Learning to Refer: Inference-Time Collaboration in Decentralized Federated Learning

Yuheng Ma; Chendi Wang; Qiong Zhang

cs.LGOct 19, 2026

Learning to Refer: Inference-Time Collaboration in Decentralized Federated Learning

Authors: Yuheng Ma, Chendi Wang, Qiong Zhang

Organizations: KLATASDS-MOE, School of Statistics, East China Normal University · Department of Statistics and Data Science, Xiamen University · Division of Computing and Mathematical Sciences, MBZUAI

Abstract

In decentralized federated learning, heterogeneous clients may develop complementary expertise, yet each query is typically evaluated only by the client where it arrives. To exploit this distributed expertise without global coordination, we formulate inference-time collaboration as budgeted local expert referral, a graph-constrained routing process in which a query can move only between neighboring clients and only visited clients contribute to its final prediction. EdgeDRM implements this framework by learning a density-based routing potential for each client: differences between neighboring potentials provide the comparisons used to select successive referrals, while local task models generate predictions that are aggregated along the resulting route. Both training and inference are decentralized, using only neighbor-local information without a central router or graph-wide client scoring. We establish estimation guarantees for the learned comparisons and characterize how local improvement and graph structure govern prior-weighted density gains from referral. Experiments on benchmark and real-world medical data show that EdgeDRM outperforms graph-matched decentralized baselines in most settings, with the clearest benefits under sparse connectivity.

Figures & tables

Panel of Figure 1 — Figure 1: Hospital analogy for inference-time routing. Gray lines indicate hospital pairs that can exchange information and know one another’s capabilities, for example because they operate in the same region or health system. Without routing, a patient with a heart condition remains at an entry hospital whose expertise lies in gastroenterology (left). A centralized router sees all hospitals and dispatches the patient directly (center), but such global coordination is often infeasible because of administrative boundaries, privacy constraints, and geographic separation. In contrast, EdgeDRM (ours) makes stepwise local referrals (right): the gastroenterology hospital first routes the patient to a general chest center, whose thoracic expertise better matches the condition. The center then identifies the condition as cardiac and routes the patient to a dedicated cardiology hospital. Thus, each hop progressively improves the match between the patient and the hospital’s expertise.

Group	Method	CIFAR-10		CIFAR-20		CIFAR-100
Group	Method	Dir-0.3	5-SPC	Dir-0.3	25-SPC	Dir-0.3	25-SPC
Reference	Local	$16.59\pm 3.78$	$18.46\pm 1.49$	$13.35\pm 0.29$	$11.17\pm 0.54$	$4.03\pm 0.23$	$2.49\pm 0.10$
Reference	FedDRM	$63.81\pm 1.54$	$61.24\pm 2.29$	$39.28\pm 0.87$	$42.42\pm 1.12$	$28.67\pm 0.58$	$33.38\pm 0.87$
Path	DFedAvgM	$28.55\pm 7.62$	$27.41\pm 0.21$	$23.94\pm 0.03$	$21.47\pm 1.04$	$9.28\pm 0.61$	$7.03\pm 0.44$
	DisPFL	$27.19\pm 8.01$	$26.87\pm 1.91$	$\mathbf{26.43\pm 0.65}$	$22.79\pm 1.68$	$10.83\pm 0.96$	$6.41\pm 0.64$
	FedSPD	$18.34\pm 5.17$	$20.00\pm 1.14$	$15.44\pm 0.99$	$14.41\pm 0.78$	$4.68\pm 0.38$	$4.30\pm 0.11$

Table 1: Eight-client decentralized CIFAR benchmark reporting system accuracy (%) across three datasets and two non-IID partitions. Local and centralized FedDRM are illustrative references. Bold cells with blue shading mark the best decentralized result within each topology and setting. All entries are means

\pm

sample SD across 3 seeds.

Figure 2: Fixed-expert hard-terminal routing ablation on CIFAR-10 and CIFAR-100 with Dirichlet-

0.3

partitions and RR4 .

	Reference	Decentralized					Reference
Setting	Local	DFedAvgM	DisPFL	FedSPD	EdgeDRM-NR	EdgeDRM	FedDRM
Dir-0.3	$16.45\pm 1.15$	$27.79\pm 3.25$	$23.71\pm 2.65$	$17.82\pm 0.69$	$21.52\pm 1.50$	$\mathbf{30.06\pm 1.16}$	$38.45\pm 0.52$
5-SPC	$18.11\pm 0.47$	$27.92\pm 1.22$	$24.87\pm 0.95$	$20.54\pm 0.75$	$22.76\pm 1.20$	$\mathbf{31.70\pm 0.39}$	$35.96\pm 0.52$

Table 2: CIFAR-10/ RR4 system accuracy with 32 clients (%; mean

\pm

SD over three seeds).

Figure 3: Referral traffic by hospital tier on two topologies . Bars show the mean share of visited-classifier calls over 3 seeds.

