter: We report the main ablation of hyperparameters in Tab. 2. Other hyperparameters are (1) set to 1, e.g. regularization weight except the second term in Eq. 11; (2) set to common values, e.g. $\beta$ = 0.25 for all VQVAE-related method; (3) selected by pseudo validation set with rotation/blurring as OODs, e.g. $\alpha_{1}$...$\alpha_{3}$ in Eq. 12. Besides, the weight $\gamma$ of $L_{mod}$ in Eq. 11 is not sensitive as shown in the table below:

3. Fairness
   1. Fairness of using intermediate features: All reconstruction-based methods (the second group in table: RD, RD++, Tilted, VQ, DMAD, BiRDM) are based on the reverse distillation framework and use multiple intermediate features.
   2. Fairness of using auxiliary data: For compared reconstruction-based methods, using auxiliary data will lead to serious performance drop. Note that only BNSim (cooperating with SmoReg) benefits from auxiliary data as we reconstruct both IDs/OODs in a unified framework to push OODs away from prototypes (see Sec. 3.4 Remark for details).
   3. Implementation about auxiliary data:
      • Number: 1 batch of auxiliary data is optimized after every 5 batches of training data.
      • Type: We use Tiny ImageNet and CIFAR100 as auxiliary data (we use Tiny ImageNet if OOD dataset is CIFAR100 to ensure fairness).
      • Construction procedure: In brief, auxiliary features $z_{aux}^{demod}$ are adapted by BNSim to $z_{aux}^{sim}$, and then we reconstruct it as raw inputs $f_{aux}$. As shown in Fig. 4, ConvBN and Memory module are omitted during the reconstructing process of auxiliary data. See App. A Detailed implementation of BNSim for more details.

[1] Better mixing via deep representations, ICML 2013.

Thank you very much for your comments. Due to time limit, we would like to seek confirmation of your suggestion on experiment before formally replying all your concerns. Since App. C.3 provides experimental results on ImageNet subset (Weaknesses 3), we'd like to know more explicitly what kind of additional experiments you're interested in (Weaknesses 4)?

1. Novelties: The comments about lack of novelties are somewhat hasty. We hope to draw your attention to the overlooked MAIN CONTRIBUTIONS (NOT ONLY ARCHITECTURE) and clear up the misunderstood points.

   • The main contribution lies in GENERAL diversity modeling WITHOUT prior assumptions about the type of diversity patterns, which is necessary for semantic shift detection. In contrast, DMAD relies on structure-guided geometric-specific inductive bias thus can only deal with geometrical anomaly and cause performance drop in natural images.
   • BiRDM is NOT just a slight modification from DMAD. It has COMPLETELY DIFFERENT GENERALITY (general diversity vs. geometrical diversity), METHOD (smooth diversity representation and BN simulation vs. strong assumption about the positive correlation), IMPLEMENTATION (diversity-agnostic modeling via SmoReg and BNSim vs. structure-guided inductive bias), and PHENOMENON EXPLANATION (about smoothness, how to shape the latent space, the behavior of BN, disentanglement, etc.). These points are discussed in both main paper and appendix.
   • Check Sec.1, 3, App. B (in BiRDM), as well as last two paragraph in Sec. 3.1, first paragraph in Sec. 3.3, Limitation, App. E (in DMAD) for detailed reasons about how BiRDM is completely different from DMAD.

2. Previous work: We have discussed related works and fundamental methods in Sec. 1, 2, 3.1 and appendix (including the difference to DMAD). We briefly summarize the main background here:

   • Fundamental methods: Unsupervised reconstruction-based methods are trained on IDs to reconstruct IDs with high quality and potential OODs with low quality.
   • Trade-off about reconstruction quality: Memory models are necessary to prevent reconstructing OODs, since all prototypes are belong to ID. But discrete memory discards non-semantic patterns and suppress diverse IDs together.
   • DMAD and the KEY ISSUE: The solution is to restore non-semantic diversity of prototypes in a well-constrained way. However, DMAD rely heavily on the strong assumption that geometrical diversity is positively correlated with the severity of distribution shift and DMAD cannot restore other diversity in open-world semantic shift detection. In contrast, our BiRDM is general in modeling diversity-agnostic non-semantic patterns to facilitate semantic shift detection.

3. Presentation: We apologize for putting some implementation details and more experiments in the appendix due to space limit. The main consideration is to help readers to focus on the high-level motivations and methods before checking the implementation details. In the camera-ready version, we will include some key details in the experiments section.

