# crossdevice_collaborative_testtime_adaptation__58718c46.pdf

Cross-Device Collaborative Test-Time Adaptation

Guohao Chen1 2 Shuaicheng Niu3 Deyu Chen1 Shuhai Zhang1 2

Changsheng Li4 Yuanqing Li1 2 Mingkui Tan1 2

1South China University of Technology, 2Pazhou Laboratory, 3Nanyang Technological University, 4Beijing Institute of Technology,

In this paper, we propose test-time Collaborative Lifelong Adaptation (Co LA), 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, Co LA 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 optimizationfree manner, termed adaptation on follower agents. Experiments verify that Co LA 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 Image Net-C while maintaining nearly the same efficiency as standard inference. The source code is available at https://github.com/Cascol-Chen/COLA.

1 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.

Equal contribution. Email: secasper@mail.scut.edu.cn, shuaicheng.niu@ntu.edu.sg Corresponding author. Email: mingkuitan@scut.edu.cn, lcs@bit.edu.cn

38th Conference on Neural Information Processing Systems (Neur IPS 2024).

Shared Knowledge

(a) Prior single-device TTA (b) Our collaborative TTA

Principal Agent

Follower Agent TTA

Different Domain Knowledge / /

Figure 1: Comparison w.r.t. (a) prior single-device TTA vs. (b) our collaborative TTA. Prior TTA operates on each device independently and may be infeasible in resource-limited devices. In contrast, our collaborative TTA allows devices to share knowledge. Based on this, on different devices, one can choose to solely aggregate the shared knowledge for TTA (Follower Agents), or further conduct backpropagation for knowledge aggregation and new domain knowledge learning (Principal Agents).

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 (Co LA) 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 Co LA. 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 Co LA 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 Image Net-C. On follower agents, we enhance the accuracy by over 30% while maintaining nearly the same computation and memory efficiency as standard inference on Image Net-C.

Weights Δ𝜽𝜽

Source 𝜽𝜽𝑙𝑙 𝑜𝑜

Shared Domain Vectors T

Weights Δ𝜽𝜽0

Weights Δ𝜽𝜽𝑛𝑛

Learnable Knowledge Aggregation Principal

Frozen Learnable

Source 𝜽𝜽𝑙𝑙 𝑜𝑜

Weights Δ𝜽𝜽𝑖𝑖

Similarity-based Aggregation

Domain Similarity

Principal Agents Collaborative TTA via Knowledge Reprogramming Learning

Follower Agents Collaborative Optimization-free TTA

Weights Δ𝜽𝜽0

Weights Δ𝜽𝜽𝑛𝑛

LN 𝜽𝜽𝑙𝑙 𝑜𝑜T +

LN 𝜽𝜽𝑙𝑙 𝑜𝑜T +

Figure 2: An illustration of our proposed Co LA. 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.

2 Problem statement and motivation

Let fθ( ) be the model trained on a labeled dataset Dtrain = {(xi, yi)} and xi P (x). After training, fθ( ) is often deployed on various devices, on each device fθ( ) 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 fθ( ) to x by optimizing some self- /unsupervised learning objective at test time:

min θl L(x; θf, θl), x Q(x), (1)

where θf and θl 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 fθ( ) 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.

Domain knowledge vectors. 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 θi,j=θi,j l θo l to denote the knowledge learned on the i-th domain of the j-th device. Here, θi,j l denotes the learned parameters on the i-th domain of the j-th device, and θo l denotes the corresponding original learnable parameters. For privacy and efficiency considerations, we select the affine parameters of the norm layers as learnable parameters θl and transmit domain vectors between devices for knowledge sharing, which consumes negligible extra cost as in Table 5. We store each knowledge vector θi,j in a set

Algorithm 1 The overall pipeline of Co LA.

Input: Test samples {Dm}M m=1, where Dm={xm t }T t=1 denotes the batches of test samples on the m-th device, the model fθ( ) and its stem (first) layer fθs( ), threshold z. 1: Initialize: shared domain vectors T ={0}, ϕd=0 for each device. 2: for t = 1, 2, . . . , T do 3: for each device (in parallel) do 4: Calculate batch statistics ˆϕt over fθs(xm t ); 5: Update distribution statistics ϕd by Eqn. (6); 6: For Principal Agent: // knowledge reprogramming learning, Sect. 3.1 7: if D(ϕd, ˆϕt) > z then domain change detection, Eqn. (7) 8: Update domain vectors T by storing the newly learned θ and reset ϕd = 0. 9: end if 10: Predict ˆym t by fθ(xm t ) based on Eqn. (2); 11: Update α and θ via Eqn. (2) with backpropagation; 12: For Follower Agent: // similarity-based aggregation, Sect. 3.2 13: Update ρi for different domain knowledge via Eqn. (5); 14: Predict ˆym t by fθ(xm t ) based on Eqn. (3); 15: end for 16: end for Output: Predictions {ˆym t | t = 1, ..., T and m = 1, ..., M}.

T ={ θi,j}n,m i=1,j=1. During the continual adaptation process, we dynamically expand T by storing a new θi,j in T once θi,j is learned. For simplicity of presentation, we omit T as { θi}N i=1 where N=mn and exploit T to devise collaborative TTA strategies in the following sections.

3 Cross-device collaborative test-time adaptation

In this paper, we propose a test-time Collaborative Lifelong Adaptation (Co LA) method. In Co LA, 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 Co LA in Figure 2.

3.1 Collaborative test-time adaptation via knowledge reprograming learning

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 ={ θi}N i=1, where θi=θi θo l . For flexibility, we denote null knowledge as θ0=0 and include it in T . We use T to illustrate our collaborative learning scheme here and put details for detecting and storing each θi 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:

min α, θ L(x; θf, θl), where θl = θo l +

i=0 αi θi + θ and θi T = { θi}N i=0. (2)

Here, θ denotes learnable parameters for current round of adaptation, and α denotes the normalized weights for different domain knowledge, i.e., P

i αi = 1. Thus, knowledge reprogramming and new knowledge learning are decoupled into the optimization of α and θ. Note that we introduce θ0 to ensure more flexibility in reprogramming, e.g., by setting α0 = 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 Tl), where β is the logit vector and Tl is a learnable temperature.

3.2 Collaborative test-time adaptation via similarity-based knowledge aggregation

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 ={ θi}N i=0 shared from m principal resource-abundant devices with each having n encountered domains and θ0 = 0, the goal of adaptation is to find appropriate normalized weights γ RN+1 such that:

γ = arg min γ L(x; θf, θl), where θl = θo l +

i=0 γi θi and θi T = { θi}N i=0. (3)

Here, since backpropagation-based learning is not supported, we directly assign the specific value of each γi 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 ϕd denote the statistics of the current distribution that is online estimated via Eqn. (6), and ϕi be the distribution statistics on which θi is adapted (i.e., the corresponding ϕd while learning θi), we re-weight the knowledge from different distributions by:

γ = softmax(ρ), where ρi = 1 / D(ϕd, ϕi) + ϵ . (4)

Here, 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 ρi shall become sufficiently large (e.g., ρi > 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 Tf to soften ρi, thereby encouraging the aggregation

of more existing knowledge. Then, ρi is re-defined as:

ρi = 1 / Tf D(ϕd, ϕi) + ϵ . (5)

Remark. It is worth noting that our Co LA 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, Co LA offers several merits for real-world implementation: 1) Co LA involves only the transmission of learned parameters θi, which preserves user privacy and imposes much less communication burden (e.g., the affine parameters of the norm layers in Vi T-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) Co LA is decentralized and flexible, which allows all agents to join or leave the collaboration at any time.

3.3 Automatic domain shift detection for constructing domain knowledge vectors T

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 Co LA 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 ϕd and the statistics of the current test batch ˆϕt. Formally, let fθs( ) be the stem layer of fθ( ), i.e., the first layer. ˆϕt comprises the mean ˆµt and standard deviation ˆσt calculated over fθs(xt). Then, we estimate the statistics ϕd from the observed test samples {xt}T t=1 via exponential moving average:

ϕd = λˆϕt + (1 λ)ϕd, (6)

where 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.

