Towards Single-Source Domain Generalized Object Detection via Causal Visual Prompts

We thank you for your constructive feedback and positive assessment of our work. We greatly appreciate your recognition of our clear and reasonable motivation, the clarity of the paper's organization and figures, and the extensive nature of our experiments. We hope our detailed responses below can address your remaining questions.

W1: Contributions are unclear and ask for clarification of how our approach differs from and innovates beyond existing methods.

We believe that our previous description may not have sufficiently highlighted the fundamental differences between our work and [1-3], which may have led to a misunderstanding of our contribution.

First, the core setting of our work is Single-Domain Generalization for Object Detection (SDGOD), which is fundamentally different in its problem definition from the Domain Adaptation (DA) field to which the cited references [1-4] belong. The core premise of DA methods is access to unlabeled target domain data during training for distribution alignment. In contrast, the SDGOD setting is far more stringent, with absolutely no access to any target domain data during training. It requires the model to learn solely from a single source domain and generalize to any unseen domains. This key distinction means that methods designed for DA, which rely on target domain data, cannot be directly applied to SDGOD.

Second, our method's design philosophy is also fundamentally different from these works. Unlike the text prompts used in works [1-3]—where text inherently carries a domain-invariant prior due to its semantic abstraction—our visual prompts do not rely on any external modality and are learned "from scratch." This forces the model to actively mine generalizable knowledge solely from the single source domain. Regarding work [4] (DA-Ada), the core of its adapter design is to learn source- and target-specific knowledge separately, which relies on accessing unlabeled target data during training. In contrast, our dual-branch adapter operates under the SDGOD setting with no visibility of the target domain, and its goal is to identify and suppress source-specific, potentially harmful spurious features. Therefore, our work is conducted under a much more challenging setting.

To illustrate the point, our method was compared with several advanced Domain Adaptation (DA) methods. On the Cityscapes -> Foggy Cityscapes and Sim10K -> Cityscapes tasks, the results are shown in the table below:

It is important to emphasize that DA methods have access to unlabeled data from the target domain (Foggy Cityscapes) during training, which gives them a natural advantage. Therefore, while our method shows significant improvement over the strong baseline (from 48.0% to 56.1), its performance is comparable to some of the DA methods.

However, the true test of generalization capability lies in scenarios with a large domain gap between the source and target domains. The Sim10K -> Cityscapes task (S->C column) represents such a stringent and realistic setting, where the source domain consists of synthetic data and the target domain is real-world imagery. In this setting, our Cauvis method significantly outperforms all Domain Adaptation (DA) methods, with a lead of 2.9% over the best-performing method, DA-Ada [4]. This strongly demonstrates the superior generalization capability of our method in the "synthetic-to-real" scenario.

Based on this, we would like to directly address your concern that "the contribution of introducing DINOv2 is not strong." In the highly challenging field of SDGOD, exploring and leveraging more powerful Vision Foundation Models (VFMs) has become a recognized trend and a core competitive point for pushing the state of the art and breaking through performance bottlenecks. For instance, prior work such as CLIP the Gap [5] explored the potential of CLIP, while UFR [6] incorporated SAM to generate masks for extracting domain-invariant representations. This indicates that the choice of VFM and how to leverage it is a core research question in this domain.

Our primary contribution, therefore, is that through systematic research and experimentation, we identify DINOv2 as a more suitable foundation model for the SDGOD task than other VFMs used in previous works (like CLIP and SAM). Our experimental results (as shown in the table below) overwhelmingly outperform prior methods based on other VFMs, which strongly validates the correctness and forward-thinking nature of our technical approach.

W2: Performance of the baseline method has greatly exceeded that of the existing algorithm, because used the DINOv2.

First, we believe that in the era of Foundation Models, exploring and leveraging more powerful pre-trained models like DINOv2 to push the performance ceiling of the highly challenging SDGOD task is an inevitable direction for the field's development. We consider the successful identification and validation of DINOv2's significant potential for the SDGOD task to be an important contribution of our work in itself, as it provides a higher and more challenging starting point for subsequent research.

