Test-Time Collaborative Classification over Multi-Agent Networks

Ping Hu; Mert Kayaalp; Ali H. Sayed

cs.MAAug 25, 2026

Test-Time Collaborative Classification over Multi-Agent Networks

Authors: Ping Hu, Mert Kayaalp, Ali H. Sayed

Organizations: School of Engineering, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland · DTI, SUPSI, Dalle Molle Institute for Artificial Intelligence (IDSIA USI-SUPSI), 6962 Lugano, Switzerland

Abstract

The increasing heterogeneity of multi-agent systems poses significant challenges for jointly training a global model across agents. At the same time, cooperative inference between agents has long been recognized as a powerful mechanism for distributed decision making over networks. Motivated by these observations, we propose a collaboration framework for distributed binary classification over multi-agent networks, where a set of independently trained agents, potentially differing in architecture, feature space, or modality, coordinate their actions during test time to form collective predictions. This coordination is achieved by exchanging local decision statistics through a distributed learning protocol. We develop a theoretical and experimental study of this independent training and cooperative inference paradigm, and examine its performance under different communication budgets and distributed learning rules. We establish classification error guarantees under sufficient, finite-round, and finite-precision communication, together with PAC-style generalization bounds. These results capture the influence of model heterogeneity, network topology, combination policy, and communication constraints on prediction accuracy. Taken together with the experimental results, they reveal both the price of independent training and the benefit of collective prediction for the proposed distributed decision making framework with models learned from data.

Figures & tables

Method	Training coordination	Additional fitting	Inference coordination
Non-cooperative	None	None	None
Avg-stat / Vote	None	None	One-shot centralized averaging / voting
Learned (simplex) fusion	None	Fusion rule fitted on aligned validation outputs	One-shot centralized fusion
AdaBoost	Centralized	Boosting-based fitting of local predictors	One-shot weighted fusion
Ours / Ours (no centering)	None	None	Iterative peer-to-peer scalar exchange
VFL-JT	Joint training on aligned labeled samples	Server-side fusion head learned jointly	One-shot server fusion

TABLE I: Training and inference coordination of the methods considered in the main baseline comparisons.

Panel of Figure 2 — Fig. 1: CIFAR-10 patch-partition benchmark. Panel (a) shows the local patch observed by each agent for a representative cat image, and panel (b) shows the communication topology used for collaboration.

Panel of Figure 3 — Fig. 2: Main CIFAR-10 patch-partition results. Panel (a) reports the empirical class-conditional decision statistics, panel (b) compares the probability of error under different values of $N_{0}$ , and panel (c) shows the error evolution over the communication rounds for $N_{0}=10000$ .

Panel of Figure 4 — Fig. 3: Conditional mutual information between CIFAR-10 patches. Panel (a) shows the estimated pairwise conditional mutual information matrix across the nine patch agents. White stars mark patch pairs that are adjacent on the $3\times 3$ grid shown in Fig. 1a , while red boxes indicate, in each row, the largest off-diagonal entries whose number matches the number of grid neighbors of the corresponding patch. Panel (b) shows the grouped summary over same-row, same-column, and far patch pairs.

Fig. 4: Collaboration gain under heterogeneous local model families on CIFAR-10. Each cell shows the relative gain when the corresponding model family is assigned to that patch location under the balanced rotation protocol.

Panel of Figure 6 — Fig. 5: Performance of heterogeneous local model families on CIFAR-10. The curve labels in panel (b) and the value of $N_{0}$ in panel (c) are the same as those in Fig. 2 .

Panel of Figure 7 — Fig. 6: ModelNet40 multi-view benchmark. Panel (a) shows the 12 rendered views associated with a nightstand object, and panel (b) shows the communication topology used for collaboration.

Panel of Figure 8 — Fig. 7: Main ModelNet40 multi-view results. Panel (a) reports the empirical class-conditional decision statistics, panel (b) compares the probability of error under different values of $N_{0}$ , and panel (c) shows the error evolution over the communication rounds for $N_{0}=400$ .

Panel of Figure 9 — Fig. 8: Performance of temperature scaling on ModelNet40. The curve labels in panel (b) and the value of $N_{0}$ in panel (c) are the same as those in Fig. 7 .

