FedSSI: Rehearsal-Free Continual Federated Learning with Synergistic Synaptic Intelligence

Thank you for your careful review and valuable comments. In the following, we give point-by-point responses to each comment.

Q1. Concerns about the storage overhead caused by PSM.

R1: Thank you for this constructive suggestion. The PSM will be trained along with the global model on the current local task. Since this is purely local training assisted by an already converged global model, the training of the PSM is very fast (accounting for only 1/40 of the training cost per task and requiring no communication). We calculate and save the parameter contributions during the local convergence process of the PSM, which can then be locally discarded after its contribution has been computed. Then, each client trains on the new task with the local model and parameter contribution scores.

The model for an FL task is practically not as large as edge clients are mostly resource-limited, and the memory demand by PSM is relatively similar to existing methods like FedProx, as it manipulates over an extra model that has the same size as the federated model.

Possible Strategy: If an FL task has large models and limited memory left on the edge, a prerequisite can be reasonably assumed satisfied: transmission capacity (probably after optimization) is sufficient for the system. In such a case, we can record the PSM model in the server, which is only downloaded and updated locally to compute parameter contributions and then uploaded to the server again.

Q2. Combination of Gernerative AI and FedSSI.

R2: Thank you for raising this concern. Generative AI has emerged as a prominent research area in recent years, as it leverages the generalization capabilities of LLMs to enhance task performance and drive productivity improvements significantly. However, even in centralized learning paradigms, continual learning for Generative AI remains hindered by multiple challenges. Unlike conventional backbone models that primarily face catastrophic forgetting, Generative AI systems more frequently encounter difficulties acquiring new knowledge. Additionally, the current deployment of Generative AI models through quantization compression on small edge devices complicates continual learning implementation under resource-constrained conditions. While the continual federated learning has not yet published studies specifically addressing Generative AI and FedSSI is designed for traditional CFL tasks, the growing deployment of edge devices equipped with Generative AI capabilities and their potential to collect real-world data from novel scenarios underscores the urgent need for such research.

Q3. Dependence on SI Algorithm.

R3: Thank you for raising this concern. Although the FedSSI algorithm uses PSM to improve the SI algorithm, the selection of the SI algorithm itself is not random. In our empirical experiments, we analyzed a vast number of existing CFL methods and techniques, as well as traditional CL techniques. The SI algorithm was chosen as the appropriate one among them, and it has been widely recognized for its efficiency and feasibility in most scenarios. We believe that this assumption is acceptable, similar to how many FL studies are based on CNN and ResNet series networks without considering the feasibility of techniques on a single Linear network.

Thank you very much for providing us with positive comments. In the following, we give detailed responses to each review.

Q1. Concerns about the selection of the hyperparameter $\lambda$

R1: Thanks a lot for raising this concern. In Table 3, $\alpha$ refers to the degree of data heterogeneity, while $\lambda$ is a control coefficient in the training process of PSM. In Proposition 1, we show that adjusting $\lambda$ can control whether the proportion of knowledge in PSM leans towards the local or global distribution (i.e., it is related to $\alpha$). When $\alpha$ has a higher value, indicating a trend towards homogeneity in distribution, clients need to focus more on local knowledge. This means that by setting a larger $\lambda$ value, PSM can rely more on local knowledge. Although we cannot directly relate $\alpha$ and $\lambda$ with a simple formula due to the complexity of the problem, even in specialized research on personalized federated learning (PFL), methods such as Gaussian mixture modeling are relied upon. This specific study goes beyond the resource-efficient CFL that we focus on in this manuscript, so we did not develop new mechanisms for this issue. In this paper, we can empirically and theoretically judge that there exists a positive correlation between $\alpha$ and $\lambda$, which is supported by Proposition 1 and extensive experiments conducted in Table 3. We will consider this issue in our future research work.

Q2. Concerns about framework of FedSSI and more details about CFL

R2: Thank you for this helpful comment. We agree that a framework diagram could improve accessibility for readers less familiar with CFL. However, the regularization-based methods in FedSSI are inherently theoretical, making it challenging to explicitly visualize their nuanced mechanisms (e.g., PSM step or SI module) within a high-level framework. To address this, we have included Algorithm 1, which details the iterative steps of FedSSI. We appreciate your suggestion and will consider providing the framework in our final version. Moreover, we will further provide the relevant experimental details in the supplementary: we assign different numbers of tasks to various datasets. Using CIFAR-10 as an example, we set five tasks for class-incremental tasks, each covering two classes without data overlap. For domain-incremental tasks, each domain represents one task.

Q3. Concerns about FedSSI's adaptability to heterogeneous models

R3: Thank you for raising this concern. FedSSI still can work under model heterogeneity, but this heterogeneity will introduce novel challenges to CFL systems that have never been addressed. FedSSI’s core mechanism utilizes a PSM Module to address data heterogeneity and employs SI for continual learning. Notably, the SI algorithm is architecture-agnostic, as it operates by quantifying parameter contributions during gradient updates. Similarly, the PSM module—an initial copy of the local model—is independent of other clients’ model architectures. However, model heterogeneity exacerbates system heterogeneity due to divergent feature representation spaces across architectures. As CFL is an emerging research area, existing studies have yet to address model heterogeneity systematically. The reviewer’s suggestion highlights a promising research direction we will prioritize in future work.

