FedSheafHN: Personalized Federated Graph Learning

• FedSheafHN is a personalized federated learning framework that leverages sheaf diffusion on a server-constructed collaboration graph to tailor GNN models to individual client subgraphs.
• It transforms local subgraphs into embeddings and enriches them via attention-enhanced diffusion, enabling the hypernetwork to efficiently generate client-specific model parameters.
• Empirical studies demonstrate faster convergence, improved robustness, and superior performance over baselines on non-IID, graph-structured datasets.

FedSheafHN is a framework for personalized federated learning on graph-structured data, specifically personalized subgraph federated learning, in which Graph Neural Networks (GNNs) are customized to individual client needs under diverse data distributions. The framework embeds each client’s local subgraph into a server-constructed collaboration graph, applies sheaf diffusion within that collaboration graph to learn client representations, and uses a server-side hypernetwork to generate personalized model parameters in parallel across clients (Liang et al., 2024). In a subsequent formulation, the same framework is described through a sheaf collaboration mechanism that unifies enhanced client descriptors with efficient personalized model generation, with reported fast model convergence and effective generalization to new clients (Liang et al., 19 Aug 2025).

1. Problem setting and motivation

FedSheafHN is designed for personalized subgraph federated learning, where clients hold private, potentially heterogeneous subgraphs of a larger, unknown graph and require personalized models rather than a single shared model. The motivating setting is explicitly non-IID: clients’ graphs and tasks may differ, so standard federated averaging does not adequately account for client-specific heterogeneity. Hypernetworks are attractive in this regime because a server can generate tailored models for each client from a client descriptor, but prior hypernetwork-based approaches are described as relying on narrow, flat descriptors that do not accurately represent complex client-specific graph structures or inter-client relationships (Liang et al., 2024).

The framework addresses two coupled issues emphasized in later descriptions of the method: how to learn and exploit underlying relationships among clients for effective collaboration, and how to retain client-specific personalization in the presence of strong heterogeneity. This emphasis places FedSheafHN within personalized federated learning rather than conventional global-model FL. Its central premise is that client descriptors should encode both local graph information and relational context derived from other clients, without requiring access to the original global graph (Liang et al., 19 Aug 2025).

This orientation is also consistent with broader personalized federated learning work on sheaf hypernetworks, which argues that graph hypernetworks suffer from over-smoothing, heterophily, and reliance on a priori client relation graphs that may be unavailable, private, or inaccessible. FedSheafHN can be read as a specialization of that broader program to graph-structured client data, with the collaboration graph serving as the relational scaffold on which personalization is constructed (Nguyen et al., 2024).

2. Client descriptors and the collaboration graph

FedSheafHN begins by converting each client’s local subgraph into a graph-level embedding. In the 2024 formulation, each client runs its local GNN for $T_c$ steps to obtain node embeddings $v_{i,m}^{(T_c)}$, then computes the graph embedding

$$x_i = \frac{1}{|M_i|} \sum_{m \in M_i} v_{i,m}^{(T_c)},$$

where $M_i$ is the node set of client $i$ (Liang et al., 2024).

These client embeddings are transmitted to the server, which constructs a collaboration graph $G_s$. In the 2024 description, the nodes of $G_s$ are clients $c_i$, the node features are the graph-level embeddings $x_i$, and the edge set is initially complete, so every client has an edge to every other client. In the later description, the client collaboration graph is created from graph-level embeddings using KNN in embedding space. Taken together, these descriptions show that the collaboration graph is a server-side relational object derived from client descriptors rather than a pre-existing global graph (Liang et al., 2024, Liang et al., 19 Aug 2025).

Stage	Operation	Output
Local encoding	Client computes node embeddings and averages them	Graph-level embedding $x_i$
Server graph construction	Server builds collaboration graph from client embeddings	$v_{i,m}^{(T_c)}$0 with client nodes and embedding features
Relational enrichment	Sheaf diffusion on $v_{i,m}^{(T_c)}$1	Enriched client representations
Personalization	Hypernetwork maps enriched embeddings to model parameters	Personalized client models

This design addresses a common difficulty in graph federated learning: client relationships are often not given explicitly. FedSheafHN treats those relationships as learnable structure. The collaboration graph is therefore not merely an implementation convenience; it is the object through which inter-client information becomes available to the personalization mechanism.

3. Sheaf-theoretic formulation and diffusion

The mathematical core of FedSheafHN is sheaf diffusion on the collaboration graph. Cellular sheaf theory provides the underlying formalism. In the graph setting, a cellular sheaf assigns a vector space to each vertex and edge and a linear restriction map to each incident vertex-edge pair; the associated sheaf Laplacian generalizes the graph Laplacian and supports diffusion with non-constant, asymmetric, and varying-dimension relations (Hansen et al., 2020).

