High-Energy Concentration for Federated Learning in Frequency Domain

The proposed FedFD method introduces a novel high-energy concentration technique for federated learning in the frequency domain to balance communication efficiency and performance. The gist: FedFD effectively utilizes energy distribution and component orthogonality of the discrete cosine transform (DCT) to promote low-frequency component quality while filtering out noise, leading to superior performance with reduced communication costs on five image and speech datasets

How it works

The core principle of FedFD is that lowenergy like high-frequency components usually contain redundant information and noise, thus filtering them helps reduce communication costs and optimize performance Specifically, the process involves several key steps:

1. The discrete cosine transform is first used to convert spatial domain features into the frequency domain

2. Low-frequency components are optimized via a designed frequency-domain alignment objective, which differs from existing spatial domain alignment

3. Real data-driven synthetic classification is introduced to enhance the quality of low-frequency components

4. A "low-frequency-based curriculum-style communication strategy is designed to further enhance global model performance by gradually increasing the low-frequency component increments while maintaining a low communication budget"

Key Objectives and Components

The frequency-domain assisted dual-view coordination objective function, denoted as FedFD, is defined as FedFD = λ1FDA + λ2RSC. This objective combines two main terms:

frequency-domain distribution alignment enhances the quality of low-frequency components by calculating the distribution loss in the frequency domain

This is formulated as FDA(Sk, Dk) = C∑k−1 c=0 νS k,c − νD k,c 2.

real data-driven synthetic classification is introduced to enhance the quality of low-frequency components

This term is RSC = CE(Sk) ⋅ (1/Dk Dk ∑ i=1I(pi = li)).

Communication Strategy and Robustness

The paper introduces a low-frequency-based curriculum-style communication strategy to manage communication costs effectively. This strategy involves:

the number of low-frequency components sent gradually increases, thus enhancing the representation capability of the global model

The problem of optimizing synthetic data is formulated as arg min DM(Sk, Dk) = C∑k−1 c=0 muS k,c −muD k,c2.

The analysis of aggregation-free FL shows that aggregation-free FL exhibits stronger robustness in the presence of data heterogeneity. Furthermore, the security analysis suggests that the sparse frequency-domain communication strategy has a lower attack success probability compared to the entire spatial-domain communication strategy.

Experimental Validation and Results

Extensive experiments on five datasets from different modalities demonstrate that FedFD achieves superior performance while maintaining high communication efficiency. The results show that FedFD outperforms state-of-the-art FL methods in both performance and communication efficiency. For example, on the CIFAR-10 with Dirichlet coefficient α = 0.01, FedFD achieves a minimum reduction of 37.78% in the communication cost, while attaining a 10.88% performance gain. The ablation study confirms that incorporating all core components leads to the best results, as shown in Table IV.

Conclusion

In summary, FedFD presents a novel method that leverages the potential of the frequency domain in FL to balance communication efficiency and performance. It successfully enhances the quality of low-frequency components through frequency-domain distribution alignment and real data-driven synthetic classification, while employing a curriculum strategy to send only necessary low-frequency components, thereby achieving state-of-the-art results across various datasets and modalities. The method's superiority is further validated by its consistent performance across different network architectures and its enhanced privacy protection through sparse frequency-domain communication.

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High-Energy Concentration for Federated Learning in Frequency Domain

Weiying Xie, Haozhi Shia, Hangyu Yea, Daixun Lia, Jitao Maa, Yunsong Lia and Leyuan Fang aState Key Laboratory of Integrated Services Networks, Xidian University, Xi’an, Shaanxi, 710071 China bCollege of Electrical and Information Engineering, Hunan University, Changsha, Hunan, 410082 China A R T I C L E I N F O Keywords: Federated learning frequency domain Synthetic data Low frequency

A B S T R A C T

Federated learning (FL) facilitates the mitigation of data heterogeneity by transmitting privacypreserving synthetic data. However, existing aggregation-free frameworks are limited by the need to optimize and transmit the entire spatial domain, resulting in redundant information and noise that impact global model performance and increase communication burden. To alleviate this issue, we propose a novel Frequency-Domain–aware FL method (FedFD), inspired by the energy concentration and component orthogonality of the frequency domain. The principle behind FedFD is that lowenergy like high-frequency components usually contain redundant information and noise, thus filtering them helps reduce communication costs and optimize performance. Specifically, the discrete cosine transform is first used to convert spatial domain features into the frequency domain. Subsequently, the low-frequency components are optimized via a designed frequency-domain alignment objective, which differs from existing spatial domain alignment. On this basis, real data-driven synthetic classification is introduced to enhance the quality of low-frequency components. Furthermore, a low-frequency-based curriculum-style communication strategy is designed to further enhance global model performance by gradually increasing the low-frequency component increments while maintaining a low communication budget. On five image and speech datasets, FedFD achieves superior performance than state-of-the art methods while reducing communication costs. For example, on the CIFAR-10 with Dirichlet coefficientalpha = 0.01, FedFD achieves a minimum reduction of 37.78% in the communication cost, while attaining a 10.88% performance gain

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High-Energy Concentration for Federated Learning in Frequency Domain Local Data Classification of Logit Embeddings Local Model Send Parameters Client k Server Local Data Distribution of Condensed Data Synthetic Data Spatial Domain Send Entire SpatialDomain Synthetic Data Server Client k Local Data Distribution of Condensed Data Synthetic Data DCT Frequency Domain Send Low-Frequency Components Server Client k (a) Aggregation-Based Federated Learning (b) Aggregation-Free Federated Learning with Spatial Domain (c) Aggregation-Free Federated Learning with Frequency Domain Figure 1: Illustration of different federated learning frameworks. (a) Sending optimized local model parameters. (b) Sending entire spatial-domain synthetic data.

1. Bold header: Frequency Domain Energy Concentration for Aggregation-Free FL

This improvement enables aggregation-free Federated Learning to reduce communication costs by only sending low-frequency components, which are identified as containing redundant information and noise, thereby directly reducing the communication burden.

2. Bold header: Frequency Domain Assisted Dual-View Coordination Objective

The system can optimize synthetic data quality by employing a loss function defined as FedFD, which combines frequency-domain distribution alignment to enhance low-frequency component quality and real data-driven synthetic classification to improve inter-class discrimination.

3. Bold header: Low-Frequency Based Curriculum Communication Strategy

This strategy enhances global model performance while maintaining a low communication budget by gradually increasing the number of sent components, as described in the paper's description of how the instance increment follows a linear growth pattern.

4. Bold header: Enhanced Privacy Protection via Sparse Frequency-Domain Communication

By utilizing binary masks to select only specific frequency components, the system can reduce attack success probability; this is supported by Theorem 3, which infers that the sparse frequency-domain communication strategy has a lower attack success probability compared to the entire spatial-domain communication strategy.

5. Bold header: Improved Model Robustness to Data Heterogeneity

The aggregation-free framework exhibits stronger robustness in the presence of data heterogeneity because it optimizes synthetic data based on the quality of the client-generated synthetic data Sk, rather than relying on potentially biased aggregation methods susceptible to data heterogeneity.

6. Bold header: Superior Performance Across Modalities and Architectures

The FedFD method consistently achieves state-of-the-art performance across image and speech datasets, and it is shown to be superior when compared against different network architectures (ConvNet vs. ResNet18) in terms of both accuracy and communication cost.