Reviewer: The results on non-spurious OOD (NSP-OOD) is missing. I understand that this work mainly focuses on the SP-OOD, however, i am wondering that whether the proposed SPROD is also effective on NSP-OOD, or at least maintain the performance on NSP-OOD. This would significantly improve the contribution of this work. Therefore, the results on NSP-OOD are expected to present. I will raise the score once this concern is addressed.

Response:

We sincerely thank the reviewer for pointing this out. We agree that performance on standard non-spurious OOD (NSP-OOD) datasets is an important aspect, as it helps demonstrate the broader applicability and robustness of our method.

We would like to clarify that we have already included a dedicated section titled “Performance on Non-Spurious OOD Datasets” (Line 200 in the supplementary material). As shown in Table 6, SPROD consistently achieves near-perfect performance on all NSP datasets. However, the ID datasets in these experiments are the five datasets we used in the main paper (which have some degrees of spurious correlations). We focused on these datasets since they align with our core problem setup and we already had extensive experiments based on them.

In light of the reviewer’s helpful suggestion, we conducted additional experiments on three widely-used Standard OOD benchmarks: CIFAR-10, CIFAR-100, and ImageNet-1k, following the OpenOOD benchmark setup. Based on Table 1 of the OpenOOD paper, the in-distribution and corresponding OOD datasets are:

• CIFAR-10:
• Near-OOD: CIFAR-100, TinyImageNet
• Far-OOD: MNIST, SVHN, Textures, Places365
• CIFAR-100:
• Near-OOD: CIFAR-10
• Far-OOD: MNIST, SVHN, Textures, Places365
• ImageNet-1k:
• Near-OOD: SSB-Hard, NINCO
• Far-OOD: iNaturalist, Textures, OpenImage-O

To provide a meaningful comparison, we include results from the top-performing methods per dataset as reported in Table 2 of the OpenOOD paper:

• CIFAR-10: KNN, VIM
• CIFAR-100: MLS, RMDS
• ImageNet-1k: ASH

Below we present the OOD detection performance of SPROD alongside these methods:

These results indicate that SPROD performs on par or better than existing top methods in both near and far-OOD settings for standard benchmarks. Specifically, SPROD shows consistent performance across all datasets without any unusual degradation. We hope this addresses the reviewer’s concern and helps clarify the general applicability of our method beyond spurious OOD scenarios.

Reviewer: To demonstrate the generalization of proposed methods, the evaluate across different models such as ViT and BiT are expected to present.

Response:

Thank you for the suggestion. We have evaluated SPROD across a wide range of backbone architectures, including both convolutional (e.g., ResNet-18/34/50/101, BiT-R50x1) and transformer-based models (e.g., ViT-S, DeiT-B, DINOv2, Swin-B, ConvNeXt-B), as detailed in the Backbone Experiments section (Supplementary, line 237). Tables 8–31 report extensive results across four OOD metrics and five datasets. Specifically, Tables 8–11 present aggregated results, showing that SPROD consistently ranks among the top performers across all backbones, further demonstrating the method’s reliability.

Reviewer: Some baseline methods are missing such as GEN [1], NN-Guide [2], NECO[3] and FDBD[4].

Response:

We thank the reviewer for pointing out the absence of several recent post-hoc OOD detection methods, such as GEN, NNGuide, NECO, and fDBD. We agree that incorporating these methods strengthens the comprehensiveness and fairness of our evaluation.

To address this concern, we have conducted additional experiments on several state-of-the-art post-hoc techniques published between 2023 and 2025. The evaluations were performed using the same pretrained ResNet-50 backbone as in our main experiments (Table 2), ensuring a consistent comparison setting. The updated results are shown below:

As evident from the results, SPROD is consistently among the best-performing methods across all datasets. We will include extended results in the final version and revise the manuscript to compare against these additional baselines.

