Geometric Knowledge-Guided Localized Global Distribution Alignment for Federated Learning

TL;DR

The paper tackles data heterogeneity in federated learning, caused by label skew and domain skew, by introducing geometry-guided data generation to locally simulate the ideal global embedding distribution. It formalizes embedding distribution geometry (GD_X) from covariance eigen-decomposition and derives a privacy-preserving method to estimate global shapes, sharing only eigenvectors and eigenvalues. The core method, GGEUR, augments local embeddings along principal directions to approximate the global distribution, with single-domain and multi-domain variants to handle cross-domain data. Empirical results across label skew, domain skew, and Office-Home-LDS show substantial accuracy gains, faster convergence, and reduced cross-domain variance, validating the approach as a scalable, privacy-aware preprocessing step for FL that complements existing methods.

Abstract

Data heterogeneity in federated learning, characterized by a significant misalignment between local and global distributions, leads to divergent local optimization directions and hinders global model training. Existing studies mainly focus on optimizing local updates or global aggregation, but these indirect approaches demonstrate instability when handling highly heterogeneous data distributions, especially in scenarios where label skew and domain skew coexist. To address this, we propose a geometry-guided data generation method that centers on simulating the global embedding distribution locally. We first introduce the concept of the geometric shape of an embedding distribution and then address the challenge of obtaining global geometric shapes under privacy constraints. Subsequently, we propose GGEUR, which leverages global geometric shapes to guide the generation of new samples, enabling a closer approximation to the ideal global distribution. In single-domain scenarios, we augment samples based on global geometric shapes to enhance model generalization; in multi-domain scenarios, we further employ class prototypes to simulate the global distribution across domains. Extensive experimental results demonstrate that our method significantly enhances the performance of existing approaches in handling highly heterogeneous data, including scenarios with label skew, domain skew, and their coexistence. Code published at: https://github.com/WeiDai-David/2025CVPR_GGEUR

Figures (9)

• Figure 1: The distribution of local data on clients is imbalanced. The "bird" category has a large number of samples, allowing its local distribution to effectively represent the global distribution. In contrast, the "truck" category has insufficient samples, resulting in a significant disparity between the local and global distributions.
• Figure 2: Example of "bird" category: in a single-domain scenario, only the local global distribution is simulated; in a multi-domain scenario, the global distribution from other data domains is also simulated on a client.
• Figure 3: In a single-domain scenario, each class's global geometric shape is used to guide sample augmentation on each client. The example shows how new samples are generated for Client 2.
• Figure 4: Federated scenario with both label skew and domain skew. Different textures represent data from distinct domains.
• Figure 5: Example with 3 clients: Step 1 generates samples for each client from its own domain, while Step 2 simulates samples from other domains for each client.

Theorems & Definitions (2)

• Definition 1: Single-Domain Global Distribution
• Definition 2: Multi-Domain Global Distribution