On the Geometric Coherence of Global Aggregation in Federated Graph Neural Networks

Chethana Prasad Kabgere; Shylaja SS

cs.LGFeb 17, 2026

On the Geometric Coherence of Global Aggregation in Federated Graph Neural Networks

Authors: Chethana Prasad Kabgere, Shylaja SS

Organizations: Department of Computer Science and Engineering, PES University, Bengaluru, Karnataka, 560085, India

Abstract

Federated learning over graph-structured data exposes a fundamental mismatch between standard aggregation mechanisms and the operator nature of graph neural networks (GNNs). While federated optimization treats model parameters as elements of a shared Euclidean space, GNN parameters induce graph-dependent message-passing operators whose semantics depend on underlying topology. Under structurally and distributionally heterogeneous client graph distributions, local updates correspond to perturbations of distinct operator manifolds. Linear aggregation of such updates mixes geometrically incompatible directions, producing global models that converge numerically yet exhibit degraded relational behavior. We formalize this phenomenon as a geometric failure of global aggregation in cross-domain federated GNNs, characterized by destructive interference between operator perturbations and loss of coherence in message-passing dynamics. This degradation is not captured by conventional metrics such as loss or accuracy, as models may retain predictive performance while losing structural sensitivity. To address this, we propose GGRS (Global Geometric Reference Structure), a server-side aggregation framework operating on a data-free proxy of operator perturbations. GGRS enforces geometric admissibility via directional alignment, subspace compatibility, and sensitivity control, preserving the structure of the induced message-passing operator.

Figures & tables

Figure 1: Geometric failure modes in federated GNN aggregation. Federated aggregation can degrade the graph-structured geometry of the learned message-passing operator $\theta$ through five interconnected failure mechanisms, from parameter misinterpretation to numerical convergence masking operator-level incoherence.

Dataset	Domain	$\|\mathcal{V}\|$	$d$	$C$	$\bar{d}$
Cora	Citation	2,708	1,433	7	3.9
CiteSeer	Citation	3,327	3,703	6	2.7
PubMed	Citation	19,717	500	3	4.5
Amazon-Comp.	CoPurchase	13,752	767	10	71.5
Amazon-Photo	CoPurchase	7,650	745	8	62.3
Coauthor-CS	CoAuthor	18,333	6,805	15	8.9

Table 1: Dataset statistics.

Arch	Method	Acc $\uparrow$	$\Gamma$ $\uparrow$	PA $\uparrow$	CDA $\uparrow$	$\sigma_{\mathrm{acc}}$ $\downarrow$	Conv 70
GCN-2	FedAvg	0.7584	0.1798	$-$ 0.0128	$-$ 0.0002	0.041	126
	FedSGD	0.7485	0.1969	$-$ 0.0026	$-$ 0.0001	0.046	135
	FedProx	0.7596	0.1805	$-$ 0.0134	$-$ 0.0003	0.039	124
	SCAFFOLD	0.7638	0.2297	$+$ 0.0771	$-$ 0.0001	0.036	119
	FedAvg+GGRS †	0.7776	0.2138	$+$ 0.0093	$+$ 0.0010	0.034	110
	FedSGD+GGRS †	0.7941	0.2479	$+$ 0.0244	$+$ 0.0019	0.032	104

Table 2: Main benchmark results (

\alpha=0.3

K=12

T=200

, 5 seeds). Steady-state metrics, rounds 181–200.

\dagger

: GGRS server wrapper. GCN-2 GGRS rows and all GraphSAGE rows are simulation-based estimates ( Est. ) pending full experimental runs.

Method	Cora	CiteSeer	PubMed	Amz-C	Amz-P	Coauth
FedAvg	0.877	0.762	0.810	0.584	0.569	0.948
FedSGD	0.764	0.705	0.748	0.601	0.748	0.924
FedProx	0.878	0.764	0.811	0.587	0.571	0.949
SCAFFOLD	0.881	0.769	0.814	0.600	0.585	0.949
FedAvg+GGRS	0.889	0.775	0.821	0.638	0.628	0.951
FedSGD+GGRS	0.782	0.721	0.762	0.640	0.771	0.930

Table 3: Per-dataset accuracy (GCN-2,

T=200

, 5 seeds, rounds 181–200). Italics : simulation-based estimates ( Est. ).