• [1] NNGuide: Nearest Neighbor Guidance for Out-of-Distribution Detection, ICCV 2023
• [2] RELATION: Neural Relation Graph, NeurIPS 2023
• [3] ASH: Activation Shaping for OOD Detection, ICLR 2023
• [4] GEN: Pushing the Limits of Softmax-Based OOD Detection, CVPR 2023
• [5] NECO: Neural Collapse Based OOD Detection, ICLR 2024
• [6] SCALE: Scaling for Training Time and Post-hoc OOD Detection, ICLR 2024
• [7] fDBD: Fast Decision Boundary-Based OOD Detector, ICML 2024
• [8] NCI: Detecting OOD through Neural Collapse, CVPR 2025

Reviewer: What is the (synthetic) datasets and model utilized to produce Figure 2?

Response:

Thank you for the question. For Figure 2, we use a synthetic dataset where class-conditional distributions are symmetric Gaussians in 2D. In the SP-OOD setting, each class contains two subgroups (majority and minority), each modeled as a Gaussian with different means and proportions to simulate spurious correlations. We will clarify these details in the final version.

Reviewer: Authors do not compare with recent baseline methods…

We appreciate the reviewer for pointing this out and fully agree that benchmarking against more recent methods is important for a comprehensive evaluation.

In our main experiments, we included 11 prominent post-hoc OOD detection methods, selected to represent a broad spectrum of prior approaches and to highlight their limitations under the spurious-OOD setting. We acknowledge, however, that several recent state-of-the-art methods from top-tier conferences have been proposed since 2023, many of which are available in the OpenOOD repository, as the reviewer correctly points out.

Using the same protocol and pretrained ResNet-50 backbone as in Table 2 of our main paper, the results are summarized below:

As seen, SPROD is consistently among the top-performing methods across datasets.

• [1] NNGuide, ICCV 2023
• [2] Relation, NeurIPS 2023
• [3] ASH, ICLR 2023
• [4] GEN, CVPR 2023
• [5] NECO, ICLR 2024
• [6] SCALE, ICLR 2024
• [7] fDBD, ICML 2024
• [8] NCI, CVPR 2025

Reviewer: This work should conduct experiments on general OOD datasets where the reasons are stated below…

We thank the reviewer for raising this important point. We agree that evaluating performance on widely used benchmarks provides a good indication of the general applicability of OOD detection methods.

While our primary focus is on the SP-OOD problem setup, we would like to clarify that SPROD is not limited to spurious OOD settings. In fact, our method does not make any assumption about the presence of spurious correlations. If unknown spurious correlations exist in the training data, SPROD aims to discover them for more robust OOD detection. This is further supported by our ablation study using datasets with only 50% spurious correlation, where SPROD still demonstrates strong performance, indicating its robustness across varying levels of spuriousness.

Following the reviewer’s concern, we have conducted additional experiments using CIFAR-10, CIFAR-100, and ImageNet-1k as in-distribution datasets. These experiments follow the standardized OpenOOD benchmark setup, where OOD datasets are selected according to Table 2 of the OpenOOD paper.

We report SPROD's performance alongside top-performing baseline methods, using values directly taken from the OpenOOD paper for fair comparison. The results are summarized in the table below:

These results show that SPROD remains competitive with the best-performing methods and achieves the highest average performance across all settings.

Reviewer: In table 2, results of FPR95 of SPROD is only the 4th comparing with other methods for the most complex dataset which is hard to insist it is the SOTA method.

We fully acknowledge that our method does not outperform all others across every scenario. However, a core strength of SPROD lies in its consistency across a wide range of datasets and model backbones. While some methods may excel on specific benchmarks, they often suffer from performance drops elsewhere. In contrast, SPROD consistently ranks among the top-performing methods across various settings. This is more comprehensively illustrated in Tables 8–11 of the supplementary material, which highlights SPROD’s stability and reliability.