D(ϕd, ˆϕt) = 1

i=1 KL(ϕd,i||ˆϕt,i)+KL(ˆϕt,i||ϕd,i), KL(ϕ1||ϕ2) = 1 2σ2 2 (σ2 1 +(µ1 µ2)2), (7)

where H denotes the dimension of statistics, and KL( || ) is the KL-divergence simplified from [19]. Here, a distribution shift is detected when D(ϕd, ˆϕt) > 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.

4 Experiments

Datasets and models. We conduct experiments on the Image Net-1k [6], as well as five benchmarks for OOD generalization, i.e., Image Net-C [16] (contains corrupted images in 15 types of 4 main categories and each type has 5 severity levels), Image Net-R (various artistic renditions of 200 Image Net classes) [15], Image Net-Sketch [55], Image Net-A [17], and Image Net-V2 [44]. We use Vi T-Base [8] as the source model unless stated otherwise. The model is trained on the source Image Net-1K [6] training set and the model weights are obtained from the timm repository [60].

Compared methods and implementation details. We compared our proposed Co LA with 1) Backpropagation-based methods: Co TTA [56], ETA [38], EATA [38], SAR [39], and De YO [25]. 2) Backpropagation-free methods: LAME [3] and T3A [21]. For Eqn. (2), We directly leverage the learnable test-time objectives from the integrated TTA methods. θ is optimized by following the update rules of the integrated baseline as listed in Appendix C. α is updated via the Adam W optimizer with a learning rate of 0.1. The shift detection threshold z is set to 0.1. For follower agents, we consistently set Tf in Eqn. (3) to 5 for all experiments. More details are put in Appendix A and C.

Table 1: Comparison on Image Net-C (level 5) regarding Accuracy (%) under lifelong adaptation for 10 rounds, in total of 150 corruptions, on a single principal resource-abundant device. We report the average accuracy of 15 corruptions in each round here and put more results in Appendix D.

Time: Round 1 2 3 4 5 6 7 8 9 10 Average

No Adapt 29.9 29.9 29.9 29.9 29.9 29.9 29.9 29.9 29.9 29.9 29.9 Co TTA [56] 44.9 40.6 35.8 32.7 30.4 28.9 27.7 27.1 27.2 26.5 32.2 EATA [38] 60.4 60.0 59.6 59.4 59.3 59.1 59.0 58.8 58.7 58.6 59.3

SAR [39] 59.1 60.6 60.9 61.2 61.3 61.4 58.3 60.4 60.8 61.1 60.5 + Co LA (Ours) 59.1 62.4 63.6 64.3 64.7 64.9 65.2 65.1 65.3 65.4 64.0(+3.5) ETA [38] 61.4 58.7 54.5 50.2 46.2 44.1 38.8 38.0 36.7 35.1 46.4 + Co LA (Ours) 62.0 63.9 64.8 65.1 65.3 65.3 65.3 65.3 65.4 65.4 64.8(+18.4) De YO [25] 59.8 48.8 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 10.9 + Co LA (Ours) 61.7 62.5 63.6 64.5 65.0 65.1 65.3 65.5 65.5 65.5 64.4(+53.5)

Table 2: Effectiveness under collaborative adaptation across principal resource-abundant devices w.r.t. Accuracy (%). Results are evaluated on Image Net-C (level 5, containing 15 corruption types of 4 groups). We share learned weights across devices post-adaptation to each group of corruptions.

Device 1 (Adapt ) Device 2 (Adapt ) Device 3 (Adapt ) Method Noise Blur Weat. Digit. Blur Noise Digit. Weat. Weat. Digit. Blur Noise Avg.

No Adapt 8.2 28.4 36.1 41.7 28.4 8.2 41.7 36.1 36.1 41.7 28.4 8.2 28.6 Co TTA [56] 28.9 41.3 50.2 47.6 36.3 37.1 50.4 52.7 50.4 55.0 42.5 38.7 44.2 EATA [38] 53.5 57.0 68.1 67.2 58.1 52.2 67.0 68.5 69.4 67.7 57.9 51.5 61.5

SAR [39] 50.4 54.4 66.3 64.5 55.1 48.3 64.0 66.4 66.5 64.3 55.4 47.7 58.6 + Co LA (Ours) 50.4 58.0 69.4 68.7 55.0 55.0 67.1 70.5 66.3 65.3 58.8 55.5 61.7

ETA [38] 55.2 56.9 67.5 66.0 59.8 51.7 65.0 67.4 70.3 67.8 58.0 49.4 61.2 + Co LA (Ours) 55.2 60.0 70.9 69.3 59.5 56.3 68.8 70.9 70.2 68.1 59.7 55.3 63.7

De YO [25] 56.3 49.9 68.1 67.8 55.6 46.7 67.2 69.0 71.1 68.8 51.1 4.3 56.3 + Co LA (Ours) 56.2 55.1 71.2 70.2 54.8 54.5 70.0 71.5 71.0 69.0 53.7 54.3 62.6

4.1 Comparison with state-of-the-art methods

Results under lifelong test-time adaptation. We evaluate the long-term effectiveness of our Co LA on Image Net-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 Co LA 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 Co TTA [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 Co LA 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 Co LA enhances ETA s performance even at the first round of adaptation, i.e., 61.4% (ETA) vs. 62.0% (ETA+Co LA), indicating that Co LA does not limit the learning ability. The sensitivity analyses on threshold z are provided in Appendix E.

Results under collaborative test-time adaptation. To evaluate our Co LA under the collaborative TTA scenario, we first assess its performance across multiple principal resource-abundant devices. From Table 2, our Co LA outperforms the integrated baseline from the adaptation to the second group of corruptions, e.g., the accuracy of 58.0% (SAR+Co LA) 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+Co LA) 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).

Table 3: Comparison on Image Net-C (level 5) regarding Accuracy (%) under lifelong adaptation on resource-limited follower devices. T3A* resets the model after adaptation on each corruption. Co LA exploits the learned weights from Table 2 (e.g., ETA + Co LA at the 7-th row) for Eqn. (3).

Noise Blur Weather Digital Method Gaus. Shot Imp. Def. Glass Mot. Zoom Snow Frost Fog Brit. Contr. Elas. Pix. JPEG Avg.

No Adapt 9.5 6.7 8.2 29.0 23.4 33.9 27.1 15.9 26.5 47.2 54.7 44.1 30.5 44.5 47.8 29.9 T3A [21] 9.5 7.0 8.7 23.3 23.3 31.2 25.9 11.9 24.2 44.0 52.2 41.0 30.1 43.0 47.0 28.2 T3A* [21] 9.5 6.5 8.1 29.8 24.1 34.3 28.2 16.0 26.9 49.0 55.5 44.5 33.1 44.5 48.2 30.5 LAME [3] 9.3 6.5 8.0 28.6 23.0 33.3 26.6 15.2 26.0 45.9 54.1 43.6 29.3 44.0 47.4 29.4

Co LA (SAR) 55.2 56.0 56.8 57.3 49.1 59.9 58.5 65.8 65.8 72.2 77.1 66.2 65.9 72.2 69.4 63.2 Co LA (ETA) 55.7 57.3 56.9 58.5 46.2 59.4 63.4 69.1 66.5 73.1 77.6 66.3 69.2 73.1 69.9 64.1 Co LA (De YO) 56.6 57.7 57.5 58.2 47.7 55.5 39.0 69.6 67.2 73.5 78.0 67.0 70.4 73.5 70.3 62.8

Table 4: Comparison under single-domain TTA (on one principal device) w.r.t. Acc (%). Results are averaged over 15 corruptions on Image Net-C (level 5). L.S denotes label distribution shifts, M.S denotes mixed domain shifts per SAR [39].

Method Mild L.S. M.S Avg.