We fully agree that the most ideal way to compare would be to integrate DINOv2 as the backbone into all prior SOTA methods (like UFR, Clip the Gap) and then conduct a fair comparison. However, in practice, we encountered an insurmountable obstacle: these key SOTA works have not released their official source code. This made it impossible for us to replace the backbone network within their frameworks to conduct a rigorous comparison, which is a practical dilemma within the field.

Therefore, to validate the effectiveness of our method (Cauvis) in the fairest and most rigorous manner, we adopted what we believe to be the most transparent and scientific alternative: we first combined DINOv2 with a standard Faster R-CNN detector to create the "Faster R-CNN + DINOv2" baseline. The performance of this baseline itself, as you noted, is already very strong. The core of our experiment, therefore, is to benchmark our method, Cauvis, against this powerful new baseline. For clarity, Table 2 and 3 from our paper is shown again below, compared to "FR + DINOv2," our Cauvis method still achieves significant performance improvements (e.g., a 2.9% increase on Night Clear, 2.3% on Dusk Rainy, 1.7% on Day Foggy and 6.3% on Cityscapes-C).

W3: More proposed methods that use prompt and adapter designs should be discussed.

We thank you for your valuable suggestion. As detailed in our response to Weakness #1, our work operates under the more challenging Single-Domain Generalization (SDGOD) setting, which is fundamentally different from the Domain Adaptation (DA) methods in [1, 4]. It is precisely this difference in setting that leads to the fundamental innovation in our methodology. For example, unlike [1], our approach does not rely on the inherent semantic invariance of text prompts. Instead, it requires our visual prompts to learn entirely "from scratch," actively mining generalizable knowledge from the single source domain without any information about the target domain. Similarly, in contrast to DA method [4], which learns specialized knowledge for specific domains, our goal is the opposite: to actively discard source-specific spurious features to achieve generalization to any unseen domain, all without ever seeing the target domain. This ultimately highlights the fundamental difference in philosophy between our work and these methods—we pursue "generalization" rather than "adaptation."

For a direct comparison, we conducted a synthetic-to-real generalization experiment (Sim10k->Cityscapes) to benchmark against DA works, with results shown in Table W1. Even without any access to target domain data, our method achieves a 2.9 improvement over [4], demonstrating its strong generalization capability.

We will add a discussion of these DA methods and make corresponding revisions in our updated manuscript.

[1] Learning domain-aware detection head with prompt tuning. NeurIPS 2023

[2] Domain adaptation via prompt learning. TNNLS 2023

[3] SEEN-DA: SEmantic ENtropy guided Domain-aware Attention for Domain Adaptive Object Detection. CVPR 2025

[4] Da-ada: Learning domain-aware adapter for domain adaptive object detection. NeurIPS 2024

[5] Clip the gap: A single domain generalization approach for object detection. CVPR 2023

[6] Unbiased faster r-cnn for single-source domain generalized object detection. CVPR 2024

[7] Stronger fewer & superior: Harnessing vision foundation models for domain generalized semantic segmentation. CVPR 2024.

[8] SoMA: Singular Value Decomposed Minor Components Adaptation for Domain Generalizable Representation Learning. CVPR 2025.

Thank you for your insightful review and for recognizing our paper's clarity (concise, easy to follow) and our method's high efficiency and substantial generalization gains. We have provided detailed responses to each of your points below.

W1: Training Cost.

In the field of Parameter-Efficient Fine-Tuning (PEFT), the standard practice for evaluating the overhead of a new module is primarily to measure the number of its additional trainable parameters. This is because for large foundation models like DINOv2, the vast majority of the inference cost is dominated by the backbone itself. The marginal latency added by lightweight PEFT modules is often too small to be reliably measured and can be heavily influenced by system-level optimizations. Therefore, trainable parameters serves as a more stable and direct metric for measuring the additional computational burden.

To quantify the overhead of our method using these standard metrics, we provide a comparison with other recent PEFT works.