One central goal of our paper is to broaden the experimental scope of Spurious-OOD detection. Prior work often focused on one or two datasets, limiting generalizability. We introduced the Animals MetaCoCo dataset to encourage evaluation under more diverse and realistic conditions. While this dataset enriches the benchmark space, it is not fully aligned with our method's assumptions: SPROD relies on misclassification signals to detect unknown spurious features. As shown in Table 5 (supplementary), the attribute imbalance in Animals MetaCoCo is highly entangled and lacks clear spurious correlations, unlike datasets such as Waterbirds or UrbanCars.

The SpuriousImageNet dataset poses additional challenges. As noted in line 192 of the supplementary material, many spurious correlations here fall under the "Class Extension" type (shortcut features that appear in one class but are not shared across others), thus not increasing misclassification risk. Since SPROD detects unknown spurious features via their impact on misclassification, it is inherently limited in such settings. We believe future methods with partial group supervision may be better suited for this dataset and further advance trustworthy AI. Nonetheless, we included SpuriousImageNet to promote more diverse evaluations, even though it is less compatible with our group-supervision-free framework.

Reviewer: Figure 4 doesn’t represent well how much the correlation between spurious correlation rate and performance drop as the results aren’t presented numerically. It doesn’t look like the best way to present the correlation as a reader.

The figure combines multiple dimensions of comparison into a single visualization (different baselines, two model backbones, two types of correlation metrics, and two training settings) and may have become too complex to clearly convey the correlation between spurious correlation rate and performance drop. To address this, we will revise the presentation by including a dedicated figure or table that focuses specifically on the correlation, with numerical values to improve clarity and interpretability for the reader. While our original intent was to offer a compact representation for breadth, we agree that a focused presentation would better serve the reader.

Reviewer: The authors argue that generative scoring is better than discriminative scoring and present proper experimental configurations. However, results show no difference when datasets get more complex. Showing better performance only on simple dataset doesn’t indicate it is a better scoring method. Therefore, I doubt the fact of this statement.

We agree that in some datasets, even for a fixed method such as SPROD, the difference between discriminative and generative scoring is negligible. Indeed, we do not claim that the generative approach will always outperform the discriminative one. As we indicated in line 132, we indicate that softmax-based (discriminative) scoring fails in certain cases.

A trivial but illustrative case is presented in Figure 2 (a), which shows a scenario where OOD samples lie far from all class distributions. In such cases, discriminative scoring, which only relies on distance to the decision boundary, may incorrectly identify far-away OOD samples as in-distribution, simply because they are marginally far from the decision boundary than some ID samples.

In contrast, as shown in Figure 2 (b), generative scoring (based on distributional distance) can easily detect these far-OOD samples. Further in the SP-OOD setting, we highlight an additional risk introduced by biased decision boundaries. A recent study also emphasizes that discriminative classifiers are particularly sensitive to spurious shortcuts [1].

Finally, we would like to point out that this discussion primarily serves as a motivational context for our proposed method and is not a core axis of the paper. We believe this direction deserves a dedicated study to fully explore its theoretical and experimental implications.

[1] Generative Classifiers Avoid Shortcut Solutions, ICLR 2025

Reviewer: Table 1 in Supplementary should be in the main manuscript as it is comparing with related methods.

We agree that Table 1 in the Supplementary provides a valuable comparison in the multi-modal domain. The main reason we did not focus on CLIP-based experiments is explained in both Section A.1 of the Supplementary and in the main paper (line 251). For example, the zero-shot setup of CLIP often bypasses spurious correlations in the training data, which limits its usefulness for studying how methods respond to spurious attributes during learning, which is a primary concern of our study.

That said, given the increasing attention on CLIP-based settings in recent research, we will include a small comparison table in the main paper for the final version.

Thank you very much for addressing the concern related to the importance of spurious correlation in common datasets and I acknowledge the importance of the spurious correlation in datasets as well as SPROD's robustness on spurious correlations. However, there are a few concerns left.

Most existing methods are over-tuned to these general benchmarks and may exhibit vulnerability in the presence of inherent biases and distribution shifts.