Thank you very much for this professional review. The critical comments have been addressed carefully, and responses have been given one by one.

Q1. Minor typos in our manuscript.

R1: Thank you very much for this helpful comment. We are sorry for the wrong spelling in Table 2 and will correct it. We will carefully polish our manuscript to further improve the presentation. In Eq.(1), we formulate the overall optimization objective of CFL. $w^t$ denotes the converged global model, and the superscript $t$ represents the number of tasks here.

Q2. Insufficient description of experimental settings.

R2: Thank you for this valuable comment. We will further provide the relevant experimental details in the supplementary: we assign different numbers of tasks to various datasets. Using CIFAR-10 as an example, we set five tasks for class-incremental tasks, each covering two classes without data overlap. For domain-incremental tasks, each domain represents one task.

Q3. Concerns about the LLM foundation for FedSSI.

R3: Thanks for raising this concern. LLMs have gained significant attention for their strong performance on conventional tasks, but their high computational and communication overheads prevent deployment on edge devices. Current CFL methods, including FedSSI, mainly focus on training with traditional architectures (e.g., CNN, ResNet), and we will later consider the LLM foundation for CFL in our future research. Moreover, calculating the contribution for each parameter incurs negligible computational overhead due to the PSM module. The PSM will be trained along with the global model on the current local task. Since this is purely local training assisted by an already converged global model, the training of the PSM is very fast (accounting for only 1/40 of the training cost per task and requiring no communication). We calculate and save the parameter contributions during the local convergence process of the PSM, which can then be locally discarded after its contribution has been computed. Then, each client trains on the new task with the local model and parameter contribution scores.

Q1&Q4. Concerns about selection of the hyperparameter $\lambda$ and its theoretical bound

R1: Thank you for this valuable comment. We conducted relative experiments in Table 3. In Table 3, $\alpha$ refers to the degree of data heterogeneity, while $\lambda$ is a control coefficient in the training process of PSM. In Proposition 1, we show that adjusting $\lambda$ can control whether the proportion of knowledge in PSM leans towards the local distribution or the global distribution (i.e., it is related to $\alpha$). When $\alpha$ has a higher value, indicating a trend towards homogeneity in distribution, clients need to focus more on local knowledge. This means that by setting a larger $\lambda$ value, PSM can rely more on local knowledge.

Although we cannot directly relate $\alpha$ and $\lambda$ with a simple formula due to the complexity of the problem, even in specialized research on personalized federated learning (PFL), strategies such as Gaussian mixture modeling are relied upon. Another possible approach can be adapted from APFL [1], where the optimal weights are empirically determined through iterative gradient descent during optimization. However, this process may introduce additional model parameters and computational overhead.

This specific study goes beyond the resource-efficient CFL that we focus on in this manuscript, so we did not develop new mechanisms for this issue. In this paper, we can empirically and theoretically judge that there exists a positive correlation between $\alpha$ and $\lambda$, which is supported by Proposition 1 and extensive experiments conducted in Table 3. We will consider this issue in our future research work.

[1] Deng Y, Kamani M M, Mahdavi M. Adaptive personalized federated learning[J]. arXiv preprint arXiv:2003.13461, 2020.

Q2. Concerns about the computational overhead brought by PSM.

R2: Thank you for raising this concern. The computational overhead of PSM is negligible compared to the overall CFL training process. The computational overhead of the PSM module scales proportionally with the complexity of learning tasks. For edge devices with limited computational capacity, their CFL tasks are typically simpler, thus the PSM’s computational demands scale down correspondingly. Specifically, the PSM will be trained along with the global model on the current local task. Since this is purely local training assisted by an already converged global model, the training of the PSM is very fast (accounting for only 1/40 of the training cost per task and requiring no communication). We calculate and save the parameter contributions during the local convergence process of the PSM, which can then be locally discarded after its contribution has been computed. Then, each client trains on the new task with the local model and parameter contribution scores. We analyze this issue in Line 232 in our submitted manuscript.

Q3. Concerns about the scalability of FedSSI.

R3: Thank you for your helpful comment. We apologize that we are unable to simulate thousands of clients to conduct scalability experiments due to hardware limitations. But we validated the scalability of FedSSI on 100 clients, which is also a common scale experiment in FL's work. We conducted further experiments by increasing the number of clients to 100 while reducing the client selection rate to 10%. We performed some related experiments on CIFAR10 and Digit10 ($\alpha=10.0$), with the results as follows:

Since the dataset needs to be divided into different numbers of tasks, an excessive number of clients can lead to a very small number of samples per client, making model training difficult. However, FedSSI still maintains a leading position.