As shown in the table, our method, Cauvis, is highly competitive in terms of parameter efficiency. With 4.9M parameters, it is on par with other state-of-the-art methods and is even more efficient than some approaches, such as AdapterFormer (6.3M). Crucially, these added parameters constitute only a tiny fraction (~1.6%) of the DINOv2 backbone's 307M total parameters. This quantitatively demonstrates that the inference overhead introduced by our prompt and dual-branch adapter is minimal, which aligns with the core philosophy of parameter-efficient tuning.

W2: Other corruption benchmarks.

Following your valuable suggestion, we have conducted comprehensive new experiments on two additional benchmarks, Foggy Cityscapes and BDD100K-C.

First, for the Cityscapes -> Foggy Cityscapes and Sim10K -> Cityscapes tasks, we used DINOv2 as the backbone and Faster R-CNN as the base detector for a fair comparison.

On the Cityscapes -> Foggy Cityscapes task (mAP column): As shown in the mAP column in the table above, compared to the strong DINOv2 baseline, our Cauvis method significantly boosts the mean Average Precision (mAP) from 48.0% to 56.1%, achieving a substantial gain of 8.1%. This clearly demonstrates that our method can effectively resist the domain shift caused by real-world weather conditions (like fog), enhancing the model's robustness.

On the Sim10K -> Cityscapes task (S->C column): This task is a more stringent and classic test of generalization capability, as it requires the model to generalize from synthetic data to a completely different real-world distribution. Under this setting, our method still achieves a significant performance improvement of 3.6% (from 66.6% to 70.2%). This indicates that our method can not only handle specific types of corruption but also learn domain-invariant essential features, thus successfully bridging the large gap between synthetic and reality.

Furthermore, we conducted a comprehensive evaluation on the more challenging corruption benchmark, BDD100K-C, with the results shown below.

This experiment clearly demonstrates that across 15 different types of real-world corruptions, our Cauvis method achieves consistent and significant performance improvements over the strong baseline (FR+DINOv2), boosting the mPC from 41.3% to 43.6%. This strongly validates that our method can effectively enhance the model's robustness in diverse, real-world scenarios.

W3: harsh-weather conditions are used as source domain.

Thank you for your valuable feedback. Considering that data collection for challenging scenarios is often difficult, the research paradigm of generalizing from simple to adverse scenarios is more widely adopted.

To thoroughly address this point, we have conducted three new sets of experiments. In these experiments, we use challenging conditions as the source domain and generalize to the clear-weather (Day Clear) target domain.

In the first generalization experiment (Day Foggy -> Day Clear), we used foggy weather as the source domain. As shown in the table, our method performed excellently, significantly boosting the mAP from 48.2% to 56.7%.

In the Dusk Rainy -> Day Clear task, our method improves the mAP from 47.0% to 58.9%, once again validating its strong performance for generalization in the "hard-to-easy" direction.

Finally, we tested the generalization from Night Clear -> Day Clear. Our method once again provides a clear advantage, raising the mAP from 63.7% to 66.1%.

Our method's generalization is robust across diverse challenges (harsh weather) because it is not tied to a specific difficulty type. It effectively disentangles essential object features from spurious domain correlations (e.g., fog, rain), ensuring strong performance in varied scenarios.

W4: Hyperparameter choices for prompt length and adapter.

Regarding the prompt length, we would like to clarify that the relevant analysis is already included in Figure 4 of our paper. To present the results more clearly in this response, we provide the data in the table below. The study shows that performance does not significantly improve as the length increases; however, the best performance is achieved when the length is aligned with the sequence ($L_{seq}$).

For our dual-branch adapter, its design does not introduce complex new hyperparameters that require tuning. Its effectiveness comes from its specific architectural components. Therefore, to justify our design, we conducted comprehensive ablation studies by replacing the core components with other common and reasonable alternatives. The following experimental data all come from Table 4 of the paper.

a) Causal Branch. We evaluated the effect of replacing our simple causal mapping function with more complex alternatives. The results below show that our current design achieves superior or highly competitive performance, validating that increasing the complexity of this branch is not beneficial.

b) Auxiliary Branch. We also validated the design of our auxiliary branch (based on FFT). The results show that our current implementation, which performs implicit regularization through the Fourier domain, is more effective than explicitly adding a mask to the Fourier components or removing the branch entirely.