No Adapt 29.9 29.9 29.9 29.9 SAR [39] 54.5 56.7 57.1 56.1 + Co LA (Ours) 57.7 58.5 58.0 58.1

ETA [38] 63.3 47.6 57.4 56.1 + Co LA (Ours) 64.4 55.2 58.3 59.3

De YO [25] 64.1 61.3 59.1 61.5 + Co LA (Ours) 64.7 63.5 59.3 62.5

Table 5: Comparison w.r.t. wall-clock time and memory on Image Net-C (Gaussian, level 5) on an A100 GPU. C/R refers to accuracy on Image Net-C/R. BP is short for back-propagation. Co LA utilizes weights of ETA+Co LA in Table 2.

Method BP C R T. (s) Mem. (MB)

No Adapt 9.5 43.1 50 816.6 T3A [21] 9.5 42.1 158 909.9 Co LA (Eqn. 3) 55.7 51.5 51 821.9

EATA [38] 49.5 56.8 113 7439.3 SAR [39] 44.0 51.8 202 7429.9

ETA [38] 51.9 57.5 109 7429.6 + Co LA (Eqn. 2) 54.3 59.0 112 7435.3

Given learned knowledge from resource-abundant principal devices (totaling 34 weights occupying 5.0 MB), we further evaluate the effectiveness of Co LA 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), Co LA achieves a substantial performance gain, e.g., enhancing the average accuracy from 29.9% to 64.1% in Co LA (ETA). Note that we also verify Co LA 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 De Yo [25], we validate our Co LA 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, Co LA 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 αi.

From Table 4, within all evaluated scenarios, incorporating Co LA consistently improves the performance by a considerable margin (e.g., +2.0% on SAR w.r.t. overall average accuracy). Interestingly, the enhancement from Co LA may even help surpass a stronger baseline, e.g., the average accuracy of 64.4% (ETA+Co LA) vs. 64.1% (De YO) 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, Co LA dynamically favors the more optimal one via loss optimization. This renders Co LA more robust to scenarios where perturbations may occur. We also visualize αi in Appendix E to offer more insights.

4.2 Ablation studies and more discussions

Effectiveness of Tl 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 (a), by leveraging the learned knowledge from other devices, ETA+Co LA achieves an up to 78.0 speed up compared with ETA, i.e., 51.7% accuracy with 640 samples (ETA+Co LA) vs. 51.37% accuracy with 49,920 samples (ETA), demonstrating the importance

1k 10k 20k 30k 40k 50k #Online Samples

Accuracy (%)

78.0 Speedup

(a) Effects of Tl in Eqn. (2)

ETA ETA + Co LA (Ours, w/o Tl)

ETA + Co LA (Ours)

1 3 5 7 9 inf The Value of Temperature Tf

Accuracy (%)

(b) Effects of Tf in Eqn. (5)

No Adapt (C) No Adapt (R) No Adapt (S) Our Co LA (C) Our Co LA (R) Our Co LA (S)

Figure 3: Ablation study of Co LA. In left, we compare the sample efficiency on Device2 in Table 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 Tf on seen (i.e., Image Net-C, Gaussian) and unseen distributions (i.e., Image Net-R/Sketch), where Co LA exploits weights of ETA+Co LA in Table 2 for Eqn. (3).

Table 6: Effectiveness of Co LA (Eqn. 2) on unseen distributions with weights learned on Image Net-C from Table 2.

Method R S Avg.

SAR [39] 51.9 33.8 42.8 + Co LA (Ours) 55.1 39.3 47.2

ETA [38] 57.7 43.1 50.4 + Co LA (Ours) 59.0 43.2 51.1

Table 7: Effectiveness of Co LA on prompt tuning. Results are reported on Image Net and its variants with CLIPRN50 [43]. Co LA exploits 78 hard prompts for Eqn. (2).

Method I A V2 R S Avg.

No Adapt 58.2 21.8 51.4 56.2 33.4 44.2 Ensemble 59.8 23.2 52.9 60.7 35.5 46.4

TPT [47] 60.7 26.7 54.7 59.1 35.1 47.3 + Co LA (Ours) 62.2 28.0 55.4 60.4 34.7 48.1

of cross-device collaboration and our effectiveness to facilitate knowledge sharing and utilization. Moreover, upon integrating Tl in Eqn. (2), Co LA demonstrates superiority without necessitating too many test samples, i.e., 53.2% accuracy (ETA+Co LA) vs. 22.2% accuracy (ETA+Co LA w.o. Tl) with 960 samples, suggesting the effectiveness of Tl to promote swift adaptation under distribution shifts. We also provide more comparison in Appendix E regarding sample efficiency on unseen distributions.

Effectiveness of Tf 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 Co LA consistently outperforms No Adapt regardless of Tf, demonstrating our effectiveness. On seen distribution, our improvement is particularly significant while the performance is insensitive to Tf in a reasonable range. However, when Tf 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., Image Net-R), aggregating a minority of knowledge may be insufficient to address distribution shifts. In this case, Tf plays an important role in enhancing robustness by aggregating the strengths of diverse knowledge. We fix Tf to 5 in experiments without careful tuning.

Memory and computation consumption of Co LA. Besides achieving strong performance across various scenarios, we demonstrate that Co LA incurs negligible computation and memory costs. From Table 5, on resource-limited follower devices, Co LA (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 No Adapt. On resource-abundant principal devices, Co LA enhances the performance of ETA by a considerable margin (i.e., +2.4% on Image Net-C) while incurring only 5.7 MB of additional runtime memory and 3s of latency, indicating that Co LA is even lighter than the regularizer introduced in EATA. Note that Co LA (Eqn. 3) determines appropriate re-weighting for different knowledge with a batch of test samples, outperforming ETA+Co LA w.r.t average accuracy on Image Net-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 Co LA can efficiently scale to over 10,000 domain vectors in Appendix E.

Generalization of Eqn. (2) on unseen distributions. Following Figure 3 (b), we further validate the effectiveness of Co LA (Eqn. 2) on unseen distributions. From Table 6, Co LA 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 Co LA is not limited to previously encountered distributions on both principal agents and follower agents.

Prompt tuning with Co LA using multiple hard prompts. Besides aggregating learned knowledge from other devices, we demonstrate that Co LA 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, Co LA enhances the adaptation performance on 4 out of 5 datasets (e.g., +1.5% on Image Net w.r.t. accuracy). These results collectively indicate that Co LA 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 Co LA conducts collaborative learning at the testing phase, whereas federated TTA conducts collaborative learning during federated source training. For instance, Fed THE+ [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 Co LA 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 Co LA paradigm can be applied to any pre-trained models, and thus offers much better flexibility in deployment. Additional comparisons with Fed Avg [32] for collaborative adaptation are also provided in Appendix E.

5 Conclusion

In this paper, we propose a multi-device Collaborative Lifelong Adaptation (Co LA) 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 Co LA, all devices/agents work collaboratively while keeping privacy preserved and communication efficient. Experiments verify that Co LA boosts the performance and efficiency of existing TTA solutions in collaborative, lifelong, and single-domain TTA scenarios.

Acknowledgments

This work was partially supported by National Natural Science Foundation of China (NSFC) 62072190 and TCL Science and Technology Innovation Fund. The authors thank Jinwu Hu and Yu Hu for discussions on domain knowledge reprogramming, and Yaofo Chen for consultations on cloud-edge test-time adaptation.

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Supplementary Materials for Cross-Device Collaborative Test-time Adaptation

A Related work 16

B More design details of Co LA 18

C More implementation details 20

C.1 More details on datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

C.2 More experimental protocols on evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

C.3 More experimental protocols on methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

D More experimental results 23

E Additional discussions 25

F Limitations and future works 29

G Broader impact 29

Table A: Characteristics of problem settings that adapt a trained model to a potentially shifted domain. Online adaptation predicts a single or batch of incoming test samples immediately. #Devices is the number of devices involved in TTA. Learned Knowledge is the knowledge from model adaptation.

