Cross-Device Collaborative Test-Time Adaptation

Authors: guohao  chen
shuaicheng  niu
deyu  chen
shuhai  zhang
changsheng  li
yuanqing  li
mingkui  tan
𝛾𝛾  𝑖𝑖
Venue: NeurIPS_cc_2024_Conference
Published: 2024-04-29 14:03:13

Abstract: In this paper, we propose test-time Collaborative Lifelong Adaptation (CoLA), which is a general paradigm that can be incorporated with existing advanced TTA methods to boost the adaptation performance and efficiency in a multi-device collaborative manner. Specifically, we maintain and store a set of device-shared _domain knowledge vectors_, which accumulates the knowledge learned from all devices during their lifelong adaptation process. Based on this, CoLA conducts two collaboration strategies for devices with different computational resources and latency demands. 1) Knowledge reprogramming learning strategy jointly learns new domain-specific model parameters and a reweighting term to reprogram existing shared domain knowledge vectors, termed adaptation on _principal agents_. 2) Similarity-based knowledge aggregation strategy solely aggregates the knowledge stored in shared domain vectors according to domain similarities in an optimization-free manner, termed adaptation on _follower agents_. Experiments verify that CoLA is simple but effective, which boosts the efficiency of TTA and demonstrates remarkable superiority in collaborative, lifelong, and single-domain TTA scenarios, e.g., on follower agents, we enhance accuracy by over 30\% on ImageNet-C while maintaining nearly the same efficiency as standard inference. The source code is available at https://github.com/Cascol-Chen/COLA.