These extensive experimental studies confirm that our method is robust to the choice of prompt length, and that our Adapter is a well-justified design, validated through comparisons with multiple alternatives. We will ensure these justifications are more prominent in the revised manuscript.

Q1: training to 12 epochs

We chose a fixed 12-epoch training schedule to strictly follow the standard baseline protocol (e.g., the 1x schedule for Faster R-CNN) to ensure a fair comparison. This ensures that our performance gains stem from the architectural design, rather than from special adjustments to the number of training epochs.

Furthermore, we fully agree that selecting the "best source-domain checkpoint" is a standard practice in Domain Generalization (DG). We analyzed the performance of each epoch (see table below)

Therefore, even if we were to adopt the "best source-domain checkpoint" strategy, we would still select the model from epoch 12. This demonstrates that our currently reported results are robust and in line with best practices.

Q2:Using harsh-weather conditions as the source domain.

For the detailed results, tables, and a full analysis, please refer to our detailed response to W3.

Thank you for your constructive review. We are very pleased that you found our paper easy to follow and our method intuitive. We also appreciate you recognizing that our experiments are extensive. We hope our detailed responses below can address your remaining questions.

W1: Domain adaptation works.

Clarifying the connections and distinctions between our work and these Domain Adaptation (DA) methods is crucial for accurately positioning our contribution. Below, we elaborate from two perspectives: technical commonalities and core differences.

First, at the level of technical tools, our work shares commonalities with [1,2]. Both leverage Parameter-Efficient Fine-Tuning (PEFT) techniques (such as prompting and adapters) to modulate a powerful pre-trained model to address cross-domain visual recognition problems. This demonstrates the significant potential of PEFT techniques in handling domain shift issues.

However, there is a fundamental difference in the core task setting and methodological innovation, which constitutes the main contribution of our work. Our work focuses on Domain Generalization (DG), which aims to learn a model from a single source domain that can generalize to any unseen target domains. In contrast, [1,2] address Domain Adaptation (DA), where the model can access unlabeled data from the target domain during the training/adaptation phase, with the goal of adapting to a specific target domain. Clearly, DG is a more challenging and more realistic scenario for real-world deployment, as it assumes no prior knowledge of the target domain.

This difference in task setting leads to our fundamental methodological innovation. The core idea of [1,2] is to use target domain data to learn "domain-aware" adapters, aiming to align the model's features with a specific target domain. In contrast, Cauvis, using only source domain data, proactively learns to disentangle "domain-invariant" universal features through our carefully designed prompts and dual-branch adapter. Our goal is not to adapt to any specific domain, but to enhance the model's core generalization ability to resist unknown domain shifts.

To ensure a fair comparison with Domain Adaptation (DA) works [1,2], we selected the highly challenging Sim10k → Cityscapes as our evaluation benchmark. This benchmark simulates a synthetic-to-real scenario and poses a rigorous test of a model's generalization capability due to the substantial domain gap between the source and target domains. The detailed experimental results are presented in the table below.

As can be seen, for generalization from synthetic to real scenarios, Cauvis still holds a 2.9% accuracy lead even without access to the target domain.

Thank you for your suggestion. We will add a discussion and comparison of these advanced DA methods in the "Related Work" section of our revised manuscript to more clearly define the contribution of our work.

W2: The computational overhead of Cauvis.

We greatly appreciate the reviewer's concern regarding computational efficiency. This is indeed a critical dimension for evaluating the practical utility of a method.

We acknowledge that choosing DINOv2 as the backbone introduces a significant base computational load. However, using powerful pre-trained models is a common and necessary practice in the current field to achieve State-of-the-Art (SOTA) performance and to ensure fair comparisons with other leading-edge works.

The core contribution of our work lies in the attached lightweight, parameter-efficient modules. Therefore, the key to evaluating our method's efficiency is the additional overhead introduced by these modules. In the field of Parameter-Efficient Fine-Tuning (PEFT), a crucial metric is the number of trainable/used parameters, as it directly reflects the computational components added during inference.