Setting Target Testing Online #Devices Learned Resource-Limited Privacy Data Data Loss Knowledge Devices Transmission

Fine-tuning xt, yt % 1 Not Considered Not Considered Continual learning xt, yt % 1 Accumulated Not Considered Unsupervised DA xt % 1 Accumulated Not Considered Test-time training xt L(xt) ! 1 Not Considered Not Considered Fully TTA xt L(xt) ! 1 Not Considered Partly Applicable Federated TTA [1, 23] xt L(xt) ! 1 Not Considered Not Considered Preserved Intensive Cloud-Edge TTA [4] xt L(xt) ! 2 Not Considered Applicable Violated Intensive

Co LA (Ours) xt L(xt) ! M Accumulated Applicable Preserved Intermittent

A Related work

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: Eco TTA [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 Co LA 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 (Mo E) 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, Fed THE+ [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.

B More design details of Co LA

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 θn+1 l initialized after encountering the domain n+1 should remain the same as θn 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 θl=θo l by setting α0=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{ 1

J PJ 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 θn+1 as:

i=0 eβi Tl !

, s = max{1, ξ

Here, βn+1 is designed so that the magnitude ξ of the recalculated θ satisfies ξ wm, where wm is a constrained value set to 0.01. Moreover, to improve numerical stability in case Tl is 0, we clip the value of βn+1 between [ 10, 10]. The preserved knowledge θn+1 is then shared across devices.

We next provide a proposition to validate the reasonableness of the design for βn+1:

Proposition 1. Given βn+1 in Eqn. (8), the constraints that θn+2 l = θn+1 l and ξ wm 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 have

θn+1 l = θo l + α0 θ0 + α1 θ1 + + αn θn + θ, where α = softmax(β Tl).

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 αn+1 for θn+1. Besides, we initialize θ in order to learn new knowledge from the (n+2)-th domain. So we have

θn+2 l = θo l + α 0 θ0 + α 1 θ1 + + α n θn + αn+1 θn+1 + θ

After adding αn+1, to maintain the vector α as normalized weights, αi will change to

α i = eβi Tl

(Pn j=0 eβj Tl) + eβn+1Tl

= eβi Tl Pn j=0 eβj Tl

Pn j=0 eβj Tl

(Pn j=0 eβj Tl) + eβn+1Tl

Pn j=0 eβj Tl

(Pn j=0 eβj Tl) + eβn+1Tl .

As we want to ensure the stability of model performance, the overall model weights θn+2 l should be the same as θn+1 l that learned on the (n+1)-th domain, so θn+1 = θn+2 l θo l = θn+1 l θo l .

Thus, we expand θn+2 l as:

θn+2 l = θo l + α 0 θ0 + α 1 θ1 + + α n θn + αn+1 θn+1 + θ

= θo l + Pn i=0 eβi Tl

(Pn i=0 eβi Tl) + eβn+1Tl (α0 θ0 + α1 θ1 + + αn θn)

(Pn i=0 eβi Tl) + eβn+1Tl θn+1 + θ

= θo l + Pn i=0 eβi Tl

(Pn i=0 eβi Tl) + eβn+1Tl (θn+1 l θo l θ)

(Pn i=0 eβi Tl) + eβn+1Tl (θn+1 l θo l ) + θ

= θn+1 l Pn i=0 eβi Tl

(Pn i=0 eβi Tl) + eβn+1Tl θ + θ .

Considering θn+2 l = θn+1 l , we have

θn+1 l Pn i=0 eβi Tl

(Pn i=0 eβi Tl) + eβn+1Tl θ + θ = θn+1 l

θ = Pn i=0 eβi Tl

(Pn i=0 eβi Tl) + eβn+1Tl θ.

As θ should be as small as possible to enable flexible adaptation, the magnitude of θ should be no larger than wm, i.e. ξ wm. So we scale θ by a factor of s, i.e. θ = 1

s θ. If the magnitude of ξ already satisfies ξ wm, we set s = 1. Otherwise, we set s = ξ wm . Thus, we have s = max{1, ξ wm } and Pn i=0 eβi Tl

(Pn i=0 eβi Tl) + eβn+1Tl = 1

i=0 eβi Tl !

C More implementation details

C.1 More details on datasets

In this paper, we conduct experiments on Image Net-1K [6] and its five variants to evaluate the out-of-distribution generalization ability, i.e., Image Net-C [16], Image Net-R [15], Image Net-A [17], Image Net-V2 [44], and Image Net-Sketch [55].

Image Net-C

Image Net-R

Image Net-S

Image Net-V2

Image Net-A

Adversarial

Adversarial

Figure A: Visualizations of images in Image Net and Image Net-C/V2/A/R/Sketch.

Image Net-C consists of various versions of corruption applied to 50,000 validation images from Image Net. 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.

Image Net-R contains 30,000 images featuring diverse artistic renditions of 200 Image Net classes. These images are predominantly sourced from Flickr and filtered by Amazon MTurk annotators.

Image Net-A comprises 7,500 images covering 200 Image Net classes. These images are derived from real-world, naturally occurring examples that lead to a notable degradation in classifier performance.

Image Net-V2 is a newly collected test dataset extracted from the same test distribution as Image Net. It comprises three test sets, each containing 10,000 new images and covering 1000 Image Net classes. Following previous TTA methods [36], we utilize the Matched Frequency subset of Image Net-V2 for evaluation, in which the images are sampled to match the class frequency distributions of the original Image Net validation dataset.

Image Net-Sketch consists of 50,899 images represented as black and white sketches, encompassing 1000 Image Net classes. Each class contains approximately 50 images.

C.2 More experimental protocols on evaluation

We use Vi T-Base [8] as the source model for all experiments except Table 7. The model is trained on the source Image Net-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 weights5 are directly obtained from the original CLIP6 repository [43]. All experiments are conducted on a single NVIDIA A100 GPUS, using Py Torch 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

3https://storage.googleapis.com/vit_models/augreg/B_16-i21k-300ep-lr_0.001-aug_medium1-wd_0.1do_0.0-sd_0.0 imagenet2012-steps_20k-lr_0.01-res_224.npz 4https://github.com/pprp/timm 5https://openaipublic.azureedge.net/clip/models/afeb0e10f9e5a86da6080e35cf09123aca3b358a0c3e3b6c78a 7b63bc04b6762/RN50.pt 6https://github.com/openai/CLIP

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., Co LA (SAR) utilizes the learned weights of SAR+Co LA from Table 2, and Co LA (ETA) utilizes the learned weights of ETA+Co LA 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 Co LA 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, Co LA 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}

C.3 More experimental protocols on methods

Co LA (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 Tl is updated via the Adam W 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/De YO 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 Tf in Eqn. (3) to 5 for all experiments. Moving average factor λ is set to 0.2.

SAR7 [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 E0 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 & EATA8 [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 E0 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.

De YO9 [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 E0 is set to 0.4 ln C and the entropy factor τEnt is set to 0.5 ln C, where C is the number of task classes. The Pseudo-Label Probability Difference (PLPD) threshold τPLPD 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.

Co TTA10 [56]. We follow all hyperparameters that are set in Co TTA 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 pth is chosen from {0.1, 0.2}. In all experiments, we consistently set the learning rate to 0.001 and pth 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 Vi T-Base.

LAME11 [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 k NN 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.

T3A12 [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.

TPT13 [47]. We follow all hyper-parameters that are set in TPT unless it does not provide. Specifically, we use Adam W 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.

7https://github.com/mr-eggplant/SAR 8https://github.com/mr-eggplant/EATA 9https://github.com/Jhyun17/De YO 10https://github.com/qinenergy/cotta 11https://github.com/fiveai/LAME 12https://github.com/matsuolab/T3A 13https://github.com/azshue/TPT

D More experimental results

In the main paper, we only report the results averaged over 15 corruptions in Image Net-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 Co LA 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 Co LA outperforms the integrated baseline in the first round of adaptation, e.g., the accuracy of 62.0% (ETA+Co LA) vs. 61.4% (ETA). This mainly stems from the latter corruptions encountered in the first round, where Co LA 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+Co LA) vs. 35.1% (ETA), further indicating our effectiveness in accumulating and utilizing learned knowledge for long-range adaptation. Note that Co LA 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 Co TTA [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 Co LA outperforms the integrated baseline from the adaptation to the second group of corruption, e.g., the accuracy of 53.6% (SAR+Co LA) 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+Co LA) 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 Co LA with existing TTA solutions enhances the adaptation performance on most corruptions under both scenarios, demonstrating our effectiveness. Specifically, Co LA 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. Co LA 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 Co LA more robust to noise. We also visualize αi in Appendix E to offer more insights.