In order to verify this statement, I recommend conducting OpenOOD full-spectrum, where distribution of ID samples are shifted, with RegNet-Y-16GF backbone for comparison.

Baseline comparison

• Despite that general OOD methods overlook the spurious correlation in datasets they still perform better than SPROD as shown in the comparison below. In this case, the practicality of SPROD is limited to datasets with high spurious correlation and won't be able to be used in general usage which is my concern related to the suggested method. For example, assuming a situation where users need an OOD model, which model would the users adopt? Even though SPROD solves the spurious correlation problem in ImageNet1k and classify classes with spurious correlations well, if it falls behind in other classes without spurious correlation in OOD detection, the practicality is doubted, which is why the general OOD performance is critical.

• Authors insist that SPROD performs 85% for OpenOOD near-OOD benchmarking with ConvNeXt-B backbone and insist that most of the methods fall behind, however, the comparison with those baselines aren't done with the same backbone, therefore, it would be fair to compare using the same ConvNeXt-B backbone with recent methods to verify this statement.

Below is the organized results of SPROD and SOTA baseline methods on OpenOOD benchmarking with near-OOD AUROC results.

• AdaScale: Authors insist that the reporting of OpenOOD is not credible as the reported value in the leaderboard and manuscripts are different. However, even with the results in the AdaScale paper Table 1, results of ResNet50 and RegNet-Y-16GF show higher performance than SPROD. Also, it is shown that their transformer baseline methods specifically show low performance, however, the CNN based methods perform well. SPROD shows advantage in transformer based methods, however, fall behind the performance for ResNet50 and RegNet-Y-16GF, and the reported results of ConvNeXt-B, which shows higher ID accuracy in ImageNet1k than RegNet-Y-16GF, falls behind AdaScale-RegNet-Y-16GF.
• Comparing with NNGuide, which is an ICCV2023 paper, the performance with RegNet-Y-16GF underperforms.
• Comparing with MDS++, the performance with RegNet-Y-16GF underperforms.
• Comparing with RMDS++, SPROD underperforms for ResNet50 and RegNet-Y-16GF.

Furthermore, authors insist the reporting of OpenOOD is not credible, then the only suggested way for the authors is to implement the methods shown above on the OpenOOD benchmark and verify the results.

Clarifications regarding AdaSCALE's reporting

AdaSCALE for OpenOOD Leaderboard Setup

Additional Datasets for Evaluation in the Paper

Note the inclusion of ImageNet-O and Places OOD datasets.

The setup for the above two are different and hence the difference in the results. The results are not inflated, please check the OOD datasets that are evaluated in the paper.

Note: I just noticed this.

Discussion of prior work:

Reviewer: My main concern is the lack of discussion or comparison with prior prototype-based OOD detection work. In recent years, several studies have explored prototype-based frameworks, and in this context, the proposed method does not appear significantly novel. The main contribution seems to lie in its focus on spurious OOD detection, rather than in introducing a fundamentally new technique.

We appreciate the reviewer’s comment and agree that prototype-based approaches form a relevant and valuable category in OOD detection research.

We would like to clarify several points regarding both novelty and comparison:

• In our main paper (line 171), we explicitly highlight the strength of the pure prototypical method (SPROD-1), which we believe has been overlooked in prior post-hoc OOD literature. To the best of our knowledge, no previous work presents this vanilla prototypical approach as a standalone post-hoc baseline for OOD detection.

• We build upon this strong baseline by introducing two further stages that aim to reduce the effect of spurious biases through prototype splitting and refinement, resulting in a novel three-stage post-hoc framework.

Regarding the third cited work, Learning with Mixture of Prototypes (PALM), we were indeed aware of it. However, PALM involves a heavy training procedure with a specifically designed objective and therefore is not compatible with our post-hoc setting. That said, we found its ideas inspiring and included a dedicated section in the supplementary material titled "Analysis of Mixture of Prototypes" (line 265). In this section, we introduce a KMeans-based variant of SPROD that mirrors PALM’s core idea of intra-class prototype diversity, but implemented in a fully post-hoc manner without any retraining. Results in Tables 32–33 show that this KMeans variant achieves competitive performance, especially on datasets where spurious correlations are less prominent (e.g., Spurious ImageNet, where the main bias is class-extension and does not induce inter-class confusion).