Panel of Figure 10 — Fig. 9: Controlled correlation stress test on ModelNet40. Panel (a) shows the average pairwise Pearson correlation across agent decision statistics, both unconditional and label-conditional, and panel (b) shows the collaboration gain after $t=20$ communication rounds.

Fig. 10: Effect of topology, the construction rule of

A

, and quantization noise.

Panel of Figure 12 — Fig. 11: Tradeoff between the probability of error and the total number of transmissions (per testing sample) under local adaptive stopping rules.

Panel of Figure 13 — Fig. 12: Robustness of collaborative classification to corrupted agents, measured by the paired excess error at the communication round $t=20$ . Panel (a) varies the Gaussian noise multiplier $\eta_{\mathrm{noise}}$ , panel (b) varies the fault type and the normalized bias level $\eta_{\mathrm{bias}}$ , and panel (c) varies the adversarial scale $\eta_{\mathrm{adv}}$ .

Ping Hu received her Ph.D. in electrical engineering from EPFL, Switzerland in 2026. She is currently a postdoctoral researcher with the Adaptive Systems Laboratory, EPFL. Her research interests include distributed learning, inference and decision-making over networked systems.

Table 14

Mert Kayaalp received his Ph.D. in computer and communication sciences from EPFL, Switzerland in 2025. He is currently a research scientist at Dalle Molle Institute for Artificial Intelligence (IDSIA USI-SUPSI), Switzerland, where he is affiliated with the UBS-IDSIA AI Lab. His research focuses on machine learning and signal analysis in networked and dynamical systems.

Table 15

Ali H. Sayed is professor and former dean of engineering at EPFL, Switzerland, where he also directs the Adaptive Systems Laboratory. He served before as a distinguished professor and chair of electrical engineering with UCLA. He is a member of the US National Academy of Engineering (NAE) and The World Academy of Sciences (TWAS). He served as a president of the IEEE Signal Processing Society in 2018 and 2019. An author of over 650 scholarly publications and 10 books, his research involves several areas including adaptation and learning theories, statistical inference, and multi-agent systems. His work has been recognized with several awards including the 2022 IEEE Fourier Technical Field Award and the 2020 IEEE Wiener Society Award. He is also a fellow of EURASIP and the American Association for the Advancement of Science (AAAS).

Table 16

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Fig. H.1: Illustration of the local labeled datasets in the CIFAR-10 patch-partition benchmark. The highlighted columns illustrate two representative images from the two classes contributing different local patches to all agents.

Method	Training	Inference per sample
VFL-JT	$KE_{\rm VFL}(2N_{\rm tr}+N_{\rm val})$	$K$
Proposed	$0$	$tE_{\rm off}(A)$

Appendix

TABLE H.1: Communication cost of VFL-JT and the proposed scheme.

Fig. H.2: Temperature scaling diagnostics for the ModelNet40 benchmark. The orange curve shows the average of

T_{k}

over agents, with error bars indicating

95\%

confidence intervals across Monte Carlo repetitions. The blue curve shows the average run-wise standard deviation of

\{T_{k}\}_{k=1}^{K}

, which quantifies the variability of the fitted temperatures across agents.

Fig. H.3: Temperature scaling diagnostics for the CIFAR-10 benchmark.

Panel of Figure 21 — Fig. H.4: Performance of temperature scaling on CIFAR-10.

Fig. H.5: Probability of error under the controlled correlation stress test. For each perturbation amplitude $\sigma_{\mathrm{pert}}$ , the figure compares the non-cooperative error at $t=0$ and the collaborative error after $t=20$ communication rounds as functions of the dependence strength $r$ . The clean non-cooperative and collaborative error levels are also shown for reference.

Panel of Figure 23 — Fig. H.6: Ring and grid communication topologies used in Fig. . Self-loops are omitted from the plots for visual clarity.

Panel of Figure 24 — Fig. H.7: Effect of the construction rule of $A$ and quantization on classification performance under different graph topologies.

Panel of Figure 25 — Fig. H.8: Effect of graph topology and quantization on classification performance under different construction rules of $A$ .

Panel of Figure 26 — Fig. H.9: Effect of graph topology and the construction rule of $A$ under different communication precisions.

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