Table B: Comparisons on Image Net-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].

Mild Scenarios Gaus. Shot Imp. Def. Glass Mot. Zoom Snow Frost Fog Brit. Contr. Elas. Pix. JPEG Avg.

No Adapt 9.5 6.7 8.2 29.0 23.4 33.9 27.1 15.9 26.5 47.2 54.7 44.1 30.5 44.5 47.8 29.9 EATA [38] 49.5 48.9 50.2 54.8 54.8 58.9 56.2 61.6 60.7 70.6 75.2 66.9 63.7 69.7 66.8 60.6

SAR [39] 44.0 24.2 45.3 53.0 49.9 55.7 51.0 57.4 45.1 66.6 74.7 64.5 55.3 66.7 64.0 54.5 + Co LA (Ours) 48.4 27.1 49.0 54.9 53.7 58.7 55.1 60.9 50.5 69.2 76.0 66.2 60.5 69.2 66.4 57.7

ETA [38] 51.9 51.9 52.8 57.6 57.6 62.2 60.0 66.1 65.1 72.5 77.4 67.6 66.1 72.0 69.2 63.3 + Co LA (Ours) 53.4 53.7 54.3 58.2 58.6 63.2 61.5 67.2 66.0 73.0 77.7 68.2 68.1 73.0 70.0 64.4

De YO [25] 53.2 53.4 54.1 58.3 58.3 63.2 56.6 67.2 66.0 73.4 78.1 68.0 67.9 73.2 70.1 64.1 + Co LA (Ours) 54.3 50.6 55.0 58.4 59.4 64.2 60.1 68.1 66.5 73.9 78.1 68.3 68.8 73.9 70.4 64.7

Label Shifts Gaus. Shot Imp. Def. Glass Mot. Zoom Snow Frost Fog Brit. Contr. Elas. Pix. JPEG Avg.

No Adapt 9.5 6.7 8.2 29.0 23.4 33.9 27.1 15.9 26.5 47.2 54.7 44.1 30.5 44.5 47.8 29.9 EATA [38] 36.1 35.7 35.4 45.0 42.8 52.0 45.1 55.0 48.7 62.1 73.0 42.9 55.8 63.9 62.7 50.4

SAR [39] 47.9 30.7 48.4 55.4 54.2 58.8 54.6 43.5 48.3 69.4 76.3 66.2 60.8 69.4 66.6 56.7 + Co LA (Ours) 49.6 50.4 50.7 56.4 56.4 60.3 57.3 40.9 36.6 71.5 77.2 67.0 64.2 71.3 68.5 58.5

ETA [38] 31.0 34.4 32.0 30.5 44.8 49.6 46.4 54.9 53.0 56.3 74.1 25.1 57.8 64.2 59.4 47.6 + Co LA (Ours) 40.2 37.6 42.4 47.1 49.6 52.5 53.0 59.7 58.4 65.0 74.6 50.9 61.3 68.9 66.3 55.2

De YO [25] 53.0 53.9 54.5 57.8 59.0 63.9 12.7 68.0 66.1 73.2 77.9 66.6 68.9 73.7 70.6 61.3 + Co LA (Ours) 52.9 54.5 54.9 58.0 59.2 63.6 43.1 68.3 66.0 73.3 78.0 66.8 69.1 73.8 70.7 63.5

Table C: Comparison on Image Net-C (severity level 5) regarding Accuracy (%) under lifelong adaptation for 10 rounds. Here, we provide additional results on the first and last rounds of adaptation.

Round 1 Gaus. Def. Snow Contr. Shot Glass Frost Elas. Imp. Mot. Fog Pix. Brit. Zoom JPEG Avg.

No Adapt 9.5 29.0 15.9 44.1 6.7 23.4 26.5 30.5 8.2 33.9 47.2 44.5 54.7 27.1 47.8 29.9 Co TTA [56] 24.4 35.2 34.6 48.3 41.9 40.0 52.6 49.8 47.0 44.5 48.8 54.6 63.7 35.7 53.1 44.9 EATA [38] 49.4 53.6 61.3 65.8 49.6 54.5 60.5 64.9 50.5 57.9 69.2 69.5 75.2 56.6 67.3 60.4

SAR [39] 44.0 51.9 58.5 63.3 48.8 53.0 61.0 63.5 51.2 57.2 66.9 69.0 76.5 54.0 67.2 59.1 + Co LA (Ours) 41.9 51.4 57.8 63.9 48.8 52.7 61.0 62.6 52.6 57.3 68.2 69.3 76.5 54.2 67.7 59.1

ETA [38] 51.9 55.6 64.5 64.6 53.2 55.5 62.4 66.4 52.1 57.9 67.5 69.8 75.3 57.7 66.2 61.4 + Co LA (Ours) 48.0 55.2 63.5 66.2 51.8 55.6 63.7 65.8 54.3 59.8 71.0 71.1 76.7 58.3 68.5 62.0

De YO [25] 52.8 56.4 65.9 65.5 54.3 57.0 63.8 68.2 54.1 60.3 69.5 71.8 76.7 20.2 60.0 59.8 + Co LA (Ours) 49.7 55.9 65.0 66.4 53.2 56.9 65.0 67.4 55.2 61.4 72.0 72.3 77.7 37.8 69.7 61.7

Round 10 Gaus. Def. Snow Contr. Shot Glass Frost Elas. Imp. Mot. Fog Pix. Brit. Zoom JPEG Avg.

No Adapt 9.5 29.0 15.9 44.1 6.7 23.4 26.5 30.5 8.2 33.9 47.2 44.5 54.7 27.1 47.8 29.9 Co TTA [56] 22.1 20.7 27.2 22.4 25.2 22.0 29.6 29.4 25.8 24.4 28.3 31.3 38.2 20.2 31.5 26.5 EATA [38] 47.6 51.5 58.7 63.9 46.8 52.4 59.3 62.6 48.3 56.2 67.0 68.3 74.2 55.8 66.1 58.6

SAR [39] 51.3 55.4 62.5 63.3 52.7 55.9 62.0 64.3 53.2 59.1 67.8 70.4 75.9 55.9 67.1 61.1 + Co LA (Ours) 56.0 58.4 67.8 67.8 57.2 59.2 66.2 69.4 57.4 63.7 72.7 73.3 77.8 63.1 70.4 65.4

ETA [38] 32.6 28.8 33.4 17.5 31.4 31.9 36.8 42.3 32.1 29.2 30.6 46.0 57.7 34.9 41.7 35.1 + Co LA (Ours) 55.8 58.3 68.4 67.9 57.1 59.2 66.3 69.7 56.9 64.2 73.1 73.2 77.5 64.2 69.8 65.4

De YO [25] 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 + Co LA (Ours) 56.9 58.9 69.7 68.2 58.1 59.8 66.9 70.8 58.2 64.7 73.7 73.9 78.0 53.9 70.9 65.5

Table D: Effectiveness under collaborative adaptation across resource-abundant principal devices w.r.t. Acc. (%). Results are evaluated on Image Net-C (severity level 5, containing 15 corruption types of 4 groups). We share learned weights across devices post-adaptation to each group of corruptions.

Device 1 Gaus. Shot Imp. Def. Glass Mot. Zoom Snow Frost Fog Brit. Contr. Elas. Pix. JPEG Avg.