To quantify this overhead, we provide a comparison of parameter counts with other PEFT methods:

As the table shows, Cauvis (4.9M parameters) is highly competitive in parameter efficiency compared to the latest methods, and is even significantly more efficient than some, such as AdapterFormer (6.3M). More critically, the 4.9M parameters we introduce account for only about 1.6% of the DINOv2 backbone's ~307M parameters. In a full forward pass, the vast majority of the computation comes from the backbone network. Therefore, the marginal inference cost introduced by our lightweight modules is minimal.

W3: The baseline performance is unclear, and evaluating portability.

To clearly demonstrate the effectiveness of our method, we first conducted rigorous baseline comparisons under two mainstream detection frameworks. The first is Faster R-CNN, where "FR+DINOv2" serves as the baseline. The second is the more advanced DETR-style detector, DINO, where "w/o Cauvis" (the detector without our module) serves as the baseline. This design is intended to comprehensively validate the beneficial effects of our method. The results are shown in Table 2 of the paper, as follows:

As shown in the table above, our method brings significant performance improvements in both detection frameworks. In the Faster R-CNN, Cauvis yields a 1.9% average mAP gain. On the stronger DINO detector, the gain is even more substantial, reaching 6.7%. These data clearly and quantitatively demonstrate that our proposed method can consistently improve the generalization ability of different detectors.

Building on this, we fully agree that portability is a core advantage of prompt/adapter tuning. Another key validation in our work is demonstrating that Cauvis can serve as a universal module that seamlessly transfers to different Vision Foundation Models (VFMs). Table 6 of our paper provides exhaustive experiments on this, with the core results shown below:

Using the "Freeze" method as a baseline, our method yields a 16.6% relative improvement on EVA02, a 5.7% improvement on SAM, and a 3.8% gain on DINOv2. These consistent and significant performance gains across multiple mainstream backbones strongly demonstrate the excellent portability and universality of our method.

Thank you for pushing us to clarify these crucial aspects. We hope our detailed response and experiments have not only made the strong baselines and relative improvements clear, but have also turned the question of portability into one of our paper's most compelling strengths. The evidence is now clear: Cauvis is not a specialized solution for one architecture. By demonstrating significant relative improvements—up to 16.6%—on diverse backbones like EVA02, SAM, and DINOV2, we confirm it functions as a truly universal enhancement module. We believe this comprehensive validation strongly addresses your concerns and highlights the practical value of our work.

[1] Learning domain-aware detection head with prompt tuning. NeurIPS 2023

[2] Da-ada: Learning domain-aware adapter for domain adaptive object detection. NeurIPS 2024

[3] SEEN-DA: SEmantic ENtropy guided Domain-aware Attention for Domain Adaptive Object Detection. CVPR 2025

We sincerely thank you for your detailed review and constructive feedback. We are greatly encouraged by your recognition of our work's main strengths, including its theoretical soundness, the clarity of its presentation, its strong experimental results, and its well-clarified motivation. We hope our detailed responses below can further address your remaining questions.

W1: The training procedure and Loss functions.

We wish to clarify that our method, Cauvis, does not introduce a separate loss term requiring hyperparameter tuning.

Instead, its guiding effect is implicitly embedded within the standard detection loss via its architectural design. This design reshapes the network's feature space, naturally steering the standard end-to-end optimization towards a more robust and generalizable solution. Therefore, the "constraint" is an emergent property of the architecture, not an explicit loss formula, which avoids introducing new hyperparameters.

To ensure full reproducibility, we have detailed most of the training parameters in the paper and will add the remaining ones to Appendix A.

W2: The role of the dual-branch adapter.

1) The seemingly simple MLP in this branch is, in fact, an intentional and empirically validated architectural choice.

Theoretically, we interpret it as a Modulating Network within a Mixture of Experts (MoE) framework. Its minimalist single MLP design serves as a powerful form of Architectural Regularization. This constraint guides the branch to capture simpler signals—what we hypothesize to be confounding patterns—and prevents it from overfitting to complex spurious correlations.