Main paper: 
 introduction: 
 The conventional pipeline of deep learning typically trains a model and deploys it across numerous devices with frozen parameters. This pipeline has demonstrated great success in various applications, such as autonomous driving cars [35, 14] , embodied robots [18] , and many other smart devices [28, 29] . However, during deployment, the model on each device may encounter test samples drawn from a domain different from the training one. In some cases, the testing environment even changes continuously and periodically, such as changes in weather. Unfortunately, the deep model often struggles to generalize to unseen testing domains and its performance may degrade significantly.To resolve domain shifts, test-time adaptation (TTA) [51, 21, 54, 64, 2, 7, 59, 26, 39, 25, 52, 37] has emerged as a promising research field. TTA updates a given model w.r.t. a testing sample using self-/unsupervised objectives, such as rotation prediction [13] , contrastive learning [2, 30, 50] , entropy minimization [54, 64, 25, 37] , etc. Compared to conventional domain adaptation [31, 45, 24] or fine-tuning [61, 33] methods that require performing offline model learning on the whole pre-collected target dataset, TTA distinguishes itself with minimal overhead by utilizing each test sample only once for immediate post-inference adaptation. This renders TTA more adaptable in real-world applications.However, prior TTA methods mainly validate their effectiveness on a single device, i.e., re-adapting the model from scratch on each. In practice, models are often deployed across multiple devices. As shown in Figure 1 , in the multi-device adaptation scenario, single-device adaptation methods suffer from the following limitations. First, single-device TTA neglects useful knowledge learned from other devices and adapts independently. Since different devices may frequently encounter similar or even identical testing domains, ignoring this shared knowledge often leads to suboptimal adaptation performance, as demonstrated in Table 2 . Second, due to limited resources or latency demands, some devices may not support the backpropagation operation required by learning-based TTA methods [54, 38] , rendering single-device TTA infeasible. Third, even on a single device, models may also encounter dynamically and periodically changing domain shifts. Although recent works have proposed continual TTA to mitigate the catastrophic forgetting issue, such as antiforgetting regularizer [38] or restoration schemes [56] , these methods still struggle to accumulate previously learned knowledge over a long-term adaptation process, as shown in Table 1 .In this paper, we propose a test-time Collaborative Lifelong Adaptation (CoLA) method to enable knowledge accumulation, sharing, and exploitation across devices. Our approach exploits both the previously learned knowledge from other devices and the device itself to achieve efficient and collaborative TTA. Specifically, we represent the knowledge learned on each domain of each device by a domain vector, and automatically detect domain changes on each device during its continual adaptation process. These domain vectors are stored and shared across devices upon domain changes for collaborative TTA and catastrophic forgetting mitigation. Based on the shared domain vectors, we first introduce a knowledge reprogramming learning method for Principal Agents, e.g., the resourceabundant devices, where we enhance TTA performance and efficiency by leveraging available shared knowledge while learning new domain-specific parameters in case existing knowledge is insufficient. The newly learned parameters/knowledge are subsequently stored for shared domain vector set updating. Furthermore, we devise an optimization-free collaborative TTA method, to reduce the computation consumption of TTA and thus enable TTA in latency-sensitive scenarios or resourcelimited devices, which we term as Follower Agents in CoLA. We achieve this by directly aggregating the domain knowledge shared by principal agents according to domain similarities.Main novelty and contributions. 1) We introduce a novel and practical collaborative lifelong adaptation paradigm to TTA. This paradigm addresses a practical demand in real-world applications to perform effective adaptation on numerous devices with varying resources and latency requirements simultaneously, meanwhile keeping privacy preserved and communication efficient. 2) We devise domain vectors to explicitly store the domain knowledge and share them across devices for collaborative TTA. Based on this, we devise two collaborative strategies, i.e., knowledge reprogramming learning for resource-abundant principal agents and similarity-based knowledge aggregation for resource-limited or latency-sensitive follower agents. 3) Extensive experiments demonstrate the superiority of our CoLA regarding the scenarios of collaborative, lifelong, and single-domain TTA in a plug-and-play manner. By leveraging available shared knowledge, on principal agents, we achieve an up to 78.0× speed up on ETA compared with the baseline without collaborative learning on ImageNet-C. On follower agents, we enhance the accuracy by over 30% while maintaining nearly the same computation and memory efficiency as standard inference on ImageNet-C. We maintain a shared domain vector set T to explicitly store the knowledge learned by each principal agent during adaptation. Based on T , for Principal Agents, we jointly learn the domain-specific parameters ∆θ and the reweighting term α via backward propagation, where the learned knowledge is then stored in T . For Follower Agents, we adaptively aggregate the shared knowledge in T in a forward-only manner, based on the domain similarities, which prioritizes knowledge derived from domains that are similar to the testing domain. 
problem statement and motivation: 
 Let f θ (•) be the model trained on a labeled dataset D train = {(x i , y i )} and x i ∼ P (x). After training, f θ (•) is often deployed on various devices, on each device f θ (•) may encounter test samples drawn from a shifted and dynamically changing domain distribution Q(x), where Q(x) ̸ = P (x). Under such domain shifts, deep models are often very sensitive and suffer from severe performance degradation. To address this, on each device, one can adapt f θ (•) to x by optimizing some self-/unsupervised learning objective at test time:EQUATIONwhere θ f and θ l denote frozen and learnable model parameters, respectively.Motivation. Eqn. ( 1) is known as a single-device test-time adaptation (TTA) method, which naively re-adapts f θ (•) from scratch on each device. In our multi-device adaptation scenario, this independent adaptation manner neglects the valuable knowledge learned from other devices and often obtains limited performance, as in Figure 3 (a). Therefore, there is an urgent demand to devise multi-device collaborative TTA methods, to enhance the adaptation performance and efficiency. To this end, the key technical challenge lies in devising a collaboration scheme that effectively exploits the knowledge from other devices while ensuring privacy preservation and communication efficiency.In real-world scenarios, a model is often deployed in environments that may change continuously and cyclically, e.g., day → night → day. Moreover, the model deployed on different devices may encounter similar environments, experiencing similar domain shifts. In such cases, when a device encounters test samples drawn from a domain previously seen by itself or by other devices, it is unnecessary to conduct adaptation from scratch. Instead, leveraging the previously acquired knowledge can achieve enhanced adaptation. Inspired by this, we seek to explicitly store the knowledge learned on each domain of each device, and then exploit this knowledge for collaborative TTA. We term this knowledge as domain vectors and introduce its definition below.Formally, given m devices with each having n domains, we use a domain vector ∆θ i,j =θ i,j l -θ o l to denote the knowledge learned on the i-th domain of the j-th device. Here, θ i,j l denotes the learned parameters on the i-th domain of the j-th device, and θ o l denotes the corresponding original learnable parameters. For privacy and efficiency considerations, we select the affine parameters of the norm layers as learnable parameters θ l and transmit domain vectors between devices for knowledge sharing, which consumes negligible extra cost as in Table 5 . We store each knowledge vector ∆θ i,j in a set Algorithm 1 The overall pipeline of CoLA.Input: Test samples {D m } M m=1, where D m ={x m t } T t=1 denotes the batches of test samples on the m-th device, the model f θ (•) and its stem (first) layer f θs (•), threshold z. T ={∆θ i,j } n,m i=1,j=1 . During the continual adaptation process, we dynamically expand T by storing a new ∆θ i,j in T once ∆θ i,j is learned. For simplicity of presentation, we omit T as {∆θ i } N i=1 where N =mn and exploit T to devise collaborative TTA strategies in the following sections. 
cross-device collaborative test-time adaptation: 
 In this paper, we propose a test-time Collaborative Lifelong Adaptation (CoLA) method. In CoLA, we seek to conduct collaborative TTA across multiple devices by exploiting a set of shared domain vectors, termed T . We automatically detect the domain changes on each device during a continual adaptation process and explicitly store the current domain knowledge in T once the testing domain is changed (c.f. Sect. 3.3). Then, based on T , we develop two distinct collaboration strategies. In practice, users can determine which strategy to use according to the computational resource of their device or their latency requirements. First, the collaborative knowledge reprogramming learning strategy (c.f. Sect. 3.1) is designed for "principal agents", i.e., the devices that will dominate the learning of new knowledge and have sufficient resources for backpropagation-based model updates. This strategy jointly learns new domain-specific model parameters and a reweighting term to reprogram the knowledge learned from previously encountered distributions from both the device itself and other devices, through backpropagation-based optimization. Second, the optimization-free collaborative TTA (c.f. Sect. 3.2) is designed for "follower agents", i.e., the devices that are resourcelimited or latency-sensitive. This strategy mainly exploits the knowledge shared from principal agents, by aggregating the valuable shared knowledge according to distribution similarities. We summarize the pseudo-code in Algorithm 1 and illustrate the overall pipeline of CoLA in Figure 2 .We conduct collaborative adaptation with both the knowledge learned from other devices and the device itself. This latter one is particularly advantageous for lifelong adaptation since, in practice, a deployed model may encounter diverse and evolving domains. By storing and reprogramming all knowledge learned from previously encountered domains, we naturally mitigate the issue of catastrophic forgetting during lifelong TTA (see results and analysis in Table 1 ). To this end, on each device, we detect domain changes and store the learned model parameters for each specific domain once the test domain changes. We then reprogram the knowledge stored in these model parameters by reweighting as below, facilitating seamless adaptation to changing environments.As aforementioned, we assume there exist N sets of parameters, i.e., domain vectors, learned from previously encountered domains across all devices, denoted as T ={∆θ i } N i=1 , where ∆θ i =θ iθ o l . For flexibility, we denote null knowledge as ∆θ 0 =0 and include it in T . We use T to illustrate our collaborative learning scheme here and put details for detecting and storing each ∆θ i in Sect. 3.3. Based on T , we learn a reweighting term that adaptively aggregates shared knowledge via backpropagation, while learning new knowledge simultaneously if existing knowledge is insufficient. The overall optimization problem is given by:EQUATIONHere, ∆θ denotes learnable parameters for current round of adaptation, and α denotes the normalized weights for different domain knowledge, i.e., i α i = 1. Thus, knowledge reprogramming and new knowledge learning are decoupled into the optimization of α and ∆θ. Note that we introduce ∆θ 0 to ensure more flexibility in reprogramming, e.g., by setting α 0 = 1, one can entirely disregard previously learned knowledge when it is not beneficial for adapting to currently encountered domain. Moreover, when no knowledge has been accumulated, i.e., T = {0}, Eqn. (2) simplifies to the conventional TTA. We put details of the initialization for α and T in Appendix B due to page limits.Adaptive temperature scaling for fast adaptation. Promptly re-weighting the appropriate knowledge for aggregation is key to fast adaptation when the testing distribution suddenly changes. However, this process is hindered when the logits of α are sharpened, making re-weighting difficult to favor another knowledge. To mitigate this, we further introduce an adaptive scaling temperature during the optimization phase, which helps adjust the sharpness of α adaptively while maintaining the smoothness of the original logits. The calculation of α can be thus expressed as α = softmax(β • T l ), where β is the logit vector and T l is a learnable temperature.The computational constraints of devices, combined with the real-time demands of various applications, often necessitate TTA to be as efficient as possible. To this end, we propose a forward-only collaborative TTA strategy for devices operating in the follower agent mode. Here, the follower agent adapts a given model by aggregating the previously learned knowledge and the knowledge shared from principal agents without learning new domain-specific parameters, aiming to maintain almost the same efficiency as pure inference. Formally, given domain vectors T ={∆θ i } N i=0 shared from m principal resource-abundant devices with each having n encountered domains and ∆θ 0 = 0, the goal of adaptation is to find appropriate normalized weights γ * ∈R N +1 such that:EQUATIONHere, since backpropagation-based learning is not supported, we directly assign the specific value of each γ i approximately according to distribution similarities. We estimate the distribution by calculating the feature statistics, i.e., the mean and standard deviation of the features from the first stem layer. Formally, let ϕ d denote the statistics of the current distribution that is online estimated via Eqn. (6) , and ϕ i be the distribution statistics on which ∆θ i is adapted (i.e., the corresponding ϕ d while learning ∆θ i ), we re-weight the knowledge from different distributions by:EQUATIONHere, ρ is a logit vector, D(•, •) is a distance for which we adopt KL divergence as in Eqn. (7) , and ϵ is a small constant for numerical stability. In this way, we can adaptively prioritize shared knowledge learned from distributions that are similar to the current distribution. Note that a principal agent with abundant resources may also leverage Eqn. (3) for efficient TTA in real-time scenarios.Exploiting diverse knowledge for aggregation. Aggregating the advantages of different knowledge is the key to achieving satisfying robustness under various distribution shifts, as shown in Figure 3 (b). However, when distributions are highly similar, the re-weighting logit ρ i shall become sufficiently large (e.g., ρ i > 10) and the softmax function tends to simplify to the max function, which hinders the potential of Eqn. (3) from aggregating a diverse set of knowledge. To alleviate this, we further introduce a pre-defined temperature scaling factor T f to soften ρ i , thereby encouraging the aggregation of more existing knowledge. Then, ρ i is re-defined as:EQUATIONRemark. It is worth noting that our CoLA can be incorporated with existing TTA techniques as a plug-and-play module for a more effective solution (as in Table 1 and Table 3 ). Furthermore, unlike prior methods [4] that impose intensive transmission of both data and model weights, CoLA offers several merits for real-world implementation: 1) CoLA involves only the transmission of learned parameters ∆θ i , which preserves user privacy and imposes much less communication burden (e.g., the affine parameters of the norm layers in ViT-Base [8] , which are typically updated in TTA [54, 38] , occupy only 0.15 MB). 