No Adapt 9.5 6.7 8.2 29.0 23.4 33.9 27.1 15.9 26.5 47.2 54.7 44.1 30.5 44.5 47.8 29.9 Co TTA [56] 17.7 28.4 40.5 37.0 43.4 46.5 38.1 39.1 49.1 48.6 63.8 41.5 42.5 54.0 52.2 42.8 EATA [38] 50.4 54.3 55.7 53.8 56.1 59.6 58.6 62.3 63.8 70.5 75.9 66.2 64.1 70.1 68.3 62.0

SAR [39] 44.5 51.8 54.8 51.3 53.6 57.7 55.0 59.7 62.0 67.2 76.3 63.1 59.4 68.5 67.2 59.5 + Co LA (Ours) 44.5 51.8 54.8 56.4 56.5 61.2 57.9 64.7 64.4 71.7 76.8 66.4 66.7 72.2 69.6 62.4

ETA [38] 51.9 56.3 57.2 53.1 56.7 58.8 58.9 62.2 63.3 68.9 75.5 62.7 64.3 69.9 67.1 61.8 + Co LA (Ours) 52.1 56.3 57.1 57.2 58.0 62.1 62.6 67.7 66.3 72.7 77.1 66.0 69.0 72.5 69.7 64.4

De YO [25] 52.9 57.7 58.3 54.9 58.0 61.4 25.5 61.5 63.9 70.1 77.0 63.5 67.0 71.6 69.2 60.8 + Co LA (Ours) 52.9 57.6 58.2 57.9 58.3 62.5 41.6 67.8 66.4 73.0 77.5 66.4 70.5 73.3 70.5 63.6

Device 2 Def. Glass Mot. Zoom Gaus. Shot Imp. Contr. Elas. Pix. JPEG Snow Frost Fog Brit. Avg.

No Adapt 29.0 23.4 33.9 27.1 9.5 6.7 8.2 44.1 30.5 44.5 47.8 15.9 26.5 47.2 54.7 29.9 Co TTA [56] 31.4 31.7 43.9 38.1 27.0 37.7 46.7 45.2 46.3 56.2 54.0 47.0 50.9 49.3 63.5 44.6 EATA [38] 55.4 57.2 60.5 59.5 48.5 53.1 55.0 65.0 64.0 70.5 68.4 62.9 64.0 71.0 76.1 62.1

SAR [39] 53.0 53.4 58.7 55.3 38.9 51.5 54.7 62.2 57.6 68.2 68.0 59.9 61.9 67.6 76.3 59.1 + Co LA (Ours) 52.9 53.4 58.6 55.1 53.6 55.4 56.1 66.4 61.9 71.1 69.2 66.2 65.6 72.9 77.3 62.4

ETA [38] 57.6 58.8 61.7 61.1 47.4 53.2 54.4 57.3 64.6 70.5 67.7 62.1 62.7 69.0 75.6 61.6 + Co LA (Ours) 57.5 58.3 61.2 61.0 54.8 57.0 57.1 64.6 68.4 72.2 70.1 67.5 66.0 72.8 77.3 64.4

De YO [25] 58.1 59.5 63.0 41.8 39.3 50.5 50.4 61.4 66.8 71.6 68.9 64.6 63.9 70.5 76.9 60.5 + Co LA (Ours) 58.3 59.1 62.6 39.3 47.9 57.5 58.2 66.6 69.9 73.0 70.5 68.3 66.9 73.0 77.7 63.3

Device 3 Snow Frost Fog Brit. Contr Elas. Pix. JPEG Def. Glass Mot. Zoom Gaus. Shot Imp. Avg.

No Adapt 15.9 26.5 47.2 54.7 44.1 30.5 44.5 47.8 29.0 23.4 33.9 27.1 9.5 6.7 8.2 29.9 Co TTA [56] 26.1 48.0 56.5 71.2 53.1 45.3 60.9 60.6 42.3 42.8 46.8 38.2 30.2 39.8 46.2 47.2 EATA [38] 63.8 65.3 71.8 76.6 66.9 64.7 70.5 68.8 55.7 56.7 60.2 59.1 47.5 52.7 54.3 62.3

SAR [39] 57.9 63.1 68.6 76.3 64.6 58.0 67.2 67.7 54.5 54.3 58.3 54.6 37.5 51.0 54.6 59.2 + Co LA (Ours) 57.9 63.0 68.0 76.2 64.6 59.7 69.1 67.8 56.5 57.9 61.6 59.2 53.9 56.3 56.5 61.9

ETA [38] 66.0 66.3 71.9 77.0 66.0 65.6 70.7 68.8 55.3 56.8 60.1 59.9 44.3 50.9 52.9 62.2 + Co LA (Ours) 66.0 66.0 71.9 76.9 65.4 66.4 71.6 69.1 56.7 58.0 61.8 62.1 54.0 56.0 55.9 63.9

De YO [25] 67.2 66.9 72.7 77.7 66.3 67.4 71.9 69.6 56.6 58.1 61.6 28.2 11.7 1.0 0.1 51.8 + Co LA (Ours) 67.0 66.6 72.7 77.6 66.1 67.6 72.5 69.7 56.5 57.5 61.4 39.6 49.1 56.9 56.8 62.5

E Additional discussions

Robustness of Co LA against potential harmful knowledge. Note that Co LA 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, Co LA 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.

Table E: Robustness of our Co LA using only pre-trained parameters and N harmful prior knowledge, i.e., the randomly initialized domain vectors. Results are obtained on Image Net-C (Gaussian, level 5).

Method N = 0 N = 2 N = 4 N = 100 N = 1, 000

ETA+Co LA (Equal α) 51.97 0.10 0.10 0.10 0.10 ETA+Co LA (Random α) 51.97 10.46 0.15 0.10 0.10

ETA+Co LA (Ours) 51.97 52.02 52.04 52.04 52.04

Scalability of Co LA with more collaborative devices. Co LA scales well with an increasing number of devices, i.e., with more shared domain vectors. From Table F, ETA/ETA+Co LA consistently benefits from additional participating devices, e.g., ETA+Co LA achieves an accuracy of 65.2% with 11 devices compared to 61.8% with one device. This highlights the importance of cross-device collaboration and Co LA s effectiveness under more large-scale multi-device collaborative TTA.

Table F: Effectiveness of Co LA with an increasing number of principal devices (with back-propagation capability). Here, each device continuously encounters 15 domains from Image Net-C (level 5) in different domain orders. Results are averaged over all principal devices.

#Devices 1 3 5 7 9 11

SAR+Co LA 59.7 62.1 62.8 63.6 63.8 63.9(+4.2) ETA+Co LA 61.8 63.9 64.3 64.9 65.0 65.2(+3.4)

Efficiency of Co LA with increasing domain vectors. Our Co LA is both computation and memory efficient at exploiting domain vectors. From Table H, Co LA efficiently scales to over 10,000 domain vectors, incurring only an additional 11s of runtime and 1,502MB of extra memory, yet remains substantially more efficient than Co TTA. We believe that 10,000 domain vectors should be adequate for handling most real-world applications with proper management.

Table G: Efficiency comparison on Image Net-C (Gaussian, level 5) using a single A100. N is the number of domain vectors, which we initialize as random parameters in this table.

Method ETA +Co LA (N = 1) +Co LA (N = 100) +Co LA (N = 10, 000) Co TTA

Time (s) 109 110 112 120 937 Memory (MB) 7,433.2 7,433.7 7,448.2 8,935.5 21,628.6

Sensitivity of threshold z for shift detection. Co LA remains effective among a wide range of threshold z, as shown in Table A. From the results, while a stricter threshold saves more domain vectors, Co LA achieves a stable performance of around 64.7%. When threshold z increases, Co LA saves significantly fewer domain vectors and still enhances the performance significantly, i.e., the average accuracy of 62.2% in ETA+Co LA (z=10) vs. 46.4% in ETA.

Table H: Sensitivity of threshold z. Experiments follow the settings of Table 1, i.e., single-device lifelong adaptation, and Co LA is incorporated with ETA. We report average accuracy over 10 rounds, each comprising 15 corruptions of Image Net-C. The average accuracy of the ETA baseline is 46.4%.