Finding DINO (PROWL) also leverages prototype ideas, but it is designed for a different domain (pixel-level OOD detection in segmentation), making it less comparable to our classification-based setting. While POT is another recent work using prototypes, it is not peer-reviewed, and we could not find a working public implementation.

Theoretical or Conceptual justification:

Reviewer: While the empirical results demonstrate the effectiveness of the method, it is not entirely clear how or why the group prototype refinement specifically helps in addressing spurious OOD detection. A deeper theoretical or conceptual justification would strengthen the contribution.

SPROD employs a two-step prototype refinement strategy to approximate group-specific prototypes within each class. First, it defines prototypes for correct and misclassified training samples, motivated by the observation that minority group instances are more prone to misclassification [JTT paper]. However, some correctly classified from minority samples may still be incorrectly assigned to biased prototypes. To address this, SPROD reassigns all training samples to their nearest prototype and recalculates the prototypes, reducing the majority prototype influence (see Figure 3).

By applying these two steps, SPROD aims to obtain nearly pure group-specific prototypes. We now provide a theoretical overview, to illustrate the systematic bias introduced by standard prototypical methods under strong spurious correlations, motivating the refinement of group-specific prototypes to eliminate this bias.

• [1] Just Train Twice, ICML 2021

Feature Decomposition

Without loss of generality, we assume a binary classification problem with classes $c \in \{0,1\}$. We consider a general decomposition of embeddings $z_i$ into three semantically distinct components: spurious, core, and irrelevant features. We model $z_i$ as a linear combination of three functionally distinct components that span the embedding space:

where the vector sets $\{u_{c,j}^{sp}\}$, $\{u_{c,j}^{core}\}$, and $\{u_{j}^{irr}\}$ form orthonormal bases for the spurious, core, and irrelevant subspaces. Each coefficient set $\{\alpha_{i,j}^{sp}\}$, $\{\beta_{i,j}^{core}\}$, and $\{\gamma_{i,j}^{irr}\}$ is specific to instance $i$. This decomposition can be expressed compactly in matrix form:

where each $U^{(\cdot)} \in \mathbb{R}^{d \times n_u^{(\cdot)}}$ is a matrix of orthonormal basis vectors. We assume the coefficient vectors for each instance $z_i$ are drawn from class-conditional distributions: $\alpha_i^{sp} \sim P_c^{sp}$ and $\beta_i^{core} \sim P_c^{core}$, while the irrelevant component is shared across classes, i.e., $\gamma_i^{irr} \sim P^{irr}$.

Group Definitions

Within each class $c$, Majority group samples $z_i \in S_c^{maj}$ satisfy $\alpha_i^{sp} \sim P_c^{sp}$, $\beta_i^{core} \sim P_c^{core}$. Minority group samples $z_i \in S_c^{min}$ satisfy $\alpha_i^{sp} \sim P_{1-c}^{sp}$, $\beta_i^{core} \sim P_c^{core}$.

The ratio $r_c = \frac{|S_c^{maj}|}{|S_c^{maj}| + |S_c^{min}|}$ quantifies the class-conditional spurious correlation strength.

OOD Sample Definition

We define an OOD sample as:

where $\alpha_{OOD}^{sp} \sim P_c^{sp}$, $\gamma_{OOD}^{irr} \sim P^{irr}$, and $\delta_{OOD}^{ext}$ and $U^{ext}$ capturs external factors not observed during training.

Hard OOD samples may also include core components drawn from a shifted distribution

For simplicity, we focus on near-OOD samples with no core or external components with $\beta_{OOD}^{core} = 0$ and $\delta_{OOD}^{ext} = 0$.