Graph	DFedAvgM	EdgeDRM
Path	28.45	28.62 (+0.18)
Cycle	27.20	28.35 (+1.15)
RR3	27.45	27.76 (+0.31)
Complete	28.93	28.79 (-0.14)

Table 3: ISIC2019 balanced accuracy (%; three-seed mean). Parentheses show the EdgeDRM change from DFedAvgM .

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Condition	Accuracy (%)	Calls/query	Large share (%)	Large calls/100	Peak share (%)
Layered: EdgeDRM-NR	$45.29\pm 1.80$	$1$	$25$	$25$	$3.125$
Layered: History, no prior	$45.74\pm 1.60$	$2.01\pm 0.03$	$19.55\pm 0.44$	$39.22\pm 1.56$	$5.04\pm 0.44$
Layered: History + prior	$47.36\pm 3.06$	$2.61\pm 0.01$	$52.02\pm 0.12$	$135.52\pm 0.63$	$7.14\pm 0.20$
Shortcut: EdgeDRM-NR	$45.49\pm 2.03$	$1$	$25$	$25$	$3.125$
Shortcut: History, no prior	$46.12\pm 1.73$	$2.01\pm 0.02$	$20.36\pm 0.33$	$40.96\pm 0.39$	$4.61\pm 0.59$
Shortcut: History + prior	$47.93\pm 2.53$	$2.46\pm 0.01$	$69.49\pm 0.10$	$170.81\pm 0.81$	$9.77\pm 0.18$

Appendix

Table 4: Accuracy and diagnostic workload in the hospital-network experiment. Large share and peak share are percentages of all visited-classifier calls; large calls/100 is the absolute number of large-hospital calls per 100 arrivals. Accuracy uses history-weighted predictions. Entries are mean

\pm

sample SD over seeds 2025–2027; EdgeDRM-NR workload quantities are fixed by uniform entry.

$\lambda$	EdgeDRM	EdgeDRM-NR	Referral gain	Calls
$0.10$	$52.11\pm 2.19$	$35.01\pm 3.55$	$+17.11\pm 3.98$	$2.16\pm 0.03$
$0.25$	$51.76\pm 2.04$	$30.29\pm 4.06$	$+21.46\pm 4.99$	$2.16\pm 0.03$
$0.40$	$51.57\pm 2.03$	$28.36\pm 4.23$	$+23.21\pm 5.36$	$2.15\pm 0.03$
$0.50$	$51.51\pm 2.04$	$27.48\pm 4.32$	$+24.03\pm 5.60$	$2.15\pm 0.03$
$0.60$	$51.26\pm 2.04$	$26.75\pm 4.40$	$+24.51\pm 5.71$	$2.14\pm 0.03$
$0.75$	$50.95\pm 2.09$	$25.96\pm 4.49$	$+24.99\pm 5.99$	$2.13\pm 0.04$

Appendix

Table 5: Task–routing weight on CIFAR-10/Dirichlet-

0.3

, eight clients, RR4 , and

L=2

. All branches reuse the same seed-specific 800-round prefix and fit heads and routers for 200 rounds. Accuracy is in percent, referral gain in percentage points, and calls per query. Entries are final-checkpoint means

\pm

sample SD across seeds 2025–2027.

Graph	Hard terminal	Uniform history	Weighted history	Calls	Incident scores
Path	$11.09\pm 0.60$	$10.43\pm 0.79$	$\mathbf{11.19\pm 0.58}$	1.72	2.35
Cycle	$12.29\pm 0.63$	$11.62\pm 0.79$	$\mathbf{12.40\pm 0.63}$	1.81	2.81
RR4	$17.28\pm 0.55$	$15.62\pm 0.47$	$\mathbf{17.59\pm 0.59}$	2.10	6.56
Complete	$\mathbf{20.05\pm 0.55}$	$17.71\pm 0.67$	$20.02\pm 0.63$	1.94	12.66

Appendix

Table 6: Prediction-rule comparison and inference costs using identical frozen models and paths. Accuracy is in percent (three-seed mean

\pm

sample SD). Hard terminal uses the final visited expert; uniform and weighted history use only visited predictions. Edge scores and classifier calls are mean logical operations per query, not measured latency.

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Decentralised federated learning, based on peer-to-peer communication, is increasingly proposed for on-device training of machine learning models, promising a privacy-preserving, communication-efficient training process with no risk of single-point failure. However, the role of structural and temporal inhomogeneities in such fully decentralised settings remains poorly understood. Here, we investigate their effects when model parameters are locally averaged during aggregation. We show that the decentralised federated learning process is governed, both in the early phase and the late, stationary limit, by the same dynamics as a lazy random-walk diffusion process on temporal networks. Based on this mapping, we demonstrate that the typical experimental scenario used in decentralised federated learning leads to unrealistically rapid convergence because of ignoring the temporal and structural inhomogeneities inherent in the communication network. We analyse real-world temporal networks and find that inhomogeneities most often dramatically slow down diffusion, hence the convergence process.

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