Co LA (z=0.01) Co LA (z=0.05) Co LA (z=0.1) Co LA (z=1) Co LA (z=10)

Avg. Acc. 64.7 64.6 64.8 63.8 62.2 #Saved Vectors 20740 369 169 110 48

Advantages of Co LA over Fed Avg [32] in collaborative TTA. We further compare our Co LA with Fed Avg [32] in cross-device collaborative/federated learning. From Table I, Co LA consistently outperforms Fed Avg when incorporated with the baseline for collaborative TTA. More importantly, Fed Avg, which simply averages the model parameters on different devices, may deteriorate model performance (i.e., the average accuracy of 61.2% in ETA vs. 58.0% in ETA+Fed Avg). This is because different devices may encounter different distribution shifts, and thus the knowledge from other devices may not be beneficial for adapting to the current domain. In contrast, our Co LA addresses this by learning at test time to optimize the aggregation of knowledge from different devices.

Table I: Effectiveness of Co LA and Fed Avg [32] for cross-device collaborative TTA w.r.t. Acc. (%). The experiments follow the settings of Table 2 in the main paper.

Device 1 (Adapt ) Device 2 (Adapt ) Device 3 (Adapt ) Method Noise Blur Weat. Digit. Blur Noise Digit. Weat. Weat. Digit. Blur Noise Avg.

No Adapt 8.2 28.4 36.1 41.7 28.4 8.2 41.7 36.1 36.1 41.7 28.4 8.2 28.6 EATA [38] 53.5 57.0 68.1 67.2 58.1 52.2 67.0 68.5 69.4 67.7 57.9 51.5 61.5

SAR [39] 50.4 54.4 66.3 64.5 55.1 48.3 64.0 66.4 66.5 64.3 55.4 47.7 58.6 + Fed Avg [32] 50.4 56.6 67.6 66.1 55.1 52.2 65.6 68.1 66.3 64.9 57.2 51.8 60.2 + Co LA (Ours) 50.4 58.0 69.4 68.7 55.0 55.0 67.1 70.5 66.3 65.3 58.8 55.5 61.7

ETA [38] 55.2 56.9 67.5 66.0 59.8 51.7 65.0 67.4 70.3 67.8 58.0 49.4 61.2 + Fed Avg [32] 55.2 58.9 65.1 62.5 59.6 51.0 63.4 63.7 70.3 46.2 54.0 46.4 58.0 + Co LA (Ours) 55.2 60.0 70.9 69.3 59.5 56.3 68.8 70.9 70.2 68.1 59.7 55.3 63.7

Robustness of Co LA under small batch sizes. The stability of Co LA under small batch sizes is primarily determined by the base algorithms, such as ETA and SAR, rather than Co LA itself. This is because Co LA 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, Co LA achieves a consistent result when incorporated with SAR, demonstrating no performance degradation as the batch size reduces from 16 to 2. Meanwhile, Co LA can also help improve stability under small batch sizes. For instance, as the batch size reduces from 4 to 2, ETA+Co LA achieves nearly no performance degradation while the baseline ETA s performance degrades by 1.4%.

Table J: Robustness of our Co LA under various batch sizes. We follow the same settings of Table 2 in the main paper and report average accuracy over all devices and corruptions here.

Method BS = 64 BS = 16 BS = 4 BS = 2

SAR [39] 58.6 58.8 58.9 58.7 + Co LA (Ours) 61.7 61.6 61.7 61.7

ETA 61.2 60.5 58.5 57.1 +Co LA (Ours) 63.7 62.8 61.7 61.5

Effectiveness of Co LA on Res Net models. Table K demonstrates the effectiveness of our Co LA on Res Net-50, where Co LA updates and stores the affine parameters of batch normalization layers in Res Net. From Table K, Co LA consistently enhances the performance of ETA/EATA/SAR throughout 10 rounds of adaptation and addresses the issue of performance degradation in long-term adaptation. These results are consistent with Table 1 in the main paper using Vi T-Base, further indicating Co LA s effectiveness in accumulating and exploiting learned knowledge with diverse model architectures.

Table K: Effectiveness of Co LA on Res Net-50 in the lifelong TTA scenarios following Table 1.

Time: Round 1 2 3 4 5 6 7 8 9 10 Average

No Adapt 18.0 18.0 18.0 18.0 18.0 18.0 18.0 18.0 18.0 18.0 18.0 Co TTA [56] 33.4 23.6 9.6 2.2 1.2 1.2 1.2 1.2 1.2 1.2 7.6

SAR [39] 35.9 17.5 21 36.2 18 13.6 35.8 16.5 13.5 36.1 24.4 + Co LA (Ours) 39.4 42 43 43.5 43.9 44.4 44.7 45 45.2 45.3 43.6(+19.2) ETA [38] 42.4 40.4 38.9 37.6 37 36 35.9 35.2 35.1 34.7 37.3 + Co LA (Ours) 46.5 46.5 49.5 49.5 49.7 49.8 49.9 49.9 49.9 49.8 49.3(+12.0) EATA [38] 47.5 47.3 47.1 46.7 46.8 46.6 46.4 46.3 46.2 46.2 46.7 + Co LA (Ours) 48.2 49.5 50.0 50.1 50.2 50.2 50.3 50.3 50.3 50.2 49.9(+3.2)

Effectiveness of Co LA in sample efficiency on unseen distributions. We validate the effectiveness of Eqn. (2) to facilitate sample-efficient TTA on unseen distributions. From Figure B, Co LA consistently enhances the sample efficiency and the overall performance, i.e., with an up to 30.0 speed up on both Image Net-R and Image Net-Sketch, indicating that the effectiveness of Co LA is not limited to previously encountered distributions. More interestingly, compared with SAR, Co LA helps mitigate overfitting on Image Net-Sketch. This can be attributed to that, in the unsupervised adaptation, SAR learns on more erroneous predictions since its performance is particularly limited at the beginning of adaptation. This phenomenon further demonstrates the importance of sample efficiency and our effectiveness in leveraging shared knowledge for efficient TTA.

1K 10K 20K 30K #Online Samples

Accuracy (%)

30.0 Speedup

(a) Comparison on Image Net-R

SAR SAR + Co LA (Ours)

1k 10k 20k 30k 40k 50k #Online Samples

Accuracy (%)

30.0 Speedup

(a) Comparison on Image Net-Sketch

SAR SAR + Co LA (Ours)

Figure B: Additional comparisons w.r.t sample efficiency on unseen distributions. Here, Co LA leverages learned weights on Image Net-C (i.e., from SAR+Co LA in Table 2, the fifth row) while the effectiveness in sample efficiency is evaluated on Image Net-R and Image Net-Sketch.

Effectiveness of Co LA in mitigating error accumulation. We provide visualization of the learned βi in Figure C. Here, all domain vectors are learned on the same domain, i.e., Gaussian Noise, where we save learned weights post-adaptation to 10 batches of samples. Generally, a later saved domain vector should be prioritized as it learns on more samples. Nevertheless, in the context of unsupervised TTA, a model may learn from erroneous pseudo-labels, where the performance would significantly deteriorate, known as error accumulation. From Figure C, Co LA adaptively assigns lower βi on domain vectors that may have accumulated error, e.g., from the 80-th to the 90-th domain vectors, according to loss optimization. Thus, Co LA demonstrates potential effectiveness in mitigating error accumulation, enhancing ETA s performance by +7.6% on Image Net-C under label distribution shifts.

0 20 40 60 80 100 120 140 160 i th domain vector

Figure C: Visualization of βi for ETA+Co LA on Image Net-C(severity level 5, Gaussian) under online imbalanced label distribution shifts. Co LA saves learned weights for every adaptation to 10 batches of samples while no weights are discarded for visualization. Learned temperature Tl is 0.49.