2) the domain vectors are preserved and shared intermittently with a shift detector, which further reduces the communication burden by a considerable margin. 3) CoLA is decentralized and flexible, which allows all agents to join or leave the collaboration at any time.In this section, we introduce the construction of the domain knowledge vectors T shared across multiple devices. As aforementioned, explicitly accumulating/storing the learned knowledge from each domain of each device in T is a key step in our CoLA for collaborative learning. However, in practice, during the lifelong adaptation process of each device, we do not have any prior information on the domain labels regarding a given test sample stream. To conquer this, we devise an efficient distribution shift detector to identify whether the test distribution changes, and then automatically store the currently learned model weights to the domain vector set T once the domain change is detected. We achieve this by measuring the discrepancy between the distribution's statistics ϕ d and the statistics of the current test batch φt . Formally, let f θs (•) be the stem layer of f θ (•), i.e., the first layer. φt comprises the mean μt and standard deviation σt calculated over f θs (x t ). Then, we estimate the statistics ϕ d from the observed test samples {x t } T t=1 via exponential moving average:EQUATIONwhere λ is a moving average factor belongs to [0, 1]. Inspired by existing distance-based detection methods [19] , we capture the magnitude of distribution shifts by a distance function D(•, •) as follows.EQUATIONwhere H denotes the dimension of statistics, and KL(•||•) is the KL-divergence simplified from [19] .Here, a distribution shift is detected when D(ϕ d , φt ) > z, where z is a pre-defined threshold. This simple design offers several merits: 1) It imposes minimal computational and memory costs without necessitating data preservation. 2) By leveraging the features from the stem layer, we can promptly detect and respond to distribution shifts, rendering it well-suited for the online nature of TTA. 
experiments: 
 Datasets and models. We conduct experiments on the ImageNet-1k [6] , as well as five benchmarks for OOD generalization, i.e., ImageNet-C [16] (contains corrupted images in 15 types of 4 main categories and each type has 5 severity levels), ImageNet-R (various artistic renditions of 200 ImageNet classes) [15] , ImageNet-Sketch [55] , ImageNet-A [17] , and ImageNet-V2 [44] . We use ViT-Base [8] as the source model unless stated otherwise. The model is trained on the source ImageNet-1K [6] training set and the model weights are obtained from the timm repository [60] .Compared methods and implementation details. We compared our proposed CoLA with 1) Backpropagation-based methods: CoTTA [56] , ETA [38] , EATA [38] , SAR [39] , and DeYO [25] .2) Backpropagation-free methods: LAME [3] and T3A [21] Time: --------------------------------------------------→ Round 1 2 3 4 5 6 7 8 9 10 Average NoAdapt 29.9 29.9 29.9 29.9 29.9 29.9 29.9 29.9 29.9 29.9 29.9 CoTTA [56] 44.9 40. 6 Results under lifelong test-time adaptation. We evaluate the long-term effectiveness of our CoLA on ImageNet-C [44] within a challenging lifelong TTA scenario where the model is online adapted to 15 corruptions over 10 rounds (total 150 corruptions), and the parameters will never be reset. We put more details of the experimental protocol in Appendix C due to page limits. From Table 1 , we derive the following observations. 1) Our CoLA achieves new state-of-the-art results on the first round, last round, and the average of adaptation, suggesting our superiority. 2) Most methods, including CoTTA [56] and EATA [38] with an anti-forgetting strategy, experience performance degradation as the number of adaptation rounds increases (e.g., ETA's performance degrades from 61.4% to 35.1% on the average accuracy), indicating the difficulty of the evaluated scenario. 3) By integrating our CoLA with existing methods, we enhance the performance steadily with more adaptations, demonstrating our effectiveness in accumulating and exploiting learned knowledge for long-term adaptation. 4) Although EATA mitigates performance degradation by introducing an anti-forgetting regularization, it suffers from the stability-plasticity trade-off, i.e., the average accuracy drops from 61.4% (ETA) to 60.4% (EATA) in the first round. In contrast, our CoLA enhances ETA's performance even at the first round of adaptation, i.e., 61.4% (ETA) vs. 62.0% (ETA+CoLA), indicating that CoLA does not limit the learning ability. The sensitivity analyses on threshold z are provided in Appendix E.To evaluate our CoLA under the collaborative TTA scenario, we first assess its performance across multiple principal resource-abundant devices. From Table 2 , our CoLA outperforms the integrated baseline from the adaptation to the second group of corruptions, e.g., the accuracy of 58.0% (SAR+CoLA) vs. 54.4% (SAR) on 'Blur' in Devices 1. Moreover, this improvement becomes increasingly more pronounced as more knowledge is shared across devices, e.g., improving the accuracy from 47.7% (SAR) to 55.5% (SAR+CoLA) on 'Noise' in Device 3. This demonstrates our effectiveness in facilitating knowledge sharing and exploitation across principal devices via our knowledge reprogramming learning scheme, i.e., with Eqn. (2) . Given learned knowledge from resource-abundant principal devices (totaling 34 weights occupying 5.0 MB), we further evaluate the effectiveness of CoLA on resource-limited follower devices. From Table 3 , we observe that existing TTA methods struggle to improve the performance of the source model without model updates, highlighting the urgent need for a more effective solution. In contrast, by exploiting shared knowledge adaptively in a forward-only manner with Eqn. (3), CoLA achieves a substantial performance gain, e.g., enhancing the average accuracy from 29.9% to 64.1% in CoLA (ETA). Note that we also verify CoLA's sample efficiency as well as its computation and memory efficiency in Figure 3 (a) and Table 5 . These results collectively underscore the importance of cross-device collaboration and our effectiveness regarding the scenario of collaborative TTA.Results under single-domain test-time adaptation. Following DeYo [25] , we validate our CoLA in both the wild scenario (i.e., imbalanced label distribution shifts and mixture of distribution shifts) and the mild scenario of single-domain TTA, where the model is reset post-adaptation to each corruption.Here, CoLA saves learned weights for every adaptation to 10 batches of samples while maintaining a maximum of 32 weights (totaling 4.7 MB) by discarding the unused ones according to α i .From Table 4 , within all evaluated scenarios, incorporating CoLA consistently improves the performance by a considerable margin (e.g., +2.0% on SAR w.r.t. overall average accuracy). Interestingly, the enhancement from CoLA may even help surpass a stronger baseline, e.g., the average accuracy of 64.4% (ETA+CoLA) vs. 64.1% (DeYO) on the mild scenario, demonstrating our effectiveness. This improvement mainly stems from our ability to alleviate error accumulation. Given multiple saved weights, instead of naively selecting the newest weight that may have adapted to noise, CoLA dynamically favors the more optimal one via loss optimization. This renders CoLA more robust to scenarios where perturbations may occur. We also visualize α i in Appendix E to offer more insights.Effectiveness of T l on sample efficiency in Eqn. (2) . Sample efficiency is particularly important in scenarios where the availability of target data is limited or early adaptation performance is paramount. As shown in Figure 3 2 , Gaussian. Model's accuracy is recorded on the entire test set after adapting to N test samples. In right, we evaluate the effectiveness of T f on seen (i.e., ImageNet-C, Gaussian) and unseen distributions (i.e., ImageNet-R/Sketch), where CoLA exploits weights of ETA+CoLA in Table 2 for Eqn. (3). of cross-device collaboration and our effectiveness to facilitate knowledge sharing and utilization. Moreover, upon integrating T l in Eqn. (2), CoLA demonstrates superiority without necessitating too many test samples, i.e., 53.2% accuracy (ETA+CoLA) vs. 22.2% accuracy (ETA+CoLA w.o. T l ) with 960 samples, suggesting the effectiveness of T l to promote swift adaptation under distribution shifts. We also provide more comparison in Appendix E regarding sample efficiency on unseen distributions.Effectiveness of T f on robustness in Eqn. (5) . We evaluate the robustness of Eqn. (3) on seen/unseen distributions (i.e., whether resource-abundant devices have encountered the evaluated distribution). From Figure 3 (b), our CoLA consistently outperforms NoAdapt regardless of T f , demonstrating our effectiveness. On seen distribution, our improvement is particularly significant while the performance is insensitive to T f in a reasonable range. However, when T f is set to infinity (i.e., averaging different weights), performance experiences degradation as appropriate knowledge plays a less significant role. On unseen distribution (e.g., ImageNet-R), aggregating a minority of knowledge may be insufficient to address distribution shifts. In this case, T f plays an important role in enhancing robustness by aggregating the strengths of diverse knowledge. We fix T f to 5 in experiments without careful tuning.Memory and computation consumption of CoLA. Besides achieving strong performance across various scenarios, we demonstrate that CoLA incurs negligible computation and memory costs. From Table 5 , on resource-limited follower devices, CoLA (Eqn. 3) substantially outperforms T3A in terms of accuracy and runtime memory (i.e., 55.7% vs. 9.5%, and 821.9 MB vs. 909.9 MB) while maintaining nearly the same efficiency as NoAdapt. On resource-abundant principal devices, CoLA enhances the performance of ETA by a considerable margin (i.e., +2.4% on ImageNet-C) while incurring only 5.7 MB of additional runtime memory and 3s of latency, indicating that CoLA is even lighter than the regularizer introduced in EATA. Note that CoLA (Eqn. 3) determines appropriate re-weighting for different knowledge with a batch of test samples, outperforming ETA+CoLA w.r.t average accuracy on ImageNet-C. This underscores the potential of collaborative TTA in real world, where a device may adapt effectively using only negligible costs given adequate shared knowledge. We also show that CoLA can efficiently scale to over 10,000 domain vectors in Appendix E.(2) on unseen distributions. Following Figure 3 (b), we further validate the effectiveness of CoLA (Eqn. 2) on unseen distributions. From Table 6 , CoLA consistently enhances performance on unseen distributions, yielding a notable 4.4% improvement on SAR in terms of average accuracy. Such improvement can be attributed to the transferability of knowledge learned from similar domains [63] . These findings collectively indicate that the effectiveness of CoLA is not limited to previously encountered distributions on both principal agents and follower agents.Prompt tuning with CoLA using multiple hard prompts. Besides aggregating learned knowledge from other devices, we demonstrate that CoLA can also benefit from aggregating diverse knowledge from humans (i.e., manual-designed hard prompts). As shown in Table 7 , compared with TPT which is limited to leveraging a single hard prompt, CoLA enhances the adaptation performance on 4 out of 5 datasets (e.g., +1.5% on ImageNet w.r.t. accuracy). These results collectively indicate that CoLA effectively exploits both the knowledge of humans and the knowledge from optimization, which may bring new perspectives to the design of learning algorithms when introducing diverse human prior knowledge is beneficial, e.g., chain-of-thoughts [58] . All used prompts are listed in Appendix C.Differences and advantages over federated TTA [1, 23] . The main difference is that our CoLA conducts collaborative learning at the testing phase, whereas federated TTA conducts collaborative learning during federated source training. For instance, FedTHE+ [23] federatedly trains a global and a local personalized model for each client, then adaptively ensemble their outputs at test time. ATP [1] federatedly learns module-specific adaptation rates across clients during training for test-time adaptation. However, these methods still conduct TTA independently on each devices during testing, and thus inherits the limitation of the single-device TTA methods. Moreover, in federated TTA [1, 23] , the training phase and test-time adaptation phase are highly correlated, which means they can only use their own federated-trained models during TTA. This makes these methods restricted for real-world applications. In contrast, our CoLA enhances test-time model adaptation performance and efficiency by leveraging knowledge from multiple devices in the application environment, which essentially establishes a new unsupervised on-time TTA paradigm. Moreover, our CoLA paradigm can be applied to any pre-trained models, and thus offers much better flexibility in deployment. Additional comparisons with FedAvg [32] for collaborative adaptation are also provided in Appendix E. 
conclusion: 
 In this paper, we propose a multi-device Collaborative Lifelong Adaptation (CoLA) paradigm for test-time adaptation (TTA), which addresses a practical scenario where multiple devices with different computational resources and latency requirements need to perform TTA simultaneously. In particular, we first accumulate a set of shared domain knowledge vectors with an efficient domain shift detector. Based on this, we develop a knowledge reprogramming learning strategy on principal agents, which leverages backpropagation-based optimization to aggregate existing knowledge while learning new domain-specific parameters simultaneously. To further improve adaptation efficiency, we introduce an optimization-free TTA strategy on follower agents, which solely aggregates the shared domain vectors based on domain similarity. In CoLA, all devices/agents work collaboratively while keeping privacy preserved and communication efficient. Experiments verify that CoLA boosts the performance and efficiency of existing TTA solutions in collaborative, lifelong, and single-domain TTA scenarios.  
safeguards: 