FedSheafHN uses this apparatus to enrich each client embedding by aggregating information from related clients through the geometry of the collaboration graph. In the later description, the sheaf Laplacian is written as

$v_{i,m}^{(T_c)}$2

with normalized form

$v_{i,m}^{(T_c)}$3

The diffusion dynamics are then specified by

$v_{i,m}^{(T_c)}$4

where

$v_{i,m}^{(T_c)}$5

and the final enriched representation matrix is $v_{i,m}^{(T_c)}$6 (Liang et al., 19 Aug 2025).

Within FedSheafHN, this diffusion layer is intended to improve the integration and interpretation of complex client characteristics. The 2024 description states that the goal is to enrich each client’s embedding vector by aggregating information from other related clients via neural sheaf diffusion, thereby producing a rich, adaptive client descriptor for the hypernetwork stage (Liang et al., 2024).

The use of sheaf diffusion also links FedSheafHN to a broader line of work that treats sheaf-based propagation as a remedy for standard graph message-passing pathologies. In personalized federated learning more generally, sheaf hypernetworks are motivated by the claim that sheaf-based message passing can mitigate over-smoothing and improve robustness to heterophily by replacing homogeneous aggregation with direction-sensitive and context-aware information flow (Nguyen et al., 2024). FedSheafHN inherits that perspective, but applies it to a server-constructed graph of clients rather than to an externally supplied client relation graph.

4. Hypernetwork personalization and training protocol

After sheaf diffusion, FedSheafHN uses a hypernetwork to generate personalized client models. The 2024 formulation emphasizes two features: an attention mechanism and efficient parallelism. The hypernetwork operates on the full matrix of enriched embeddings and simultaneously generates personalized parameter vectors for all clients in a single forward pass,

$v_{i,m}^{(T_c)}$7

where $v_{i,m}^{(T_c)}$8 aggregates all clients’ generated parameters (Liang et al., 2024).

The later formulation makes the attention stage explicit: $v_{i,m}^{(T_c)}$9 followed by

$$x_i = \frac{1}{|M_i|} \sum_{m \in M_i} v_{i,m}^{(T_c)},$$0

In that description, each client model contains backbone parameters $$x_i = \frac{1}{|M_i|} \sum_{m \in M_i} v_{i,m}^{(T_c)},$$1, initialized from the server and partially updated locally, together with head parameters $$x_i = \frac{1}{|M_i|} \sum_{m \in M_i} v_{i,m}^{(T_c)},$$2, updated only locally (Liang et al., 19 Aug 2025).

The training loop is server-centric but not globally monolithic. In the 2024 description, the server collects graph-level embeddings, updates the collaboration graph, applies sheaf diffusion, uses the hypernetwork with attention to generate model parameters for all clients, distributes parameters, and iterates using client feedback. Clients receive personalized models, perform local updates, and may recompute graph embeddings for the next round (Liang et al., 2024). In the later description, clients send only backbone parameter deltas $$x_i = \frac{1}{|M_i|} \sum_{m \in M_i} v_{i,m}^{(T_c)},$$3, while the server updates sheaf and hypernetwork parameters through the chain rule (Liang et al., 19 Aug 2025).

A defining property of this design is that the generated model for a client reflects both the client’s own graph and its relationships to other clients, as encoded by the collaboration or sheaf-diffused embedding. The 2024 account also states that new clients can be handled by generating new embeddings and passing them through the trained system, requiring only one round of communication and no retraining (Liang et al., 2024).

5. Subsequent theoretical formulation

The 2024 paper is primarily architectural and empirical, but a later FedSheafHN formulation supplements the framework with explicit convergence and generalization guarantees. That account presents a convergence bound in Theorem 1,

$$x_i = \frac{1}{|M_i|} \sum_{m \in M_i} v_{i,m}^{(T_c)},$$4

which is stated to imply that the expected average gradient norm vanishes as the number of rounds $$x_i = \frac{1}{|M_i|} \sum_{m \in M_i} v_{i,m}^{(T_c)},$$5 and clients $$x_i = \frac{1}{|M_i|} \sum_{m \in M_i} v_{i,m}^{(T_c)},$$6 grow (Liang et al., 19 Aug 2025).

The same formulation gives a high-probability generalization statement in Theorem 2. If each client has sample size $$x_i = \frac{1}{|M_i|} \sum_{m \in M_i} v_{i,m}^{(T_c)},$$7, then

$$x_i = \frac{1}{|M_i|} \sum_{m \in M_i} v_{i,m}^{(T_c)},$$8

so the generalization gap can be made arbitrarily small with sufficient data (Liang et al., 19 Aug 2025).