Effectiveness of our domain shift detector. We provide additional results to demonstrate the effectiveness of our domain distance function, i.e., Eqn. (7), for shift detection. In our experiments,

we consistently set ϕd to 0.1 for shift detection. From Figure D, our domain shift detector demonstrates sensitivity between corruptions from different groups, e.g., with a distance of 99 between impulse noise and contrast , and a distance of 32 between gaussian noise and defocus blur .

gaussian noise

impulse noise

defocus blur

motion blur

gaussian noise

impulse noise

defocus blur

motion blur

0 0.0058 0.0001 32 20 11 8.6 0.65 1.3 15 0.8 1e+02 1.1 2.2 1.2

0.0058 0 0.0066 34 21 11 9.2 0.74 1.5 16 0.91 1.1e+02 1.2 2.4 1.3

0.0001 0.0066 0 32 20 11 8.6 0.64 1.3 15 0.8 99 1.1 2.2 1.2

32 34 32 0 0.1 0.3 0.44 6.8 3.5 0.22 4.9 1.2 4 2.2 4.2

20 21 20 0.1 0 0.059 0.11 3.7 1.9 0.22 2.7 2.3 2.1 1.1 2.1

11 11 11 0.3 0.059 0 0.016 2.1 0.99 0.27 1.5 3.2 1.1 0.51 1.2

8.6 9.2 8.6 0.44 0.11 0.016 0 1.6 0.76 0.35 1.2 3.8 0.83 0.36 0.9

0.65 0.74 0.64 6.8 3.7 2.1 1.6 0 0.17 3.8 0.11 26 0.17 0.41 0.17

1.3 1.5 1.3 3.5 1.9 0.99 0.76 0.17 0 1.8 0.17 14 0.21 0.2 0.25

15 16 15 0.22 0.22 0.27 0.35 3.8 1.8 0 3.1 1.4 2.5 1.4 2.7

0.8 0.91 0.8 4.9 2.7 1.5 1.2 0.11 0.17 3.1 0 20 0.12 0.26 0.13

1e+02 1.1e+02 99 1.2 2.3 3.2 3.8 26 14 1.4 20 0 18 11 19

1.1 1.2 1.1 4 2.1 1.1 0.83 0.17 0.21 2.5 0.12 18 0 0.11 0.008

2.2 2.4 2.2 2.2 1.1 0.51 0.36 0.41 0.2 1.4 0.26 11 0.11 0 0.14

1.2 1.3 1.2 4.2 2.1 1.2 0.9 0.17 0.25 2.7 0.13 19 0.008 0.14 0

Figure D: Effectiveness of our domain distance function, i.e., D( , ) defined in Eqn. (7), to capture the magnitude of domain shift. Here, we estimate the domain distance between each corruption in Image Net-C (level 5, with 15 corruptions). The statistic of each domain is estimated via Eqn. (6).

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 Co LA performs stably with small stds and it lowers the std of ETA&De Yo, suggesting Co LA s stability.

Table L: Statistical comparison. Experiments follow the settings of Table 2.

Device 1 (Adapt ) Device 2 (Adapt ) Device 3 (Adapt ) Method Noise Blur Weat. Digit. Blur Noise Digit. Weat. Weat. Digit. Blur Noise Avg.

ETA [38] 55.1 56.8 67.3 58.5 59.7 51.6 52.2 66.0 70.4 67.8 57.9 49.5 60.2 1.8 + Co LA (Ours) 55.1 59.7 70.3 68.7 59.5 56.3 65.2 70.3 70.3 68.0 59.2 54.6 63.1 0.7 SAR [39] 50.3 54.4 66.3 64.7 55.1 48.0 63.9 66.5 66.5 64.4 55.6 47.0 58.6 0.1 + Co LA (Ours) 50.3 57.9 69.1 68.1 55.0 54.8 67.2 70.1 66.4 65.1 58.7 54.5 61.4 0.3 De YO [25] 56.3 50.5 67.6 67.9 55.4 44.9 53.5 55.4 71.1 68.9 52.0 26.6 55.8 3.9 + Co LA (Ours) 56.2 54.7 70.4 69.2 54.1 55.9 68.8 70.6 71.1 68.7 52.4 54.2 62.2 0.3

F Limitations and future works

Finetuning LLM. We mainly verify our Co LA 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 Co LA on more scenarios. For instance, finetuning the large language models, where multiple finetuned weights, e.g., using Lo RA [20], are publicly available.

Shrinking the shared vectors. Our Co LA 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 αi in Table 4. Nevertheless, it s still challenging to perform share vectors shrinking across multiple devices and we leave it for future works.

G Broader impact

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.

Neur IPS Paper Checklist

Question: Do the main claims made in the abstract and introduction accurately reflect the paper s contributions and scope? Answer: [Yes] Justification: This paper proposes Co LA, a collaborative lifelong adaptation framework for deep models, enabling efficient cross-device domain adaptation by sharing and accumulating knowledge across devices during test-time adaptation, significantly enhancing performance in varying domain scenarios without sacrificing efficiency. Guidelines:

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5. Open access to data and code

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. Please see the Neur IPS code and data submission guidelines (https://nips.cc/ public/guides/Code Submission Policy) for more details. While we encourage the release of code and data, we understand that this might not be possible, so No is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for a new open-source benchmark). The instructions should contain the exact command and environment needed to run to reproduce the results. See the Neur IPS code and data submission guidelines (https: //nips.cc/public/guides/Code Submission Policy) for more details. The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc. The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only a subset of experiments are reproducible, they should state which ones are omitted from the script and why. At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable). Providing as much information as possible in supplemental material (appended to the paper) is recommended, but including URLs to data and code is permitted. 6. Experimental Setting/Details

Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results? Answer: [Yes] We have provided detailed experimental settings in Appendix C. Guidelines:

The answer NA means that the paper does not include experiments. The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them. The full details can be provided either with the code, in appendix, or as supplemental material. 7. Experiment Statistical Significance

Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments? Answer: [Yes] Justification: Error bars are reported in Appendix E. Guidelines:

The answer NA means that the paper does not include experiments. The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper. The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions). The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)

The assumptions made should be given (e.g., Normally distributed errors). It should be clear whether the error bar is the standard deviation or the standard error of the mean. It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have a 96% CI, if the hypothesis of Normality of errors is not verified. For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative error rates). If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text. 8. Experiments Compute Resources

Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments? Answer: [Yes] Justification: We have provided detailed information about our compute resources in Appendix C. Guidelines:

The answer NA means that the paper does not include experiments. The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage. The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute. The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn t make it into the paper). 9. Code Of Ethics

Question: Does the research conducted in the paper conform, in every respect, with the Neur IPS Code of Ethics https://neurips.cc/public/Ethics Guidelines? Answer: [Yes] Justification: The paper meets the Neur IPS Code of Ethics. Guidelines:

The answer NA means that the authors have not reviewed the Neur IPS Code of Ethics. If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics. The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction). 10. Broader Impacts

Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed? Answer: [Yes] Justification: We have discussed this in Appendix G. 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).

11. Safeguards

Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?

Answer: [No]

Justification: This paper poses no such risks.

Guidelines:

The answer NA means that the paper poses no such risks. Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters. Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images. We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.

12. Licenses for existing assets

Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?

Answer: [Yes]

Justification: The creators or original owners of assets (e.g., code, data, models) used in the paper are properly credited, and the license and terms of use are explicitly mentioned and properly respected.

Guidelines:

The answer NA means that the paper does not use existing assets. The authors should cite the original paper that produced the code package or dataset. The authors should state which version of the asset is used and, if possible, include a URL. The name of the license (e.g., CC-BY 4.0) should be included for each asset. For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided. If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset.

For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided. If this information is not available online, the authors are encouraged to reach out to the asset s creators. 13. New Assets

Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets? Answer: [No] Justification: We will release new assets upon acceptance. Guidelines:

The answer NA means that the paper does not release new assets. Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc. The paper should discuss whether and how consent was obtained from people whose asset is used. At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file. 14. Crowdsourcing and Research with Human Subjects

Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)? Answer: [NA] Justification: The paper does not involve crowdsourcing nor research with human subjects. Guidelines:

The answer NA means that the paper does not involve crowdsourcing nor research with human subjects. Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper. According to the Neur IPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector. 15. Institutional Review Board (IRB) Approvals or Equivalent for Research with Human Subjects Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained? Answer: [No] Justification: The paper does not involve crowdsourcing nor research with human subjects. Guidelines:

The answer NA means that the paper does not involve crowdsourcing nor research with human subjects. Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper. We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the Neur IPS Code of Ethics and the guidelines for their institution. For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.