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 Appendix: We summarize our main differences in Table A and discuss the related works in the following.Test-time adaptation (TTA) seeks to enhance the model performance on unseen, potentially shifted test data, by directly learning from the test data itself. We categorize the related TTA works into the following four groups for discussion, according to 1) the number of devices involved in adaptation; 2) their dependence on backward propagation; and 3) the availability of multiple models.• Single-device backpropagation-based TTA. Test-Time Training (TTT) [51] first proposes this pipeline. During the training phase, TTT methods train a source model with both a supervised and a self-supervised branch. Given a test sample during testing, they typically update the shared encoder with the self-supervised objectives, such as rotation prediction [51] , contrastive learning [30, 2] , reconstruction learning [11] . To avoid altering the model training phase and access to source data, Fully TTA methods directly update an on-the-fly model via unsupervised learning objectives, including, but not limited to, entropy minimization [54, 39] , prediction consistency maximization [64, 10] and feature distribution alignment [34] .In pursuit of efficient backpropagation-based TTA, the attempts of existing methods can be generally categorized into: 1) Sample Efficiency. As test data are not equally important for adaptation, some recent works [38, 39, 47, 25] have devised various sample selection strategies to identify reliable and non-redundant samples for test-time learning. It reduces the noise in the gradient and the number of samples for TTA, thereby enhancing adaptation performance and efficiency. 2) Memory Efficiency: EcoTTA [48] reduces run-time memory by optimizing only the parameter-efficient adapters. MECTA [19] reduces the batch size at testing, while it further proposes a domain-aware batch normalization layer to stabilize TTA using only a small batch size.Nevertheless, these methods focus on single-device adaptation, where all devices adapt from scratch. In this sense, valuable knowledge learned from other devices is neglected, damaging the adaptation performance and efficiency. Moreover, these methods still rely on computationally intensive backpropagation for model updates, which hinders their applicability in resource-limited devices or latency-sensitive scenarios. To address this, we propose a gradient-based and forward-only collaboration paradigm, facilitating knowledge accumulation, sharing, and utilization across devices.Recently, TTA-CDKM [49] proposes to learn and reuse multiple groups of model parameters for better adaptation, with each group representing the knowledge of a domain. However, TTA-CDKM exploits only a parameter group during inference, and thus fails to aggregate the strength of diverse domain knowledge. On the other hand, TTA-CDKM updates the stored parameters when adapting to each batch of test samples, which introduces intensive communication costs for weight synchronization that are impractical for multi-device collaboration. In contrast, our CoLA effectively learns to aggregate diverse strengths of domain vectors at testing while ensuring communication efficiency.• Single-device forward-only TTA. In the development of BP-free TTA, early research mostly focused on calibrating the statistics of batch normalization layers by leveraging the test data to estimate test statistics [36, 46] . Nevertheless, these strategies only conduct adaptation on batch normalization layers, limiting their applicability to various architectures. In pursuit of a more general forward-only TTA solution, existing methods can be generally divided into: 1) Input-Level Adaptation,where the corrupted test images are reconstructed before making predictions based on a diffusion model [12, 40] . 2) Output-Level Adaptation, where T3A [21] proposed a prototype-based classifier for adaptive predictions, and LAME [3] directly corrects the predicted logits. However, since BP-free TTA does not leverage model feedback, i.e., un/self-supervised learning objectives, for knowledge acquisition, it often results in suboptimal performance when dealing with out-of-distribution testing data. In our paper, we address this by facilitating knowledge sharing and utilization across devices, where we adaptively aggregate the learned knowledge of other devices in a forward-only manner.• Single-device test-time aggregation. Given multiple pretrained models, one can leverage unsupervised objectives at test time to adaptively aggregate their diverse strengths. Based on the level on which aggregation is performed, existing solutions can be generally divided into:1) Output-wise test-time aggregation: Early research mainly focuses on output-wise test-time aggregation, where the aggregation is conducted on the output logit of each model. EMEA [57] first proposed this pipeline. Given multiple models trained on different datasets or different label distributions, this paradigm introduced a reweighting vector to aggregate the outputs logit of various models during testing, where the reweighting vector is optimized based on entropy minimization [57, 65] , consistency loss [5] , etc. More Recently, Mute [9] jointly updates the reweighting vector and all pretrained models at test time. Nevertheless, these strategies necessitate forward passes for each candidate model, i.e., O(N ) forward passes with N the number of candidate models. Thus, they typically consume substantially more computation power, impeding their feasibility at edge devices.2) Parameter-wise test-time aggregation. In contrast, parameter-wise test-time aggregation methods directly merge several candidate parameters into a single model without necessitating additional forward passes, i.e., O(1) forward passes neglect of N , rendering it more efficient in computation.To this end, Adamerging [62] first introduces the learnable parameter-wise weighting vectors, which aggregate various models before performing forward passes. Building upon this, WEMOE [53] further introduces the mixture of experts (MoE) into this paradigm, where the parameters from different models are considered as different experts, while the parameter-wise weighting vector is generated by a router that is trained during testing, with the entropy minimization objective.Nevertheless, existing test-time aggregation solutions assume the availability of pretrained models from the target domain, which struggles to fulfill the conventional TTA settings. Unlike these methods, we perform both new knowledge learning and existing knowledge aggregation simultaneously at test time, where knowledge is accumulated across all devices from previous learning.• Multi-device test-time adaptation. Existing TTA methods typically conduct adaptation on a single device, where multi-device test-time adaptation is heavily overlooked. In recent academics, FedTHE+ [22] proposes a global-local scheme for federated test-time adaptation. Specifically, during each round of federated training, each device trains the global model on the local data, where the trained model is then sent back to the server. During testing, it adaptively merges the output logit of the global and local model based on entropy minimization and feature alignment loss. Nevertheless, it necessitates alteration to model training, limiting their applicability to scenarios where training data is unavailable. ATP [1] obtains module-specific adaptation rates via federated learning across clients and applies the adaptation rates in TTA. However, these methods still conduct TTA independently on each devices, and thus inherits the limitation of the single-device TTA method. More recently, CEMA [4] proposes a cloud-edge collaboration paradigm for TTA. In CEMA, edge devices perform pure inference to filter reliable and informational samples to reduce communication burden, where the computationally intensive model updates are offloaded to the cloud server. Nevertheless, CEMA necessitates intensive transmission of both data and model weights, which introduces a heavy communication burden and may violate user privacy. Unlike these methods, we conducts collaborative adaptation at test time and necessitate only the intermittent transmission of updated model parameters, which is more practical in real-world implementation.Unsupervised domain adaptation (UDA). Conventional UDA tackles distribution shifts by jointly optimizing a source model on both labeled source data and unlabeled target data to learn domaininvariant features [31, 41, 45, 67, 66] . To avoid access to source data, recently CPGA [42] generates feature prototypes for each category with pseudo-labeling. SHOT [27] learns a target-specific feature extractor by information maximization for representation alignment. Nevertheless, these methods necessitate pre-collected target datasets for offline adaptation, which limits their applicability in the real world. In contrast, our method adapts in an online manner and does not access the model training phase or access to source data, which facilitates a more practical adaptation paradigm.In the section, we further elaborate more details of our methods regarding the design of saving domain knowledge upon distribution shifts Initialization of α and ∆θ in Eqn. (2) for stable adaptation warm-up. Since ground-truth labels are absent in our online TTA scenario to provide stable learning signals for Eqn. (2), a careful initialization of α and ∆θ is crucial upon distribution changes. In this sense, to ensure the stability of model performance pre and post encountering a new domain while enabling flexible aggregation of existing knowledge, we devise the initialization strategy by considering the following requirements: 1) the overall model weights θ n+1 l initialized after encountering the domain n+1 should remain the same as θ n l that learned on the n-th domain; 2) ∆θ should be as small as possible to enable flexible adaptation, e.g., when the new samples are all from in-distribution, one can obtain the solution of θ l =θ o l by setting α 0 =1 if ∆θ is negligible; 3) for α=softmax(β), the initial β should not be very sharp, e.g., β=[0, inf, 0, ..., 0], as it will hinder the model learning from selecting diverse knowledge. Formally, let {∆θ (i) } L i=1 be the learned parameter on the i-th layer in ∆θ. We define ∆θ's magnitude as the maximum scale of parameters across different layers ξ = max{ 1J J j=1 |∆θ (i,j) |} L i=1, where J is the number of parameters in each layer. To this end, we satisfy the above constraint by defining the reweighting logit ∆θ n+1 as:EQUATIONHere, β n+1 is designed so that the magnitude ξ ′ of the recalculated ∆θ satisfies ξ ′ ≤ w m , where w m is a constrained value set to 0.01. Moreover, to improve numerical stability in case T l is 0, we clip the value of β n+1 between [-10, 10]. The preserved knowledge ∆θ n+1 is then shared across devices.We next provide a proposition to validate the reasonableness of the design for β n+1 :Proposition 1. Given β n+1 in Eqn. (8) , the constraints that θ n+2 l = θ n+1 l and ξ ′ ≤ w m holds.Proof. Assume that the model has learned from n previously domains. According to Eqn. ( 2), when the model adapts on the (n+1)-th domain, we haveθ n+1 l = θ o l + α 0 ∆θ 0 + α 1 ∆θ 1 + • • • + α n ∆θ n + ∆θ, where α = softmax(β • T l ).When encountering the (n+2)-th domain, we should save learned knowledge ∆θ from the (n+1)-th domain. To adaptively aggregates prior knowledge and saved knowledge, we initialize α n+1 for ∆θ n+1 . Besides, we initialize ∆θ ′ in order to learn new knowledge from the (n+2)-th domain. So we haveθ n+2 l = θ o l + α ′ 0 ∆θ 0 + α ′ 1 ∆θ 1 + • • • + α ′ n ∆θ n + α n+1 ∆θ n+1 + ∆θ ′After adding α n+1 , to maintain the vector α as normalized weights, α i will change to Thus, we expand θ n+2 l as:α ′ i = e βiT l (θ n+2 l = θ o l + α ′ 0 ∆θ 0 + α ′ 1 ∆θ 1 + • • • + α ′ n ∆θ n + α n+1 ∆θ n+1 + ∆θ ′ = θ o l + n i=0 e βiT l ( n i=0 e βiT l ) + e βn+1T l (α 0 ∆θ 0 + α 1 ∆θ 1 + • • • + α n ∆θ n ) + e βn+1T l ( n i=0 e βiT l ) + e βn+1T l • ∆θ n+1 + ∆θ ′ = θ o l + n i=0 e βiT l ( n i=0 e βiT l ) + e βn+1T l (θ n+1 l -θ o l -∆θ) + e βn+1T l ( n i=0 e βiT l ) + e βn+1T l • (θ n+1 l -θ o l ) + ∆θ ′ = θ n+1 l - n i=0 e βiT l ( n i=0 e βiT l ) + e βn+1T l • ∆θ + ∆θ ′ . Considering θ n+2 l = θ n+1 l , we have θ n+1 l - n i=0 e βiT l ( n i=0 e βiT l ) + e βn+1T l • ∆θ + ∆θ ′ = θ n+1 l ⇒ ∆θ ′ = n i=0 e βiT l ( n i=0 e βiT l ) + e βn+1T l • ∆θ.As ∆θ ′ should be as small as possible to enable flexible adaptation, the magnitude of ∆θ ′ should be no larger than w m , i.e. ξ ′ ≤ w m . So we scale ∆θ by a factor of s, i.e. ∆θ ′ = 1 s • ∆θ. If the magnitude of ξ ′ already satisfies ξ ′ ≤ w m , we set s = 1. Otherwise, we set s = ξ wm . Thus, we have s = max{1, ξ wm } and ImageNet-C consists of various versions of corruption applied to 50,000 validation images from ImageNet. The dataset encompasses 15 distinct corruption types of 4 main groups, including Gaussian noise, shot noise, impulse noise, defocus blur, glass blur, motion blur, zoom blur, snow, frost, fog, brightness, contrast, elastic transformation, pixelation, and JPEG compression. Each corruption type is characterized by 5 different levels of severity, with higher severity levels indicating a more severe distribution shift. In our experiments, we specifically utilize severity level 5 for evaluation.ImageNet-R contains 30,000 images featuring diverse artistic renditions of 200 ImageNet classes. These images are predominantly sourced from Flickr and filtered by Amazon MTurk annotators.ImageNet-A comprises 7,500 images covering 200 ImageNet classes. These images are derived from real-world, naturally occurring examples that lead to a notable degradation in classifier performance.ImageNet-V2 is a newly collected test dataset extracted from the same test distribution as ImageNet.It comprises three test sets, each containing 10,000 new images and covering 1000 ImageNet classes. Following previous TTA methods [36] , we utilize the Matched Frequency subset of ImageNet-V2 for evaluation, in which the images are sampled to match the class frequency distributions of the original ImageNet validation dataset.ImageNet-Sketch consists of 50,899 images represented as black and white sketches, encompassing 1000 ImageNet classes. Each class contains approximately 50 images.We use ViT-Base [8] as the source model for all experiments except Table 7 . The model is trained on the source ImageNet-1K training set and we directly obtain the model weights3 from timm4 repository [60] . In Table 7 , we adopts CLIP-RN50 [43] as the source model by following TPT [47] .The model weights 5 are directly obtained from the original CLIP6 repository [43] . All experiments are conducted on a single NVIDIA A100 GPUS, using PyTorch framework with version 1.8.0.Evaluation on lifelong TTA. In Table 1 , the model is online adapted to 15 corruptions over 10 rounds (total 150 corruptions), where the parameters will never be reset. Specifically, the corruptions comes in the following order for each round: Gaussian Noise → Defocus Blur → Snow → Contrast → Shot Noise → Glass Blur → Frost → Elastic Transform → Impulse Noise → Motion Blur → Fog → Pixelate → Brightness → Zoom Blur → JPEG Compression. Here, subsequent corruptions differ in type, which poses a more significant challenge for TTA methods to leverage previously learned knowledge for adaptation.Evaluation on collaborative TTA. In Table 2 , we evaluate our effectiveness in collaborating on multiple resource-abundant principal devices, where the learned knowledge on each device is shared with others post-adaptation to each type of corruption. Specifically, the corruption order in each type of corruption is as follows. 1) Noise: Gaussian Noise → Shot Noise → Impulse Noise. 2) Blur: Defocus Blur → Glass Blur → Motion Blur → Zoom Blur. 3) Weather:Snow → Frost → Fog → Brightness. 