4. Experiments: As you pointed out in W.3, we do have provided experimental results on ImageNet subset in App. C.3. And we add more experiments on ImageNet as you suggested in W.4. Besides, CIFAR10 is not simpler than large-scale ImageNet dataset according to [1], and the performance does not saturate as well.

   IN30	CUB	Dogs	Pets	Flowers	Food	Places	Caltech	DTD
   RD	62.6	67.2	68.0	87.4	65.4	64.3	54.6	81.5
   RD++	57.4	70.3	73.0	$\underline{91.0}$	66.6	61.3	50.6	$\underline{85.5}$
   Tilted	66.9	78.8	81.4	90.4	67.8	61.8	58.0	79.6
   VQ	67.0	$\underline{80.3}$	$\underline{81.9}$	87.7	67.9	66.1	$\underline{66.4}$	82.5
   DMAD	$\underline{67.7}$	74.2	76.3	87.8	$\underline{79.3}$	63.7	62.2	73.9
   BiRDM	82.0	84.8	87.2	93.7	86.0	$\underline{65.5}$	70.1	89.9

   IN100	iNaturalist	SUN	Places	DTD
   RD	85.0	60.3	56.8	$\underline{81.9}$
   RD++	83.5	49.9	52.8	80.4
   Tilted	73.4	$\underline{76.1}$	$\underline{72.3}$	76.4
   VQ	60.7	64.5	58.6	76.5
   DMAD	90.2	64.9	58.7	81.7
   BiRDM	$\underline{86.8}$	85.6	80.7	85.9

   [1] OpenOOD: Benchmarking Generalized Out-of-Distribution Detection, NeurIPS 2022.

Dear Reviewer CShN,

As the rebuttal period is ending soon, we kindly wonder if our responses answer your questions and address your concerns. Please let us know if there are any further questions.

W2-2.2&6.1-6.4 Alleviating the reconstruction-suppression trade-off is what BiRDM tries to do. Different components(memory, smooth diversity modeling, BN simulation) do not contradict to each other.

1. Since prototype learning is a relatively independent process constrained by VQ loss before modulation, the memory representation ability is affected by the number of prototypes but not diversity modeling.
2. BiRDM makes diversity representation capacity large enough to restore the residual ID diversity removed by memory, while OODs are much more difficult to be reconstructed by imposing SmoReg. The two targets are actually consistent with the smoothness regularized diversity modeling.
   • ID reconstruction: smoothly changing diversity modulation encourages ID projections to uniformly distribute in diversity space with low reconstruction error.
   • OOD suppression: Since OODs are also projected and truncated to this bounded, smooth and dense(via enough sampling $\tilde{z}_{diver}^{proj}$) diversity space, the projections will be close to IDs with high reconstruction error.
   • From the view of information theory, for OODs, information preserved in prototype quantization is $I(z_{OOD};Z_{ID}^{proto})$, and information preserved in diversity space after demodulation is $I(z_{OOD};Z_{ID}|Z_{ID}^{proto})$. Thus, a lot of OOD information has been lost:$H(z_{OOD}) - I(z_{OOD};Z_{ID}|Z_{ID}^{proto})- I(z_{OOD};Z_{ID}^{proto})>0$,causing high reconstruction error.
3. Non-semantic factors refer to ID diversity (e.g. style variations) and semantic factors refer to different clusters with semantic shift (e.g. different classes).
4. The only constraint contradictive to reconstruction target is $L_{mod}$ which constrains the modulation amplitude, but we show $\gamma$ is not sensitive:

W3 For compared methods, reconstructing auxiliary data leads to serious performance drop due to the undesired generalization. And we use auxiliary data in totally different way from previous works as mentioned in Sec. 3.4 Remark: 1. labels are not required for excluding IDs in auxiliary data; 2. we optimize both IDs and OODs with unified reconstruction objective to preserve enough semantic information.

W4 For compared methods, we search their hyperparameters on testing set (to save tunning skills), so their performance we reported should be higher than the reality. For our method, hyperparameters are: 1. set to 1, e.g. regularization weight except $L_{mod}$(not sensitive as shown above); 2. set to common values, e.g. $\beta$=0.25 is widely used for VQ-related method; 3. selected on pseudo validation set with rotation/blurring as OOD, e.g. $\alpha$ in Eq. 12. Hyperparameter tuning cost is comparable.

