Reliable Test-Time Adaptation via Agreement-on-the-Line

Could the authors include more results regarding more advanced network models in Figures 1 -3, including but not limited to VisionTransformers(Tiny/Small/Base/Large and with different input resolutions) and SwinTransformers from the Timm repository?

We hope our responses in here clarified the reviewer's concern about the empirical evidence of the OOD and ID performance/agreement correlation.

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Are there any (or potential) solutions that can modify the proposed method to be an online version? In other words, how about the performance of Algorithm 1 work in an online setting?

We hope our responses in here sufficiently addressed the concern about the offline nature of the proposed methods.

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Are there any sensitivity analyses about $n$ in Algorithm 1?

We hope our responses in here sufficiently addressed the concern about the sensitivity of our method to the number of models $n$.

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For Calibration and Hyper-parameter Selection, how many ID samples are needed? Will this ID sample number affect the performance significantly?

We examined the sensitivity of our method on the number of ID samples here, and we hope this sufficiently addressed the concern.

We appreciate the reviewer's feedback, and we are pleased to provide more details about the modifications made in our method for an online setup. The algorithms (https://tinyurl.com/5n72hev6) directly compare the online version (above) and the offline-version (below). Blue-colored comments highlight the newly added detail from the algorithm in the original submission.

A key modification is that we apply ALine-S/D only to the predictions of current ID and OOD batch at each iteration (Line 10 in Algorithm 1) in the online version. In this case, $\mathcal P_\text{ID}$ and $\mathcal P_\text{OOD}$ contain predictions of $n$ models on the current test batch ($x_\text{ID}$ and $x_\text{OOD}$), and ALine-S/D is applied to these.

On the contrary, in the offline version, we apply ALine-S/D at the end of the algorithm (Line 11 in Algorithm 2) after saving predictions on the entire test set ($\mathcal X_\text{ID}$ and $\mathcal X_\text{OOD}$) in $\mathcal P_\text{ID}$ and $\mathcal P_\text{OOD}$, with ALine-S/D then applied to these aggregated predictions.

Please let us know if there are any additional questions.

Insufficient Evidence for OOD and ID Performance Correlation Claims (Transformers, More complex tasks like object detection and semantic segmentation)

We additionally included Vision Transformers (ViT) and Swin Transformers as our models to observe AGL/ACL in here.

To the best of our understanding, the utilization of agreement to assess the generalization of models is well-established in the existing literature [1,2,3,4,5], particularly in the context of image classification tasks. Our work aligns with this convention, concentrating on leveraging the AGL phenomena to enhance reliability of TTA in image classification. However, we agree with the reviewer’s point that it is promising to extend the exploration of these phenomena to more complex tasks beyond image classification. We will make sure to augment our discussions on this aspect in the camera-ready version of our work.

[1] Madani et al., “Co-Validation: Using Model Disagreement on Unlabeled Data to Validate Classification Algorithms”, NeurIPS’04

[2] Nakkiran and Bansal, “Distributional generalization: A new kind of generalization”, Arxiv’21

[3] Jiang et al., “Assessing generalization of SGD via disagreement”, ICLR’22

[4] Baek et al., Agreement-on-the-Line: Predicting the Performance of Neural Networks under Distribution Shift, NeurIPS’22

[5] Lee et al., “Demystifying Disagreement-on-the-Line in High Dimensions”, ICML’23

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Heavy Reliance on Full Access to In-Distribution Data

We hope our responses in here clarified the reviewer's concern about the reliance on full access to ID data.

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Discrepancy Between the Offline Nature of Methods and Practical Needs

We hope our responses in here sufficiently addressed the concern about the offline nature of the proposed methods.

The authors have empirically observed the occurrence of agreement-on-the-line (AGL) and accuracy-on-the-line (ACL) following test-time adaptation (TTA). To enhance the manuscript, it would be beneficial for the authors to provide a more extensive explanation and discussion regarding this observed phenomenon.

We have added detailed explanations about their definitions as well as characteristics in the related work (Section 4) in our revised manuscript.

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Figures 1-3 are difficult to understand. For example, it is unclear what the values of the horizontal and the vertical axes in Figure 1 represent. More explanations should be provided.