4) Digital: Contrast → Elastic Transformation → Pixelate → JPEG Compression.Then, given learned knowledge from Table 2 , we further verify our effectiveness on resource-limited follower devices in Table 3 , e.g., CoLA (SAR) utilizes the learned weights of SAR+CoLA from Table 2 , and CoLA (ETA) utilizes the learned weights of ETA+CoLA from Table 2 . Here, the resource-limited follower devices adapt in a lifelong manner per EATA [38] , where the corruptions come in the following order:Gaussian Noise → Shot Noise → Impulse Noise → Defocus Blur → Glass Blur → Motion Blur → Zoom Blur → Snow → Frost → Fog → Brightness → Contrast → Elastic Transformation → Pixelate → JPEG Compression.Evaluation on single-domain TTA. In Table 4 , we validate our CoLA in both the wild scenario (i.e., imbalanced label distribution shifts and mixed domain shifts) and the mild scenario of single-domain TTA, where the model is reset post-adaptation to each corruption. Here, imbalanced label distribution shifts denotes scenarios where test data come in a class order, mixed domain shifts denotes scenarios where test data are drawn from multiple randomly mixed domains with different distribution shifts.Evaluation on prompt tuning. In Table 7 , CoLA aggregates 78 diverse hard prompts with the class token at the end for Eqn. (2) , where different prompts are padded to the same length by inserting empty spaces at the beginning. Note that adaptation is conducted in an episodic manner by following TPT [47] , where we reset ∆θ = 0 post-adaptation to each test sample in Eqn. ( 2), while α is continually optimized without reset due to its stability benefit from normalization. Results in Table 7 further demonstrate our effectiveness across various TTA scenarios. The utilized hard prompts for Eqn. ( 2) are originally developed by [43] , as listed below:List of Hard Prompts: a drawing of the {class}, art of a {class}, itap of the {class}, a drawing of a {class}, a origami {class}, a photo of a nice {class}, a blurry photo of a {class}, a close-up photo of the {class}, a photo of a clean {class}, a photo of a weird {class}, a photo of a small {class}, a photo of the large {class}, a pixelated photo of the {class}, a embroidered {class}, a photo of the clean {class}, the origami {class}, the plushie {class}, a photo of a cool {class}, a sculpture of the {class}, a low resolution photo of the {class}, a bad photo of the {class}, a jpeg corrupted photo of a {class}, a rendition of the {class}, a photo of the cool {class}, a low resolution photo of a {class}, a cropped photo of the {class}, the plastic {class}, a sculpture of a {class}, a pixelated photo of a {class}, itap of a {class}, a doodle of a {class}, a sketch of a {class}, a plastic {class}, itap of my {class}, a close-up photo of a {class}, a bright photo of a {class}, art of the {class}, graffiti of the {class}, a tattoo of a {class}, a sketch of the {class}, a dark photo of a {class}, a tattoo of the {class}, a photo of the dirty {class}, a black and white photo of the {class}, a photo of a {class}, a painting of the {class}, a cropped photo of a {class}, a photo of a large {class}, a photo of the weird {class}, graffiti of a {class}, a painting of a {class}, a cartoon {class}, the cartoon {class}, a good photo of the {class}, a jpeg corrupted photo of the {class}, a bad photo of a {class}, a photo of the small {class}, a rendering of the {class}, a photo of a dirty {class}, a rendition of a {class}, a blurry photo of the {class}, the toy {class}, the embroidered {class}, a rendering of a {class}, a photo of a hard to see {class}, a dark photo of the {class}, a doodle of the {class}, a good photo of a {class}, a photo of the {class}, a photo of many {class}, a plushie {class}, a photo of the nice {class}, a bright photo of the {class}, a toy {class}, a photo of the hard to see {class}, a photo of one {class}, a photo of my {class}, a black and white photo of a {class}, a sketch of a {class}CoLA (Ours). For principal agents, We directly leverage the learnable test-time objectives from the integrated TTA methods, as listed below. In Eqn. ( 2), ∆θ is optimized by following the update rules and the hyper-parameters of the integrated baseline, α and T l is updated via the AdamW optimizer with a learning rate of 0.1, and we introduce a weight decay of 0.1 on α. We set the shift detection threshold z to 0.1 for all experiments. Moreover, we introduce a weight decay on ∆θ for Table 1 and Table K , i.e., 0.1/0.4/0.4 for SAR/ETA/DeYO in Table 1 and 0/0.4/10 for EATA/ETA/SAR in Table K , respectively. This weight decay, which can be viewed as a simple implementation of the regularizer in EATA [38] , helps learn compact and non-redundant knowledge in the domain vectors, thereby benefiting knowledge accumulation. For follower agents, we consistently set T f in Eqn. (3) to 5 for all experiments. Moving average factor λ is set to 0.2.SAR 7 [39] . We follow all hyper-parameters that are set in SAR unless it does not provide. Specifically, we use SGD as the update rule, with a momentum of 0.9, batch size of 64, and a learning rate of 0.001. The entropy threshold E 0 is set to 0.4× ln C, where C is the number of task classes. The trainable parameters are the affine parameters of the layer normalization layers from blocks 1 to blocks 8.ETA & EATA 8 [38] . We follow all hyper-parameters that are set in ETA/EATA unless it does not provide. Specifically, we use SGD as the update rule, with a momentum of 0.9, batch size of 64, and a learning rate of 0.001. The entropy threshold E 0 is set to 0.4× ln C, where C is the number of task classes. For EATA, i.e., ETA with an anti-forgetting regularizer, we use 2,000 samples to estimate the importance of each parameter. The trainable parameters are all affine parameters of layer normalization layers.DeYO 9 [25] . We follow all hyper-parameters that are set in SAR unless it does not provide. Specifically, we use SGD as the update rule, with a momentum of 0.9, batch size of 64, and a learning rate of 0.001. The entropy threshold E 0 is set to 0.4× ln C and the entropy factor τ Ent is set to 0.5× ln C, where C is the number of task classes. The Pseudo-Label Probability Difference (PLPD) threshold τ PLPD is set to 0.3 in Table 4 , and 0.2 for other experiments by following the original paper. Trainable parameters are the affine parameters of the layer normalization layers from blocks 1 to blocks 8.CoTTA 10 [56]. We follow all hyperparameters that are set in CoTTA unless it does not provide. Specifically, we use SGD as the update rule, with a momentum of 0.9, and a batch size of 64.The learning rate is chosen from {0.05, 0.01, 0.005, 0.001, 0.0005, 0.0001} and the augmentation threshold p th is chosen from {0.1, 0.2}. In all experiments, we consistently set the learning rate to 0.001 and p th to 0.1 given the optimal accuracy observed in Table 1 . For images below the threshold, we conduct 32 augmentations including color jitter, random affine, Gaussian blur, random horizontal flip, and Gaussian noise. The restoration probability of is set to 0.01 and the EMA factor α for teacher update is set to 0.999. The trainable parameters are all the parameters in ViT-Base.LAME 11 [3] . For fair comparison, we maintain a consistent batch size of 64 for LAME, aligning it with the same batch size used by other methods in our evaluation. We use the kNN affinity matrix with the value of k chosen from {1, 5, 10, 20}, and for all experiments, we consistently set it to 5 based on the optimal accuracy observed in Table 3 .T3A 12 [21] . We follow all hyper-parameters that are set in T3A unless it does not provide. Specifically, the batch size is set to 64. The number of supports to restore M is chosen from {1, 5, 20, 50, 100}, and for all experiments, we set it to 20 based on the optimal accuracy observed in Table 3 .TPT 13 [47] . We follow all hyper-parameters that are set in TPT unless it does not provide. Specifically, we use AdamW as the update rule, with batch size of 1 and a learning rate of 0.005. Learnable tokens are initialized from the hard prompt of 'a photo of a'. The confidence threshold ρ is set to 0.1 and the number of TPT steps is set to 1.In the main paper, we only report the results averaged over 15 corruptions in ImageNet-C (i.e., in Table 1 and Table 4 ) or over each group of corruptions (i.e., in Table 2 ) due to page limit. In this section, we offer additional results to enable a more comprehensive comparison.Results under lifelong test-time adaptation. The knowledge sharing scheme in CoLA can also be used to mitigate catastrophic forgetting in lifelong TTA, similar to the aim of conventional supervised continual learning [68] . To further verify this, we provide more detailed results of Table 1 , regarding the Accuracys on the first and last rounds of adaptation. From Table C , our CoLA outperforms the integrated baseline in the first round of adaptation, e.g., the accuracy of 62.0% (ETA+CoLA) vs. 61.4% (ETA). This mainly stems from the latter corruptions encountered in the first round, where CoLA demonstrates superiority by leveraging the learned knowledge from previous adaptation with Eqn. (2) . More importantly, our enhancement becomes particularly significant at the last round of adaptation, e.g., the accuracy of 65.4% (ETA+CoLA) vs. 35.1% (ETA), further indicating our effectiveness in accumulating and utilizing learned knowledge for long-range adaptation. Note that CoLA applies weight decay on ∆θ as claimed in Section C, thus achieving a lower performance on the first corruption. Here, the relatively limited performance of CoTTA [56] is attributed to its sensitivity to corruption order, as shown in Table D .Results under collaborative test-time adaptation. We provide more detailed results of Table 2 , regarding the Accuracys on each device. From Table D , our CoLA outperforms the integrated baseline from the adaptation to the second group of corruption, e.g., the accuracy of 53.6% (SAR+CoLA) vs. 38.9% (SAR) on 'Gaussian' in Device 2. Moreover, this improvement becomes increasingly more pronounced as more knowledge is shared across devices, e.g., improving the accuracy from 37.5% (SAR) to 53.9% (SAR+CoLA) on 'Gaussian' in Device 3. This phenomenon underscores the importance of cross-device collaboration and our effectiveness regarding collaborative TTA.Results under single-domain test-time adaptation. We provide more detailed results of Table 4 , regarding the Accuracys under mild scenarios and online imbalanced label distribution shifts. From Table B , incorporating CoLA with existing TTA solutions enhances the adaptation performance on most corruptions under both scenarios, demonstrating our effectiveness. Specifically, CoLA showcases a more pronounced improvement in SAR and ETA. This can be attributed to the inadequacy of prediction entropy to identify reliable samples for model updates, thereby suffering more from error accumulation. CoLA alleviates this by dynamically favoring a more optimal checkpoint based on loss minimization instead of the newest saved one that may have learned from erroneous predictions, rendering CoLA more robust to noise. We also visualize α i in Appendix E to offer more insights.Table B : Comparisons on ImageNet-C (level 5) regarding Accuracy (%) under single-domain TTA.In mild scenarios, the test samples come in random order by following Tent [54] . Label Shifts is short for online imbalanced label distribution shifts, where test samples come in class order per SAR [39] . Robustness of CoLA against potential harmful knowledge. Note that CoLA conducts test-time learning to adaptively aggregate prior knowledge. If the prior knowledge shared from some devices is harmful, using such knowledge shall not decrease the test-time objective. Thus, such prior knowledge will not be used for model adaptation. In this sense, CoLA remains stable even with harmful prior knowledge (e.g., the domain knowledge in some devices is not helpful for principal agents to do TTA). This stability also benefits from our initialization strategy as shown in Table E , which carefully initializes α and ∆θ to prevent the aggregation of potentially harmful knowledge for stable warm-up. Advantages of CoLA over FedAvg [32] in collaborative TTA. We further compare our CoLA with FedAvg [32] in cross-device collaborative/federated learning. From Table I Robustness of CoLA under small batch sizes. The stability of CoLA under small batch sizes is primarily determined by the base algorithms, such as ETA and SAR, rather than CoLA itself. This is because CoLA is a plug-and-play module designed to be incorporated with existing methods. We provide further empirical results to verify this robustness. From Table J , CoLA achieves a consistent result when incorporated with SAR, demonstrating no performance degradation as the batch size reduces from 16 to 2. Meanwhile, CoLA can also help improve stability under small batch sizes. For instance, as the batch size reduces from 4 to 2, ETA+CoLA achieves nearly no performance degradation while the baseline ETA's performance degrades by 1.4%. 1 . Statistical comparison. We re-run Table 2 in the main paper with 5 different seeds and report the mean and std of each method in Table L . The results show that CoLA performs stably with small stds and it lowers the std of ETA&DeYo, suggesting CoLA's stability. EQUATIONFinetuning LLM. We mainly verify our CoLA with vision models in the context of test-time adaptation. Since our formulation in Eqn. (2) does not necessitate being optimized during testing, it's an interesting future work to verify CoLA on more scenarios. For instance, finetuning the large language models, where multiple finetuned weights, e.g., using LoRA [20] , are publicly available.Shrinking the shared vectors. Our CoLA continuously expands the size of the shared domain vectors across devices. Intuitively, on the same domain, one can reduce memory consumption by preserving only the best-performing domain vector. Although we have demonstrated a feasible strategy for shared vectors shrinking on the single-domain adaptation, where we discard the unused ones according to α i in Table 4 . Nevertheless, it's still challenging to perform share vectors shrinking across multiple devices and we leave it for future works.This paper aims to advance the field of test-time adaptation for out-of-distribution generalization. The societal impact of our work lies primarily in its potential to expand the usability of machine learning models in real-world settings, particularly on self-driving cars, embodied agents/robots, etc. By enhancing the performance of machine learning models on various real-world devices, our method helps make AI technology more broadly accessible. Ethically, our approach eliminates the need for data transfer between devices, thereby improving data privacy and security.Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material? Answer: [Yes] Justification: We have provided all source code in the introduction. Guidelines:• The answer NA means that paper does not include experiments requiring code. Guidelines:• The answer NA means that there is no societal impact of the work performed.• If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact. • Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.• The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster. • The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology. • If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML).https://storage.googleapis.com/vit_models/augreg/B_16-i21k-300ep-lr_0.001-aug_medium1-wd_0.1-do_0.0-sd_0.0-imagenet2012-steps_20k-lr_0.01-res_224.npz4 https://github.com/pprp/timm5 https://openaipublic.azureedge.net/clip/models/afeb0e10f9e5a86da6080e35cf09123aca3b358a0c3e3b6c78a 7b63bc04b6762/RN50.pt 6 https://github.com/openai/CLIP 