These theoretical claims should be understood as belonging to the later version of the framework rather than to the original 2024 presentation. They nevertheless clarify the intended analytical status of FedSheafHN: not only as a heuristic for descriptor enrichment and weight generation, but as a method for which convergence and generalization can be formalized under explicit assumptions.

6. Empirical behavior

FedSheafHN is evaluated on several graph-structured datasets. The 2024 experiments use citation networks—Cora, Citeseer, Pubmed, and ogbn-arxiv—and Amazon product graphs—Computer and Photo—under non-overlapping and overlapping subgraph partition scenarios. The primary metric is Federated Accuracy,

$$x_i = \frac{1}{|M_i|} \sum_{m \in M_i} v_{i,m}^{(T_c)},$$9

that is, average test accuracy across clients (Liang et al., 2024).

The reported baselines include FedAvg, FedPer, FedSage+, pFedHN, pFedGraph, and FED-PUB; the later formulation additionally lists FedProx, FGGP, and Flow (Liang et al., 2024, Liang et al., 19 Aug 2025). Across these studies, the principal empirical claims are consistent. The 2024 abstract states that FedSheafHN outperforms existing methods in most scenarios, in terms of client model performance on various graph-structured datasets, and also has fast model convergence and effective new clients generalization (Liang et al., 2024). The detailed 2024 summary strengthens this to the claim that FedSheafHN consistently outperforms all baselines across all datasets and both partition scenarios, with the performance boosts most pronounced in high-heterogeneity, non-overlapping settings (Liang et al., 2024).

Several qualitative findings recur. Convergence plots are reported to show faster and more stable convergence than baselines. Generalization to new clients requires only generating a new embedding and a single round of communication, with new-client accuracy nearly the same as that for training clients and only minor drops. Ablation studies report that the collaboration graph, dynamic embedding updates, sheaf diffusion, advanced hypernetwork, and attention each contribute positively to performance, with collaboration graph and hypernetwork providing the biggest single gains. The same ablations state that sheaf diffusion outperforms using regular GNNs such as GCN and GAT as the collaboration aggregator (Liang et al., 2024).

Robustness is another recurrent theme. The 2024 summary states that the method remains effective even when some clients behave maliciously by sending manipulated embeddings, while the later formulation reports greater resilience to malicious or abnormal client embeddings and lower performance variation across clients in the non-overlapping setting (Liang et al., 2024, Liang et al., 19 Aug 2025). At the same time, the 2024 experiments note that increasing local training steps yields diminishing or even negative returns because of divergence of client models, indicating that local-epoch tuning remains dataset-dependent (Liang et al., 2024).

7. Relation to broader sheaf-based learning

FedSheafHN belongs to a broader body of work that uses sheaf-theoretic operators to enrich graph learning. Sheaf Neural Networks generalize graph convolutional networks by replacing standard diffusion with sheaf Laplacian-based diffusion, allowing edge relations that are non-constant, asymmetric, and varying in dimension (Hansen et al., 2020). Sheaf Hypergraph Networks extend the same idea to higher-order relations and introduce linear and non-linear sheaf hypergraph Laplacians, with the claim that the sheaf formulation provides a more expressive inductive bias than standard hypergraph diffusion (Duta et al., 2023).

Within federated learning specifically, “Sheaf HyperNetworks for Personalized Federated Learning” proposes sheaf hypernetworks for multi-class classification, traffic forecasting, and weather forecasting, and reports improvements of up to 2.7% in accuracy and 5.3% in lower mean squared error over the best-performing baseline in complex non-IID scenarios (Nguyen et al., 2024). FedSheafHN is more specialized: it targets graph-structured client data, derives client descriptors from local subgraphs, and performs sheaf diffusion on a collaboration graph constructed at the server (Liang et al., 2024).

Two misconceptions are worth clarifying. First, FedSheafHN does not require the original global graph to be known; the motivating setting explicitly allows clients to hold private subgraphs of a larger, unknown graph, and the server constructs its own collaboration graph from graph-level embeddings (Liang et al., 2024). Second, its sheaf component is not interchangeable with a conventional graph aggregator in the reported experiments; the ablation results state that sheaf diffusion outperforms regular GNNs such as GCN and GAT when used as the collaboration aggregator (Liang et al., 2024).

Taken together, these features make FedSheafHN a graph-specific personalized federated learning framework in which client collaboration is mediated through sheaf-structured diffusion and model personalization is realized by a server-side hypernetwork. The method is therefore best understood not as a variant of simple model averaging, but as a federated architecture for learning and exploiting inter-client relational structure under graph heterogeneity.