For spurious-OOD groups, $\alpha_{\text{OOD}}^{\text{sp}}$ is non-zero; in challenging cases, it follows the same distribution as the class spurious component $\alpha_{\text{OOD}}^{\text{sp}} \sim P_c^{\text{sp}}$.

Prototype Calculation

We define the expected coefficient vectors for each subspace:

Using these, we define the majority and minority group prototypes for class $c \in \{0,1\}$ as:

The overall class prototype is a convex combination of subgroup prototypes:

Bias in Prototype Distances Under Strong Spurious Correlation

Consider spurious-dominated regimes where $r_c \approx 1$, then we have

Let $z_{\text{OOD}} \in S_c^{\text{OOD}}$ be an OOD sample with spurious alignment to class $c$. The score is defined as the negative Euclidean distance to the nearest prototype. The expected squared distance to the biased class prototype is:

Here, the first term corresponds to core bias, the second to spurious variance, and the third to irrelevant variance. Now consider an in-distribution sample from the minority group. Its expected squared distance to the majority prototype (biased class prototype) is:

In this case, the first term represents spurious bias, followed by core variance and irrelevant variance, respectively. Although $z_{min}$ is an in-distribution sample, its distance to the biased prototype includes a spurious bias term, while the OOD sample differs only in the core direction. Depending on the relative magnitudes of the core and spurious bias terms, this highlights the potential for erroneous OOD detection.

For example, in the Waterbird dataset, the background (water or land) represents the spurious means $\mu_c^{sp}$ and $\mu_{1-c}^{sp}$. The difference $\|\mu_c^{sp} - \mu_{1-c}^{sp}\|$ may exceed the core bias in OOD distances, leading to incorrect OOD detection.

Why SPROD Mitigates Distance Bias

If prototypes can be accurately estimated to match each group's distribution, then each in-distribution sample $z_i \in S_c^g$ can be compared to its corresponding prototype $\hat{p}(z_i) = p_c^g$, where $g \in \{maj, min\}$. Because the prototype shares the same spurious basis alignment, the spurious bias is eliminated. The expected squared distance becomes:

reflecting variance only, with no bias terms. In contrast, the standard prototype-based approach contains a spurious bias for minority samples:

For a spurious-OOD sample, we also observe a core bias component:

Comparing this to the expected squared distance of in-distribution samples using group-specific prototypes, we also conclude:

Dear Reviewer, we would appreciate an opportunity to further discuss/address any concerns that might remain after our rebuttal response.We hope to hear back from you. Thanks!

Hi Reviewer jXq2,

Could you check whether the authors' rebuttal address your concerns? If further clarification is needed, please engage in the discussion during the discussion phase.

AC

In view of the extended discussion period, we hope to still hear back from you regarding the unresolved concerns!

Reviewer Comment: Although the article pays more attention to the experimental performance of SP-OOD, we still hope that the author can provide some experimental results on the NSP-OOD and conventional OOD datasets. The real-world OOD dataset should be a combination of multiple OOD data. We can see that this method in the paper can improve the detection performance of SP-OOD without sacrificing the detection performance of other OOD types.

Response:

We thank the reviewer for highlighting this important point. We agree that demonstrating robustness beyond SP-OOD serves as a valuable complementary analysis to further validate the general applicability of our method.

Regarding NSP-OOD, we refer the reviewer to the dedicated section titled "Performance on Non-Spurious OOD Datasets" (line 200) in the supplementary materials. As shown in Table 6, SPROD consistently achieves near-perfect detection performance across all NSP datasets, further supporting its broad robustness.

Regarding conventional OOD datasets, we initially focused on SP-OOD-related benchmarks due to their alignment with our problem setting and the extensive number of experiments required. However, we have now extended our evaluation to conventional datasets including CIFAR-10, CIFAR-100, and ImageNet-1k to demonstrate the reliability and generality of SPROD. We follow the OpenOOD benchmark protocol for post-hoc methods. For fair comparison, we selected the best-performing methods for each dataset as reported in Table 2 of the OpenOOD paper:

• CIFAR-10: KNN and VIM for near-OOD and far-OOD, respectively
• CIFAR-100: MLS and RMDS for near-OOD and far-OOD, respectively
• ImageNet-1k: ASH as the top-performing method

The following table reports SPROD’s performance alongside these methods, with values for baselines taken directly from the OpenOOD paper:

These results show that SPROD remains competitive with the best-performing methods on general OOD benchmarks and achieves the highest average performance across all settings.