Decision: This paper considers test-time adaptation in multi-device scenarios and proposes Collaborative Lifelong Adaptation (CoLA). Domain knowledge vectors, as interactive objects on devices, are maintained and stored by measuring KL-divergence between the current test batch and the online estimated distribution. This paper categorizes different devices into principal agents and follower agents based on computational resources and latency demands, and uses different strategies for online prediction or parameter updates during testing. 

The reviewers were initially mixed with both positive and negative scores. They agreed that the approach is novel and interesting, the paper is well written, the method is of practical importance. The positive reviewers noted that CoLA is simple and efficient, demonstrating good performance in collaborative, lifelong, and single-domain TTA tasks. It also considers the application for devices with different computational resources and latency demands in practice, and  is technically sound. The negative reviewers mostly raised concerns about lack of citations and comparisons to previous work, limited experimental evidence, and various other questions of detail. The authors addresses these concerns in their rebuttal and extensive discussion with the reviewers. In the end, all reviewers were positive towards the paper. The ACs concur that the paper merits publications

Reviews: review: paper_summary: paper_summary: Prior test-time adaptation (TTA) methods focused on single-device setups only, despite models being deployed to multiple devices in the real world. This paper presents Collaborative Lifelong Adaptation (CoLA) to leverage this situation and improve performance. Specifically, this paper introduces Principal Agents and Follower Agents concepts and proposes knowledge reprogramming, similarity-based knowledge aggregation, and automatic domain shift detection for efficient collaboration. Experiments with various settings and state-of-the-art (SOTA) TTA methods demonstrate the effectiveness and applicability of CoLA.
strength_weakness: strength_weakness: 1. Lack of deeper analysis on when prior knowledge helps and when it harms. As environments are diverse and KL-divergence-based distance metrics are not always accurate in neural networks, utilizing knowledge from other devices might be harmful. It would be better to have a deeper investigation into when prior knowledge is beneficial, how much prior knowledge is required to get the benefit, the extent of the benefit, and how many such cases are observed in the experiments.
2. The domain shift setup is a bit unrealistic. In real-world scenarios, domain shifts are often gradual rather than sudden. It is unclear whether the proposed method can handle gradual domain shift scenarios.
3. No error bars are reported, which weakens the statistical significance of the results.
4. This submission doesn't include code, which limits the validity and transparency of the work.
questions: questions: 1. What is the impact of this initialization strategy compared to randomized/equal weights?
2. Where does the communication cost reduction come from? Is it only from utilizing BN layers?
3. What is the accuracy of automatic domain detection?
4. Why is CoLA better than the baseline in the first round as well, before the shift happens (Table 1)?
limitations: limitations: The authors adequately addressed the limitations.
paper_summary: paper_summary: This paper considers test-time adaptation in multi-device scenarios and proposes Collaborative Lifelong Adaptation (CoLA). Domain knowledge vectors, as interactive objects on devices, are maintained and stored by measuring KL-divergence between the current test batch and the online estimated distribution. This paper categorizes different devices into principal agents and follower agents based on computational resources and latency demands, and uses different strategies for online prediction or parameter updates during testing. Experiments in various TTA settings demonstrate that CoLA has good adaptability and anti-forgetting capabilities. Rigorous ablation studies well support the viewpoints in the paper.
strength_weakness: strength_weakness: - The hyperparameter z is used for detecting distribution shift and influences the storage of new domain vectors. The paper lacks ablation studies on the threshold z.
- In the setting of lifelong TTA, the smooth and stable updating of the affine parameters of norm layers relies on a sufficiently large batch size. It is necessary to analyze the robustness of CoLA under conditions where the batch size is extremely small.
- It’s insufficient to use only ViT-Base as the source model in the main experiments. Analyzing the effects of CoLA on different source models can provide more comprehensive evidence, such as ResNet and MobileNet.
- (minor) The experiments are all targeted at classification. It is intriguing to explore the effectiveness of CoLA in detection and segmentation tasks.
questions: questions: It appears that domain knowledge vectors play a pivotal role in CoLA. Apart from using the affine parameters of norm layers, are there any other potential methods to determine these vectors?  (Just in terms of discussion)