Most importantly, this simple design is driven by our experimental results. We found that increasing the complexity of this branch (e.g., by using an explicit bottleneck MLP structure) did not yield performance gains and could even be detrimental. As shown in the table below, our current single MLP design achieves comparable or superior performance:

Our single MLP (60.2) outperforms the more complex Bottleneck MLP, proving that a simpler design is more effective for isolating confounding factors and better supports robust Causal Representation Learning.

2) We thank the reviewer for this insightful question about the theoretical justification of the IFT(FT(x)) operation. In the forward pass, its crucial role lies in structuring the model's learning process through implicit regularization and functional complementarity.

Our approach is grounded in the well-established principle that the Fourier domain separates domain-invariant structural information (encoded in the phase spectrum) from domain-specific style and noise (encoded in the amplitude spectrum) [1,2]. By forcing the optimization to pass through this decomposed domain, the model is implicitly regularized to prioritize the stable phase information over the volatile amplitude. This achieves a similar goal to state-of-the-art methods that explicitly manipulate the amplitude [2], but through a more elegant, parameter-free architectural design.

Crucially, this branch serves a complementary purpose: it compensates for the main MLP's known low-frequency spectral bias by providing a direct path for high-frequency information. This synergy ensures a more complete representation, making the branch a structured regularizer, not merely an identity function.

W3: Justification of Cross-Attention Prompts.

1) We thank the reviewer for their insightful suggestion (W3). To directly and rigorously validate that our method (Cauvis) can disentangle causal and spurious features, we have designed and completed a new counterfactual quantitative experiment.

This experiment follows the "Worst-Group Accuracy" (WGA) evaluation paradigm. In terms of concrete steps, we first removed all "bus" and "truck" samples from the training data, then added data of only yellow buses. The test set was a specially-designed small-sample set where all "bus" instances were set to white. In this way, we deliberately created a strong spurious correlation in the training set (color=yellow ↔ class=bus).

Our test set, in contrast, consists entirely of "white buses," which the model has never seen during training. The purpose of this counterfactual test set (i.e., the "worst group") is to directly test whether the model, when making predictions, relies on the learned spurious shortcut (color) or has truly grasped the invariant causal features (e.g., shape, structure).

The experimental results clearly show that, compared to the baseline model (FR+DINOv2), our method (Cauvis) demonstrates significant superiority in this highly challenging setting, robustly proving its ability to suppress spurious correlations.

2) Considering the restrictions on adding new images during the rebuttal, and to quantitatively address your insightful suggestion regarding attention visualization, we propose and measure the Foreground Attention Ratio (FAR). FAR is defined as the percentage of a specific feature component's energy that is spatially concentrated within the ground-truth object bounding box. This metric serves as a rigorous, quantitative proxy for visual focus: a high FAR value demonstrates that the feature is "attending" to the causal object, whereas a low FAR value implies it is attending to the spurious background. The inference weights used for this evaluation are taken from 1). The results are presented in the table below.

Analysis of feature components from top and bottom singular values reveals a striking difference. Top-value features consistently target the foreground object, whereas bottom-value features scatter across the background. For instance, with k=3, the attention disparity is over 915x, which validates our hypothesis that high-energy components represent causal features and low-energy ones are spurious.

3) To answer directly: k is not a hyperparameter that requires tuning. It is a theoretical concept for analyzing our model's output, not an input that controls its operation.

Our method is designed to automatically learn a sharp separation in the feature energy spectrum, creating a large gap between a few high-energy "causal" components and a long tail of low-energy "spurious" ones. The FAR experiment confirms this, revealing a stark energy gap (915x for k=3) between the causal and spurious components. This separation is so robust that any reasonable k used for analysis successfully isolates the same causal features.

In short, the model learns the separation, not a specific value of k. This eliminates the need for manual k-selection, fully resolving the hyperparameter concern.

W4: Figure 1 and 4

Thank you for pointing this out. We will revise Figures 1 and 4 in our revised manuscript to improve clarity using larger fonts and thicker, high-contrast lines.

Minor and Typos, grammartical errors

We sincerely thank the reviewer for their meticulous reading and valuable suggestions for improving the paper's clarity. We will incorporate all these changes in our revised manuscript. Specifically, we will add a brief explanation for the do(X) operator as suggested, and we will correct all noted typos while conducting a thorough proofread of the entire manuscript.