W5 We use TinyImageNet/CIFAR100 as auxiliary data(use TinyImageNet if OOD is CIFAR100 to ensure fairness); The modulation layer($M_{1}…M_{3}$) exactly matches StyleConv in StyleGAN2(receives an input from previous decoder layer and a style vector from corresponding diversity mapping); BiRDM uses the same decoder($D_{1}…D_{3}$) as Reverse Distillation(RD) to reconstruct encoded features, i.e. the architecture of our decoder layer is related to RD.

W6.5 BN somewhat increases the discriminative ability based on reconstruction error. However, reconstruction error alone may be disturbed by factors including background and texture. Therefore, quantization error is used to enhance the discriminative ability. To this end, BNSim is introduced to preserve semantic information of OODs so that they distribute far away from prototypes. We will clear up this point in our paper.

W6.6 We assume the question is: Since BNSim tracks ConvBN and ConvBN cannot discriminate between ID and OOD, why is the quantization error from BNSim features discriminative?

1. BNSim tracks ConvBN features only for training IDs. For auxiliary data including potential OODs, their BNSim features are different from ConvBN features and can be discriminative.
2. BNSim performs warped transformation in contrast to global affine transformation. By reconstructing auxiliary data without memory quantization, BNSim features of OODs tend to distribute far from prototypes with high quantization error.

EC.1 We revise explanation and illustration about Fig. 6 in the updated submission App. C3. Data split: 1. Training data is composed of ellipses located away from the centric region; 2. Auxiliary data contains hearts at all locations; 3. Testing data contains ellipses at the centric region(ID), and squares(OOD) at all locations;Model: BiRDM without SmoReg & BNSim; BiRDM with SmoReg only; full-components BiRDM.

Dear Reviewer k7Jp,

As the rebuttal period is ending soon, we kindly wonder if our responses answer your questions and address your concerns. Please let us know if there are any further questions.

We figure that the comment is a hasty copy paste from the review of our previous submission. There are full of serious misunderstandings and errors of fact for this paper.

1. Reviewer's intuition about compact prototypes is WRONG. We make clarification again as follows:

   1. Diversity modeling is necessary for semantic shift detection too. According to the basic assumption of reconstruction-based methods, our target is reconstructing diverse IDs with low reconstruction error and suppressing OOD reconstruction. Sec. 3.1, as well as DMAD, shows that if we learn finite prototypes (even though they are ``compact and discriminative'') only, diverse IDs beyond prototypes will be reconstructed as poor as OODs due to the limited representation capacity of prototypes and we cannot discriminate them by comparing reconstructed error.
   2. Due to the lack of real OODs, it is DIFFICULT for previous methods capture discriminative features, especially between diverse IDs and near-OODs. This is the reason why BiRDM tries to maintain the discriminative features by shaping a smooth non-semantic ID region and pushing potential OODs away.
   3. Although ID diversity is mainly related to covariate shifts, that DOES NOT implies that modeling ID diversity CANNOT benefits semantic shift detection. Actually, it can.
   4. For semantic detection, the geometrical prior used in DMAD is no longer available. We have to solve the trade-off dilemma in diversity-agnostic way, which makes BiRDM a completely different method to DMAD.

2. Most comments on experiments are not relevant at all.

   1. The paper only shows improvements on CIFAR10, ... The benchmarks used in [1] should also be considered

      Actually, We do have reported the performance on benchmarks used in [1], including ImageNet (in App. C as mentioned in Sec. 4.2).

   2. on FashionMNIST, authors claimed that it only contains image-level geometrical diversity ...

      We DO NOT claim like that in this paper. (By the way, we HAVE made clarification on this point in previous rebuttal which didn't get any attention.)

   3. The benchmarks used in [14] should also be considered.

      There is NO citation [14] at all. If you are referring to surveillance video and industrial images reported in DMAD (the citation index of DMAD used in our previous manuscript is [14]), researchers in OOD community never test these datasets (AD setting) because they include covariate shifts rather than semantic shifts.

   4. the ablation experiments are only conducted on a specific class of CIFAR10 ... It is important to show the overall-class performance.

      We DO have reported the overall-class performance in our ablation study, as shown in Tab. 2(a).

Dear Reviewer BvVD,

As the rebuttal period is ending soon, we kindly wonder if our responses answer your questions and address your concerns. Please let us know if there are any further questions.