I hope that the code can be released.
limitations: limitations: Yes
paper_summary: paper_summary: This paper explores test-time adaptation (TTA) in scenarios involving varying computational resources across multiple devices. To address this, the paper proposes storing and sharing domain knowledge among devices to improve adaptation. For resource-abundant devices (referred to as principal agents), domain knowledge is either newly learned or reprogrammed based on current inputs. Conversely, for resource-limited devices (referred to as follower agents), existing domain knowledge is efficiently aggregated according to domain similarities. The proposed method demonstrates superior performance across diverse experimental settings.
strength_weakness: strength_weakness: 1. Consideration of Multi-Device Test-Time Adaptation Literature:

- While multi-device test-time adaptation literature is mentioned in the supplementary material, there are no direct mentions or experimental comparisons in the main paper. This omission may confuse readers about the paper's originality.
- The multi-device test-time adaptation literature should be more accurately described in the main paper, including conceptual comparisons in the introduction section.
- Benchmarking multi-device test-time adaptation methods (e.g., Cloud-Edge TTA [4], CEMA [5], FedTHE+ [21]) within the same experimental settings is crucial to demonstrate the superiority of the proposed method. The concepts of cloud and edge in [4,5] align with the notions of principal and follower agents in this paper.

2. Similarity to Prior Continual Test-Time Adaptation Work [A]:

This paper and prior continual test-time adaptation work [A] show high similarity in the following aspects:
- Both papers store and reuse domain knowledge for better adaptation.
- Both store domain knowledge in the affine parameters of norm layers.
- Both retrieve related domain knowledge based on the measured domain similarity between the current input and previous domains.
Given these similarities, it is essential to correctly reference the prior work [A] and include experimental comparisons on detailed design aspects.
[A] Test-time Adaptation in the Dynamic World with Compound Domain Knowledge Management, IEEE Robotics and Automation Letters, 2023

3. Additional Ablation Study and Analysis:

To improve the completeness of the paper, I suggest including the following:
- An ablation study on the impact of domain knowledge "stored from multi-devices" in multi-device scenarios. A baseline where each device has restricted access to its own domain knowledge. Comparing this baseline to the proposed method would highlight the impact of domain knowledge "stored from multi-devices."
- An analysis of the proposal's efficiency in terms of memory overload and inference time.
- An analysis of the ratio of selected domain knowledge for reprogramming/aggregation.
- Experimental results on the diverse order of domains for multiple devices.

4. Limited Representation of Real-World Scenarios:

While this paper targets more realistic scenarios, the experiments are somewhat limited in representing real-world conditions. It would be beneficial to include experimental results from (for example) autonomous driving scenarios under diverse weather conditions.
questions: questions: 1. Have you considered moving Figure A from the supplementary material to the main document? Figure A could help readers quickly grasp the overall concept of the proposed method.

2. Could the proposed methods be applied to the EATA method? Given that EATA is a strong baseline on several benchmarks, the synergy of the proposed method and EATA might set a new state-of-the-art.
limitations: limitations: This paper faithfully describes its limitations and potential negative impacts in general.
paper_summary: paper_summary: This paper proposes a novel Collaborative Lifelong Adaptation (CoLA) method for test-time adaptation (TTA) across multiple devices. The key idea is to accumulate and share knowledge learned during adaptation across devices, enabling more efficient and effective adaptation to distribution shifts at test time. The authors evaluate CoLA in various scenarios, showcasing the effectiveness of the plug-and-play CoLA method.
strength_weakness: strength_weakness: Although the paper proposes an innovative research direction, I have concerns about its positioning and presentation of the results.

1. **Limited comparisons with test-time federated learning [1, 2]**. Collaborative TTA could be considered as a variation of federated learning. Please thoroughly discuss the relation with federated learning. The paper should thoroughly discuss this relationship and provide comparative experimental results if possible.
1. **Insufficient scalability analysis**. The paper does not address how the method scales with an increasing number of devices and domains, particularly regarding the growth of the shared domain vector set T.
1. **Vague approach to lifelong adaptation**. While the paper claims to address lifelong adaptation, it doesn't fully explain how the method performs in lifelong scenarios. It's unclear how the proposed methods tackle potential performance or memory issues arising from accumulating domain vectors over time.
1. **Incomplete experimental details**:
   - Lack of explanation on the detailed experiment settings, including the details of resource-abundant and resource-limited devices.
   - The authors only applied CoLA on ETA, SAR, and DeYO. Please discuss why these specific methods were chosen and whether they are applicable to other TTA methods.
   - The experiment results use different baselines on each table; please elaborate on the baseline selection criteria.
1. **Lack of statistical significance**. The paper does not report any error bars of the experimental results.



[1] Bao, Wenxuan, et al. "Adaptive test-time personalization for federated learning." Advances in Neural Information Processing Systems 36 (2024).