$\alpha$	FedAvg	GGRS	$\Delta$ Acc	att
0.05	0.380	0.450	$+$ 0.070	0.58
0.10	0.470	0.525	$+$ 0.055	0.52
0.20	0.540	0.580	$+$ 0.040	0.46
0.50	0.630	0.652	$+$ 0.022	0.40
1.00	0.680	0.685	$+$ 0.005	0.28

Table 4: Heterogeneity sweep: FedAvg+GGRS vs. FedAvg (GCN-2, 3 seeds). All values: simulation-based estimates pending full run. att: attenuation fraction.

Variant	Acc	$\Gamma$	$\Delta$ Acc	Dir	Sub	Clip
FedAvg	0.540	0.110	—	×	×	×
GGRS $-$ Dir	0.551	0.121	$+$ 0.011	×	✓	✓
GGRS $-$ Sub	0.570	0.145	$+$ 0.030	✓	×	✓
GGRS $-$ Clip	0.578	0.157	$+$ 0.038	✓	✓	×
Full GGRS	0.581	0.160	$+$ 0.041	✓	✓	✓

Table 5: Ablation study (GCN-2,

\alpha=0.2

, 5 seeds,

T=200

). ✓/×: active/disabled. All values: simulation-based estimates ( Est. ).

Panel of Figure 2 — Figure 2: (a) Per-client, per-round attenuation heatmap ( $\alpha=0.2$ , seed 0; colour: $\gamma_{k}^{(t)}$ on RdYlGn; black markers: attenuation events; right bar: total per-client count, domain-coded Citation/CoPurchase/CoAuthor). (b) Directional alignment $\Gamma^{(t)}$ over 200 rounds (GCN-2, all 8 methods; 7-round running average; shaded: $\pm 1$ std). (c) Per-dataset steady-state accuracy, GCN-2, all methods (solid: completed; hatched: estimated). (d) Heterogeneity monotonicity: $\Delta$ Acc vs. $\alpha$ (inverted axis); GGRS gain strictly increasing, FedProx/SCAFFOLD flat.

Panel of Figure 3 — Figure 3: (a) SBM conflict: attenuation differential $\overline{\mathrm{att}}_{\mathrm{Sharp}}-\overline{\mathrm{att}}_{\mathrm{Smooth}}$ per round (5 seeds; positive gap validates mechanistic prediction). (b) Self-regulation ( $\alpha=0.2$ ): aggregate attenuation rate $\bar{\beta}^{(t)}$ and $\Gamma^{(t)}$ over training for FedAvg+GGRS; monotone decay confirms GGRS self-deactivation. (c) Ablation training curves (GCN-2, $\alpha=0.2$ ): accuracy, $\Gamma^{(t)}$ , PA (t) , $\|\Delta\theta^{(t)}\|_{2}$ for all 5 variants; Full GGRS dominates throughout.

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Federated Learning Aggregation Domain Generalization Non-IID Federated Learning Federated Graph Learning Federated Learning

Open paper AskPDF arXiv

Federated graph learning (FGL) is a natural paradigm for social-media user graphs, where language communities, regional markets, and service boundaries can prevent raw graph pooling. We use the Twitch Gamers networks as the primary live-streaming social-media benchmark, and study a question that is often hidden by representation-level evaluation: after local message passing, what update signals are actually exposed to server aggregation? Through update-space measurements, we identify an aggregation-level failure in which graph-domain clients gradually place salient update signals on less shared parameter coordinates, while message-passing backbones show weaker cross-domain directional compatibility than an MLP control. This update-support fragmentation means that standard averaging can dilute locally important coordinates even when no raw graph data are exchanged. Across five backbones, homophily remains relevant but is not the dominant correlate of support retention; feature, label, and degree discrepancies show stronger associations. These findings indicate that graph-domain shifts damage not only local representations, but also the coordinate support on which aggregation operates. Motivated by this diagnosis, we propose FedIA, a plug-and-play server-side importance-aware aggregation method. Importance Masking selects a shared high-magnitude coordinate support, and Contribution-Aware Momentum Weighting smooths client contributions within that support. FedIA requires no raw graph sharing, no graph-statistics upload, and no auxiliary communication payload, while adding only

O(D+N)

persistent server state for

D

model coordinates and

N

clients.

Abstract

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