Q1: What does p in eq. (1) represent?

p is the learnable prompt, and p* is its optimal value post-training. The subscript $|_{p=p*}$ in Eq. (1) means "evaluated at this learned optimal state." This describes a training outcome, not a pre-supposed condition. We will clarify these definitions in the revision.

Q2: L199.

The equality in Eq. (7) represents the ideal theoretical goal of our optimization. It is intended to hold strictly under the condition that our model's representation (the right side) has perfectly learned to model the true interventional quantity (the left side). Our use of "is equivalent to" (L199) referred to this idealized outcome. We will revise the text to explicitly state the theoretical conditions for this equality, clarifying it as the target of our optimization. Thank you for helping us improve the paper's precision.

Q3: L202-203.

To be precise, the suppression of confounding effects is achieved by the cross-attention between prompts and image features, not by the prompts acting alone. The prompts simply provide the "directions" for this mechanism. We acknowledge the description in L202-203 was a simplification and will revise it for clarity. Thank you.

Q4: L220.

We apologize for the ambiguity. You are correct about L220: we meant the visual prompts after the Cross-Attention Prompts, not the prompt parameter p itself. We will revise the text to make this distinction explicit.

Q5: The 'w/o DINOv2' ablation.

In the 'w/o DINOv2' case, the backbone was a ResNet-50 (R50) pre-trained on ImageNet-1K, integrated within the DINO detector.

[1] A fourier-based framework for domain generalization. CVPR 2021.

[2] Reducing domain gap by reducing style bias. CVPR 2021.

def forward(self, x):
    x = self.mlp(x)   # Eq. (10)
    out = self.fourier_transform(x) # Eq. (11)  
    return out + x

ifft_feats = torch.fft.ifft(fft_feats, dim=1).real  # take real part

x = torch.randn(10)
fft_feats = torch.fft.fft(x)
ifft_feats = torch.fft.ifft(fft_feats).real

x: tensor([-0.7516, -1.2641,  0.3750,  0.5544,  2.1979,  2.8577,  0.6314,  0.8554,
         0.9650,  0.7984])

fft_feats: tensor([ 7.2195+0.0000j, -6.2967+1.1389j,  0.6120+3.6212j, -2.5346-0.0520j,
         1.0437+1.8583j, -0.3839+0.0000j,  1.0437-1.8583j, -2.5346+0.0520j,
         0.6120-3.6212j, -6.2967-1.1389j])

ifft_feats: tensor([-0.7516, -1.2641,  0.3750,  0.5544,  2.1979,  2.8577,  0.6314,  0.8554,
         0.9650,  0.7984])

import torch
torch.set_printoptions(precision=10, sci_mode=False)
x = torch.randn(10)
fft_feats = torch.fft.fft(x)
ifft_feats = torch.fft.ifft(fft_feats).real
print(x == ifft_feats) # [False, False,  True, False, False, False, False,  True, False, False]
x [-0.4920912981, -0.2312953621, -1.9472221136, -0.8723965287,
         0.3732707798, -0.8995720744, -0.2371343225, -0.6218926907,
        -0.1697061062, -0.6967265606]
ifft_feats [-0.4920912683, -0.2312953025, -1.9472221136, -0.8723964691,
         0.3732709289, -0.8995721936, -0.2371342927, -0.6218926907,
        -0.1697060615, -0.6967265010]

fft_feats = fft_feats / (torch.norm(fft_feats, dim=1, keepdim=True) + 1e-10)
ifft_feats = torch.fft.ifft(fft_feats, dim=1).real 

import torch
x1 = torch.randn(8)
x2 = 2 * x1
F1 = torch.fft.fft(x1)
F2 = torch.fft.fft(x2)
F1n = F1 / torch.norm(F1)
F2n = F2 / torch.norm(F2)
print(torch.allclose(F1n, F2n))  # True
print(torch.allclose(torch.fft.ifft(F1n), torch.fft.ifft(F2n)))  # True