[2] Jiang, Liangze, and Tao Lin. "Test-Time Robust Personalization for Federated Learning." The Eleventh International Conference on Learning Representations.
questions: questions: 1. Please explain details on the limitations above.
1. What are the overheads of the shared domain vectors? Can you provide any numerical example of the growth of shared vectors?
1. Given that CoLA involves optimizing both $\alpha$ and $\Delta \theta$, how does the method achieve such minimal computational overhead (only a 3-second increase) compared to the baseline ETA, as reported in Table 5?

**Important**: I will raise the ratings if concerns are resolved.
limitations: limitations: The paper properly discussed the limitations and societal impacts.
Still, it's worth mentioning the limited applicability and scalability of continuously stacking shared domain vectors, which is discussed by the authors.

Comments: title: Thank you for increasing your score!
Thanks for author's feedback
Thanks for your feedback and further response
Response to the Author's rebuttal.
Thanks again for your invaluable feedback!
Thank you and looking forward to your response
Thanks and a kind reminder for discussion
Thanks and a kind reminder for discussion
Thank you for your positive feedback!
Thank you for the reseponse
Thank you for increasing your score!
comment: Dear Reviewer SsoW,

Thank you for upgrading your score! 

Your comments are immensely beneficial in improving the quality of our paper. We will be glad to include the new discussions and results in our revised paper.

Best Regards,

The Authors
Thank you for your detailed feedback regarding Q3-1.

Overall, the authors' responses have thoroughly addressed my original concerns. While the original manuscript missed some important aspects, I will increase my score toward the positive side, trusting that the authors will make careful revisions. Thank you again for your comprehensive feedback.
Dear Reviewer SsoW,

We deeply appreciate your expertise and the detailed feedback. We provide further explanation regarding Q3-1 below.

We would like to highlight that the success of CoLA mainly benefits from **reprogramming** previously-stored useful knowledge to aid current adaptation. Here, with and without CoLA(NoShare) achieves the same performance is because **Table A is a special case** in lifelong adaptation, in which reprogramming is not activated. In this special case, the same type of domains comes subsequently and occurs only once on each device, e.g., Gaussian Noise$\rightarrow$Shot Noise$\rightarrow$Impulse Noise. In this sense, reprogramming is unnecessary as the most useful knowledge for current adaptation **comes from exactly the previous domain**. Thus, CoLA has little room for improvement but, importantly, does not deteriorate performance.


In addition to this special case, Baseline+CoLA(NoShare) can outperform Baseline in lifelong adaptation under various scenarios, such as when 1) **distinct domains come alternatively**, as evidenced in the first round of adaptation in Table 1, in which corruption order follows Gaussian Noise$\rightarrow$Snow$\rightarrow$Shot Noise; or when 2) **domains occur more than once**, e.g., Gaussian Noise$\rightarrow\cdots\rightarrow$Gaussian Noise. We further verify this in Table C by conducting long-term adaptation on each device following Table 2 of the main paper. Here, each device experiences two rounds of lifelong adaptation with identical domain orders. From Table C, CoLA enhances the accuracy of SAR by 2.2% at the second round of adaptation. This is because **reprogramming becomes critical to reuse useful knowledge from previous adaptations**. 


We believe that CoLA's flexibility to share and exploit learned knowledge would benefit TTA in more challenging scenarios and will explore more in our future works. We ensure to include the new discussions and results in our revised paper. Once again, we thank you for your thoughtful and invaluable reviews.

Table C. Effectiveness of CoLA(NoShare) in lifelong TTA when domains occur more than once. We follow the settings as Table 2 in the main paper but extend it to the two-round lifelong adaptation for each device. For example, on Device 1, the domains come in the following order: N->B->W->D->N->B->W->D. We report average accuracy over three devices on each round of adaptation.

|Method|Round 1|Round 2|
|-|:-:|:-:|
|SAR|58.6|59.8|
|SAR+CoLA(NoShare)|58.6|62.0|
I have carefully reviewed the authors' responses and the comments from other reviewers. First of all, I would like to express my sincere appreciation for the authors' thoughtful and detailed responses. These have made me more positive about this submission. Below, I provide my thoughts on each of the authors' rebuttal points.

Regarding Q1: The additional explanations provided in the general response have clarified the advantages of the proposed settings and methods. However, I still believe that the original submission did not fully emphasize these advantages, as the relevant explanations are scattered between the main paper and the supplementary material, and some crucial experimental comparisons are missing. Therefore, it is essential to include these new insights in a revised and reformatted manuscript.

Regarding Q2: I appreciate the authors' careful discussion comparing their approach to TTA-CDKM, and I generally agree with their perspective. As the authors mentioned, including such a discussion would indeed highlight the superiority of the proposed methods.

Regarding Q3-1: I have some questions regarding this part. According to the results, knowledge from the same devices does not seem to affect performance. I am curious about the nearly identical scores with and without CoLA (Noshare). Is there another reason that might explain this observation?

Regarding Q3-2: Thank you for pointing out that the information on efficiency was already included. I apologize for overlooking this. The additional details provided are also very helpful.

Regarding Q3-3, Q3-4, Q4, and Q5, I have also carefully read the authors' responses to these points. The additional analysis and results presented make sense. If this submission is accepted, I hope that this information will be properly included in the final version of the paper.

In summary, could you please provide further clarification on the questions I raised regarding Q3-1? For the other points, I’ve shared my thoughts on various aspects of the paper. I believe it would be sufficient to share your perspective if there are any issues or misunderstandings in my comments.
Dear Reviewer 1r2f,

We are glad to hear that all your concerns are addressed. Thanks again for your expertise and invaluable feedback on improving the quality of our paper!

Best Regards,

The Authors
Thanks for the response. 

The rebuttal addressed all my concerns. 

I will keep my score.
Dear Reviewer SsoW,

We appreciate your invaluable feedback and would be glad to include the new discussions and results in our revised paper.


However, **if we have addressed your concerns, we kindly ask for your consideration in increasing the score for our paper.**

We believe that our paper is distinct from existing literature and has made sufficient contributions, including:

- To the best of our knowledge, **we are the first to study collaborative adaptation across multiple devices at test time and the first to enhance TTA on devices with varying resources**, meanwhile keeping privacy preserved and communication efficient.
- **We devise two distinct collaborative learning paradigms for TTA.** With backpropagation, we jointly learn new domain-specific parameters and a reweighting term to reprogramm existing knowledge. With only forward passes, we aggregate different domain knowledge based on domain similarities in an optimization-free manner.
- Our proposed CoLA **covers a wide range of real-world scenarios**, which include multi-devices with multi-domains (collaborative TTA), a single device with multi-domains (lifelong TTA), and a single device with a single domain (single-domain TTA).
- We achieve notable results. Our proposed CoLA is plug-and-play with advanced TTA solutions and achieves **superior performance with negligible computation and memory overhead**. CoLA on forward-only agent significantly boosts the performance, *e.g.*, by 30% regarding accuracy on out-of-distribution samples, with nearly the same efficiency as standard inference.


Our novelty and contribution are also recognized by other reviewers, such as:

- *"The authors propose **a new and novel setting of cross-device collaborative TTA**."* [by **Reviewer L5Gu** and **Reviewer sr9b**]
- *"The method **considers practical scenarios** such as communication cost, devices without training capability, etc."* [by **Reviwer sr9b** and **Reviewer 1r2f**]
- *"The method is **plug-and-play with existing TTA methods**."* [by **Reviewer sr9b**]
- *"CoLA is **simple and efficient**, demonstrating **excellent performance** in collaborative, lifelong, and single-domain TTA tasks."* [by **Reviewer 1r2f**]

We sincerely hope our clarifications above can improve your opinion of our work and can help you reconsider your score. We look forward to your response and are happy to continue the discussion if you have further questions.

Best Regards,

The Authors
Dear Reviewer 1r2f,

We would like to thank you for recognizing the contributions of our work and also for the invaluable feedback. We are wondering if our response has addressed your questions appropriately and can further improve your opinion of our work.

We truly value your expertise and are happy to continue the discussion if you have further questions.

Best Regards,

The Authors
Dear Reviewer SsoW,

We would like to thank you for your invaluable feedback on improving the quality of our paper. In the previous response, we have re-clarified the novelty and contributions of our CoLA and demonstrated its efficiency and stability in diverse scenarios. 

We are wondering if our response has addressed your questions appropriately and can improve your opinion of our work? Kindly let us know if you might have further comments, and we will do our best to address them.

Best Regards,

The Authors
Dear Reviewer sr9b,

We are happy to hear that your concerns have been addressed and sincerely thank you for recognizing our novelty and practicality.

In this sense, **could we kindly request you to reconsider the possibility of improving your initial score?**

**We truly value your expertise and are hopeful for a favorable reconsideration.** We are happy to continue the discussion if you have further questions.

Best Regards,

The Authors
Thanks for the rebuttal. I've read it carefully and it addressed most of my concerns. I will keep my score on the positive side.
Dear Reviewer L5Gu,

Thank you for upgrading your score! Your comments are immensely beneficial in improving the quality of our paper.

**We value your expertise and are happy to continue the discussion if you have further questions.**

Best Regards,

The Authors
Thanks for the detailed response. The rebuttal addressed most of the concerns. Also, positioning the paper compared to Federated TTA and Cloud-Edge TTA makes the problem more novel.

I would raise the scoring to 5.