Towards Federated Long-Tailed Graph Learning: An Energy-Guided Dual Decoupling Approach

Abstract: Federated Graph Learning facilitates collaborative graph modeling across distributed clients while preserving data privacy. However, real-world data categories frequently exhibit long-tailed distributions. Such statistical scarcity severely degrades performance in two ways: it biases the global model toward majority classes, and it structurally isolates minority nodes by submerging them in heterophilic, head-dominated neighborhoods. While existing methods attempt topology-agnostic statistical compensations, they often fail under data scarcity. Instead of recovering tail nodes, they overfit the structural noise from adjacent dominant classes, leading to representation degradation. To address these limitations, we propose FedEPD, a framework built on a dual decoupling paradigm that separates topological purification from semantic recalibration. Specifically, FedEPD utilizes distribution-aware Dirichlet energy pruning to filter spatial heterophilic edges. It then overcomes Non-IID distribution shifts by extracting robust global prototypes from topologically central nodes, which are incorporated into local representations via a spatial low-pass prototype injection. Furthermore, a two stage alternating optimization strategy strictly protects majority decision boundaries while improving minority accuracy. Extensive experiments demonstrate that FedEPD achieves state-of-the-art performance across diverse long-tailed benchmarks, yielding absolute improvements of up to 4.97% in Accuracy and 5.48% in Macro-F1.

• The paper presents FedEPD, which integrates energy-based topological purification with decoupled semantic recalibration to resolve majority-minority conflicts in federated graph learning.
• It employs distribution-aware Dirichlet energy pruning and server-assisted local consensus to enhance minority class recovery in imbalanced, heterophilic graphs.
• Empirical evaluations on diverse graph datasets show up to 4.97% accuracy improvements and stable convergence under non-IID conditions.

Energy-Guided Dual Decoupling for Federated Long-Tailed Graph Learning

Introduction

Federated Graph Learning (FGL) presents unique challenges in real-world applications where data distributions are non-IID and highly imbalanced, often following power law dynamics. Traditional federated learning paradigms and graph neural network (GNN) frameworks are increasingly deployed in domains with strict privacy requirements, including finance, healthcare, and collaborative scientific discovery. However, the prevalence of long-tailed class distributions and structural heterophily fundamentally limits the effectiveness of current methodologies by amplifying representation degradation in minority (tail) classes. The paper "Towards Federated Long-Tailed Graph Learning: An Energy-Guided Dual Decoupling Approach" (2606.24237) introduces FedEPD, an advanced federated learning framework that systematically addresses statistical-topological misalignment and majority-minority optimization conflict through a dual decoupling strategy.

Problem Formulation and Challenges

Empirical graph networks frequently manifest extreme class imbalance and heterophilic structures. In decentralized federated settings, individual clients encounter amplified data scarcity for minority classes and lack global structural visibility due to privacy. Conventional FGL and long-tailed learning approaches typically employ numerical logit adjustments and spatial oversampling but fail to reconcile topological structure with statistical frequency. Such methods inherently risk overfitting to structural noise, particularly when minority nodes are submerged within majority-dominated neighborhoods. The fundamental limitations include:

• Statistical-Topological Misalignment: Topology-agnostic numerical corrections distort decision boundaries and reinforce misclassification in heterophilic environments.
• Majority-Minority Optimization Conflict: Direct logit adjustments intermixed with feature extractors induce optimization trade-offs, sacrificing majority-class accuracy for tail-class recovery and vice versa.

FedEPD: Dual Decoupling Paradigm

FedEPD operationalizes a dual decoupling paradigm by separating topological purification from semantic recalibration. The framework executes the following components:

Topological Purification

FedEPD introduces a distribution-aware Dirichlet energy pruning mechanism, evaluating edge discrepancies through degree-normalized Euclidean distance and semantic similarity. This multi-metric pruning adaptively filters heterophilic edges in the spatial domain, yielding purified local topologies that suppress structural noise. The methodology leverages client-specific quantile thresholds derived from structural noise intensity, ensuring robust denoising without dataset-specific parameter tuning.