Reviewer Comment: The article lacks some ablation experiments. The author can supplement some relevant ablation experiments, such as proving the effectiveness of stage 2 and stage 3.

Response: We agree that ablation studies are important for understanding the effectiveness of individual components. In Section Ablation Study on SPROD Stages (Supplementary, line 216), we include a dedicated analysis isolating each of the three stages of SPROD on the Waterbirds dataset under varying spurious correlation strengths (50% and 90%). Results in Figures 6 and 7 show that while Stage 1 provides a strong baseline, Stages 2 and 3 further enhance robustness under stronger spurious correlations.

Reviewer Comment: Currently, the application of CLIP in OOD detection is a research hotspot. I wonder how the proposed method can be used in OOD detection based on CLIP. Because the comparison method in the article lacks the comparison of 2023-2025 methods in recent years.

Response:

Regarding CLIP-based methods

We appreciate the reviewer’s interest in recent CLIP-based approaches, which indeed represent an important direction in OOD detection research. We would like to clarify that our submission includes a dedicated comparison with CLIP-based methods in the supplementary material, specifically in Subsection A.1 (line 75). In this subsection, we present both quantitative results (Table 1) and detailed performance plots (Figures 1 and 2). Our results show that SPROD achieves state-of-the-art performance in this CLIP-based setup, further validating its generality and robustness.

Additionally, in both this subsection and the main paper (line 251), we briefly discussed our reasons for not focusing extensively on CLIP-based experiments. In particular, the zero-shot setup of CLIP tends to bypass the effects of spurious correlations in the training data (which are central to our study) making it less suitable for analyzing how methods handle spurious attributes during learning.

Regarding 2023-2025 methods

In our main experiments, we selected 11 prominent post-hoc OOD detection methods, aiming to cover a broad range of representative techniques and to highlight their limitations in the spurious-OOD setting.

To further address the concern regarding more recent methods (2023–2025), we additionally evaluated SPROD against 8 state-of-the-art post-hoc methods on the pretrained ResNet-50 backbone (mirroring our second table in the main paper). The results are summarized below:

SPROD maintains consistently strong performance across all tasks and achieves the highest average AUROC among all methods.

1. NNGuide: Nearest Neighbor Guidance for Out-of-Distribution Detection, ICCV, 2023
2. RELATION: Neural Relation Graph: A Unified Framework for Identifying Label Noise and Outlier Data, NeurIPS, 2023
3. ASH: Extremely Simple Activation Shaping for Out-of-Distribution Detection, ICLR, 2023
4. GEN: Pushing the Limits of Softmax-Based Out-of-Distribution Detection, CVPR, 2023
5. NECO: NEural Collapse Based Out-of-distribution Detection, ICLR, 2024
6. SCALE: Scaling for Training Time and Post-hoc Out-of-distribution Detection Enhancement, ICLR, 2024
7. fDBD: Fast Decision Boundary based Out-of-Distribution Detector, ICML, 2024
8. NCI: Detecting Out-of-distribution through the Lens of Neural Collapse, CVPR, 2025

Reviewer Comment: In Figure 3 of the article, the square ICONS and other items are not specified.

Response:

Thank you for pointing this out. The purple squares in Figure 3 represent spurious OOD samples. We labeled them in Figure 2 but inadvertently omitted the legend in Figure 3. We will correct this oversight in the camera-ready version.

Dear Reviewer, we would appreciate an opportunity to further discuss/address any concerns that might remain after our rebuttal response.We hope to hear back from you. Thanks!