The figures mainly show the TTAed models’ accuracy (%) tested on ID (x-axis) and OOD (y-axis), represented as dots with blue color. At the same time, these models’ agreement (%) tested on ID and OOD are plotted in the same x-axis and y-axis, denoted as pink dots. In addition, we plot the blue and pink lines that represent the linear fit of each dot, corresponding to the linear correlations between ID and OOD. In Figures 1 and 2, each dot represents the accuracy/agreement of the models with different architectures, while in Figure 3, they denote that of the models adapted with different adaptation hyperparameters. We provided such detailed explanations on each caption of the figures in the revised version of our submission.

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In the Introduction, the authors claim that "Baek et al. (2022) show that the ID and OOD agreement between classifiers shows a strong linear correlation". However, Baek et al. (2022) only study the correlation of disagreement and error between classifiers. It would be preferable to provide a more precise description.

We would like to clarify that our original claim in the Introduction was that “Baek et al. (2022)[1] show that the OOD agreement between classifiers shows a strong linear correlation with their ID agreement.” To expound on our intention, we quote the specific sentence from Baek et al.(2022)[1] that encapsulates the core observation: “ Whenever accuracy-on-the-line holds, we observe that the OOD agreement between the predictions of any two pairs of neural networks (with potentially different architectures) also observes a strong linear correlation with their ID agreement.” We clarified our claim in the Introduction (Section 1) of our revised submission.

[1] Baek et al., Agreement-on-the-Line: Predicting the Performance of Neural Networks under Distribution Shift, NeurIPS’22

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In Table 2, the authors only provide insufficient results on several domains of the test datasets to demonstrate the effectiveness of the proposed performance estimation.

We supplemented Table 2 by providing the performance prediction results across every 15 corruption of CIFAR10-C, CIFAR100-C, and ImageNet-C in Section A.6 and Table 7 of the appendix in our revised submission. The results show that our methods consistently predict the actual effectiveness of the tested TTA methods across diverse corruptions and datasets, without relying on the labels.

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From Table 1 to Table 3, the authors only study the effect of the proposed methods using different architectures or different training checkpoints. More ablation study using different hyperparameter setup is suggested.

To supplement the incomplete results the reviewer pointed out, we provide the results of accuracy estimation and calibration using different hyperparameter setups, which include learning rates, adapt steps, batch sizes, and checkpoints. In the Table below, we compare the estimation results (MAE (%)) of our methods (on ETA) with other baselines on ImageNet-C (averaged over every corruption). The results show that our methods with different hyperparameters achieve state-of-the-art performances across various hyperparameters and datasets (Results on CIFAR10-C/CIFAR100-C (TENT) are provided in Section A.6 and Table 8 of the appendix in our revised submission).

ImageNet-C [MAE (%)]

We also provide the calibration results using different hyperparameters when applying TENT on CIFAR10-C and CIFAR100-C (averaged over every corruption). Similar to Table 3, our methods effectively reduce the calibration error using the adapt steps, learning rates, or batch sizes.

The novelty of this method is relatively limited; it is an application of Baek et al. (2022) to the TTA setup.

While acknowledging the insights from Baek et al. (2022), we want to emphasize that our work explores the AGL phenomenon in adaptive setups. In contrast, Baek et al. (2022) primarily focused on pretrained models with their weights unchanged during test time. We specifically identify an unexpected condition where linear trends persist or even hold stronger, as evidenced by the extensive results across datasets, TTA baselines, and experimental setups.

Furthermore, our proposed methods for accuracy estimation, calibration, and hyperparameter optimization, represent a novel contribution. These methods facilitate the reliable utilization of TTA, an aspect rarely explored or addressed by previous studies due to a lack of access to OOD labels.

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Given that TTA usually operates on a stream of OOD data and provides a stream of predictions, it is unclear how predictions will be made at test time.

We elaborate on the detailed procedure for making predictions during TTA in our method. TTA operates as it usually does: it updates model parameters online with a stream of OOD data. At each iteration, after parameter updates, we perform inference on batches of OOD and ID data, storing their predictions. After running these procedures on multiple models, we calculate their accuracy and agreement using predictions. Subsequently, we utilize ALine-S/D to estimate OOD accuracy based on the AGL/ACL. We have provided the detailed explanation on how we obtain models’ predictions in the ID and OOD during TTA in Section 3.1 of the revised submission.

Moreover, as demonstrated here, our method is applicable in the online setup. To make predictions, for each iteration, we update models with streamed OOD batch and perform inference on both OOD and ID batches to obtain predictions. Instead of storing predictions until the entire test set, we calculate accuracy and agreement on the current batch using AGL/ACL and apply our methods for accuracy estimation and calibration.