Server-Assisted Local Consensus

To compensate for the structural deficiency induced in tail nodes, FedEPD employs a server-assisted local consensus mechanism. Structurally central elite nodes are identified via iterative Personalized PageRank approximations, and global prototypes are constructed by aggregating the encoded features of these elites from the purified topology. This process ensures that minority node prototypes are semantically anchored and decoupled from local heterophilic interference, facilitating reliable cross-client semantic reference.

Decoupled Recalibration and Optimization

The semantic calibration phase is strictly decoupled from representation learning. The graph encoder is frozen, isolating classification updates to the classifier component. Spatial low-pass prototype injection incorporates the global prototype only into the low-frequency component of the node representations, preserving individual high-frequency features while avoiding label leakage during inference. Topology-aware logit adjustment, utilizing node-level and class-level homophily gating, delivers targeted calibration for minority classes based on structural reliability.

A two-stage alternating optimization pipeline—first learning base representations via purified topology, then calibrating classifier logits—enforces the separation of gradients, preventing majority-tail trade-offs and yielding uniform performance gains across all classes.

Empirical Evaluation

FedEPD is evaluated on six graph datasets with naturally severe long-tailed distributions: citation networks (CoraFull, ogbn-arxiv), product copurchase graphs (Amazon-Electronics, Amazon-Clothing), communication networks (Email), and heterophilic social graphs (Roman-Empire). Experiments utilize Balanced Accuracy (bAcc), Macro-F1, and Overall Accuracy metrics to handle skewed class distributions. Baselines spanned standard federated, centralized long-tailed, and federated long-tailed graph learning paradigms.

FedEPD consistently yielded superior performance, with absolute improvements up to 4.97% in Accuracy and 5.48% in Macro-F1 on large-scale graphs. Tail-class recovery is notably robust, with accuracy maintained in extreme tail bins where baseline methods collapsed. Ablation studies confirmed the necessity of all core components: removal of Dirichlet energy purification or prototype injection substantially degraded performance, especially on heterophilic graphs.

The hyperparameter analysis demonstrates broad optimal plateaus rather than narrow tuning windows. FedEPD is resilient to variations in calibration intensity and prototype injection scaling, supporting deployment flexibility.

Efficiency analysis reveals negligible computational and communication overhead due to the caching of purification and prototype extraction operations. Convergence stability is enhanced: FedEPD’s alternating optimization trajectory avoids gradient conflict-induced fluctuations, achieving faster and more stable convergence relative to federated and centralized baselines.

Implications and Future Developments

FedEPD establishes a rigorous foundation for federated learning in the presence of structural and statistical imbalance. The dual decoupling paradigm—energy-based spatial denoising followed by decoupled semantic calibration—eliminates majority-minority optimization conflict and restores minority-class semantics without compromising head-class stability.

Practically, the framework is applicable to privacy-preserving collaborative scenarios with massive non-IID, long-tailed graphs, and is computationally efficient for scaled deployments. Theoretically, FedEPD sets the direction for future federated models to integrate topology-aware signal processing with decoupled optimization. Extensions may include adaptive prototype construction in dynamic graphs, further spectral decoupling for persistent heterophily, and communication-efficient aggregation in multi-party settings.

Conclusion

FedEPD advances federated long-tailed graph learning by enforcing strict separation of structural purification and semantic recalibration through an energy-guided dual decoupling paradigm. The integration of distribution-aware Dirichlet energy pruning, server-assisted global prototype consensus, and two-stage alternating optimization delivers robust minority-class recovery and superior convergence stability across a diverse set of naturally imbalanced, heterophilic graphs. The approach is both empirically validated and theoretically sound, constituting a scalable, flexible solution for federated learning in highly skewed complex environments (2606.24237).