High-Energy Concentration for Federated Learning in Frequency Domain

TL;DR

FedFD introduces a frequency-domain-aware, aggregation-free federated learning framework that preserves energy-rich low-frequency components of synthetic data via a DCT-based binary masking scheme, significantly reducing communication while maintaining or improving accuracy. It employs a frequency-domain assisted dual-view coordination objective that aligns low-frequency distributions and enhances inter-class discrimination through real-data-guided synthetic classification, coupled with a low-frequency curriculum-style communication schedule to gradually increase transmitted information under a fixed budget. The approach is validated on five datasets spanning image and speech modalities, where FedFD consistently outperforms state-of-the-art methods and demonstrates notable communication savings and robustness to non-IID data. This work highlights the practical impact of frequency-domain techniques in aggregation-free FL for efficient, privacy-preserving collaborative learning.

Abstract

Federated Learning (FL) presents significant potential for collaborative optimization without data sharing. Since synthetic data is sent to the server, leveraging the popular concept of dataset distillation, this FL framework protects real data privacy while alleviating data heterogeneity. However, such methods are still challenged by the redundant information and noise in entire spatial-domain designs, which inevitably increases the communication burden. In this paper, we propose a novel Frequency-Domain aware FL method with high-energy concentration (FedFD) to address this problem. Our FedFD is inspired by the discovery that the discrete cosine transform predominantly distributes energy to specific regions, referred to as high-energy concentration. The principle behind FedFD is that low-energy like high-frequency components usually contain redundant information and noise, thus filtering them helps reduce communication costs and optimize performance. Our FedFD is mathematically formulated to preserve the low-frequency components using a binary mask, facilitating an optimal solution through frequency-domain distribution alignment. In particular, real data-driven synthetic classification is imposed into the loss to enhance the quality of the low-frequency components. 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 dataset 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.

Figures (11)

• Figure 1: Illustration of different federated learning frameworks. (a) Sending optimized local model parameters. (b) Sending entire spatial-domain synthetic data. (c) Our FedFD: Sending low-frequency components of synthetic data.
• Figure 2: Overall architecture of FedFD. The lower left corner illustrates the key of FedFD: retaining low-frequency components with high-energy concentration via frequency domain filtering. Notably, a frequency-domain-assisted dual-view coordination loss $\mathcal{L}_\mathrm{FDD}$ is designed to optimize the low-frequency components of $S_k$, as shown at the bottom. Subsequently, a low-frequency-based curriculum-style communication strategy is adopted to enhance the performance of the global model. Finally, on the server, the low-frequency data is zero-padded and processed using the IDCT to train the global model.
• Figure 3: Comparison of cumulative energy ratios in the spatial and frequency domains as dimensions increase. (a) Dimensions are added sequentially from the top-left corner. (b) Dimensions are added in descending order of energy.
• Figure 4: Comparison of the cumulative communication costs of spatial and frequency domain communication strategies.
• Figure 5: Convergence performance of different FL methods on image datasets.