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What is considered to be h(x)? Is it the most probable class under h? If so, why not define agreement in terms of the entire distribution on the output space for models, e.g., some kind of expected divergence between h(x) and h'(x)?

As noted by the reviewer, h(x) denotes the most probable class predicted by the model h given data x. We clarified the definition of h(x) in Section 2.1 of the revised version of our submission.

We want to clarify that in our work, we employed the definition of agreement by following prior studies that have established the concept of (dis)agreement between classifiers to assess their generalizations in both in-domain contexts [1,2,3] and OOD scenarios [4]. These studies empirically showcased the superiority of assessing generalizations of the models via (dis)agreement between models trained in different setups. A recent paper [5] attempted to demystify the effectiveness of employing such (dis)agreement between models for predicting OOD performances within a theoretical framework.

[1] Madani et al., “Co-Validation: Using Model Disagreement on Unlabeled Data to Validate Classification Algorithms”, NIPS’04

[2] Nakkiran and Bansal, “Distributional generalization: A new kind of generalization”, Arxiv’21

[3] Jiang et al., “Assessing generalization of SGD via disagreement”, ICLR’22

[4] Baek et al., Agreement-on-the-Line: Predicting the Performance of Neural Networks under Distribution Shift, NeurIPS’22

[5] Lee et al., “Demystifying Disagreement-on-the-Line in High Dimensions”, ICML’23

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How many models were used to get the agreement / accuracy lines at the figures?

Here’s the detailed setups for the figures:

• Figures 1,2: a total of 11 and 9 models of different architectures for CIFAR10-C, and ImageNet-C, respectively.
• Figure 3 first row: a total of 10 models of different learning rates, five of adapt steps, 9 of batch sizes, and 10 of checkpoints in CIFAR10-C
• Figure 3 second row: a total of 7 models of different learning rates, five of adapt steps, 8 of batch sizes and 10 of checkpoints in ImageNet-C

Heavy reliance on multiple models (Reviewer mLJy, gmmt).

It's worth noting that in practice, the validation in TTA involves running TTA iteratively with various hyperparameters, and selecting the one that yields the highest validation accuracy based on a labeled set. Our methods allow the same validation, which leverages multiple TTAed models and evaluate their performances, which might require a similar cost in memory in obtaining the final TTA model. Note that our methods do not require the labeled data for evaluation.

Moreover, we have conducted the ablation study on the number of models in our original submission, which can be referred to Section A.4 and Figure 6 of the appendix (tested on Gaussian Noise of CIFAR10-C and ImageNet-C) in our revised submission.

Here, we additionally provide the accuracy estimation results averaged over all corruptions in ImageNet-C as below. The tested setups are 1) architectures (2-4 columns), 2) learning rates (5-7 columns), and 3) batch sizes (8-10 columns). We showed that the MAEs when using three (minimum) or four models, are competitive to those using the full available set of models (denoted as full). These results indicate that in the memory-limited scenarios, practitioners can still robustly operate our methods with the minimal number of models to achieve reliable TTA performance predictions.

ImageNet-C (MAE (%))

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The proposed method works in offline manner (Reviewer a5t4, 72ab, gmmt).

To address the concern, we validated the efficacy of our method in an online setup, where we dynamically conducted accuracy estimation and calibration on the data streamed in, as opposed to waiting for the completion of predictions on the entire test set (i.e., offline). Specifically, we calculated the AGL/ACL using the predictions of the current batch (or a few batches), and performed the real-time accuracy estimation and temperature-scaling of them.

We examined our methods by using different setups on CIFAR10-C (averaged over every corruption), and employed only four models for memory efficiency. We tested 10 different combinations of models for each setup (4 for adapt step), and reported the mean and standard deviation of their results. In addition, to evaluate our method’s sensitivity to the size of data streamed, we systematically vary the number of batches to collect the predictions. For instance, if our method works only on the current batch, there is no delay (fully online), and if it waits until 2 batches of data are collected, there is 1 batch-delay.

The table below demonstrates how our methods, when applied an online setup, effectively perform accuracy estimation and calibration. The gap between the fully online and offline version highlights that practitioners can utilize our methods in an online fashion to achieve low estimation error and ECE, comparable to those of offline version.

CIFAR10-C [MAE (%)]

CIFAR10-C [ECE (%)]