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PACE: Propagation-Aware Collaborative Correction for One-Shot Personalized Federated Graph Learning

Ruizhe Huang, Chengran Li, Xiaochuan Shi

arXiv:2609.04832v1cs.LG

TL;DR

Personalized federated graph learning needs to share complementary subgraph knowledge without overriding reliable local predictions, especially when one-shot communication prevents repair. PACE transports a propagation-aware low-rank correction around a complete Local model and uses convex NLL calibration to choose its logit contribution. The correction improves Accuracy and weighted-F1 over Local on five datasets, while α = 0 preserves Local predictions on ogbn-arxiv.

  • Problem

    Heterogeneous subgraphs may provide complementary knowledge, but incompatible collaboration can override reliable Local predictions in one-shot personalized federated graph learning.

  • Method

    PACE constructs a propagation-aware, receiver-anchored low-rank correction and uses CNLL on validation nodes to select one coefficient between Local and External logits without updating parameters or sending feedback.

  • Results

    PACE improves both Accuracy and weighted-F1 over Local on five datasets, while ogbn-arxiv receivers select α = 0 and preserve Local predictions exactly.

  • Takeaways & Limitations

    A compact transported correction can augment a complete Local model when receiver evidence supports it while leaving Local predictions unchanged otherwise.

  • Takeaways & Limitations

    The evaluated communities are a controlled proxy, Rank-6 is specific to the backbone and serialization scheme, and the protocol provides no formal privacy guarantee or worst-client safety guarantee.

Abstract

from arXiv · show

Client heterogeneity creates both an opportunity and a risk in personalized federated graph learning. Knowledge held by other subgraphs may complement a receiver's Local model, but an incompatible transfer can override reliable predictions. One-shot communication sharpens this tension because an unsuitable server return cannot be corrected later. We introduce PACE, which treats collaborative knowledge as a compact correction to a complete Local predictor rather than as its replacement. Each client uploads a rank-r update carrier and a diagonal sketch of propagated message moments. The server uses them to construct a propagation-aware, receiver-anchored correction, while the receiver retains its full Local model. Convex negative-log-likelihood calibration (CNLL) then selects one coefficient between Local and External logits using validation nodes; model parameters remain fixed and no feedback is sent. At Rank-6, personalized returns occupy 9.6-17.6% of dense tensor bytes across the six evaluated datasets. The correction receives nonzero weight and improves both Accuracy and weighted-F1 over Local on five datasets; on ogbn-arxiv, CNLL assigns zero predictive weight to the correction and preserves Local predictions exactly. Applying the same CNLL rule to matched baselines on three citation datasets does not account for these gains. The central result is therefore that a small transported correction can augment a complete Local model when receiver evidence supports it while leaving the Local prediction unchanged otherwise.

Introduction

Personalized federated graph learning must preserve complementary knowledge across local subgraphs without allowing incompatible collaboration to overwrite reliable local predictions. PACE addresses this one-shot tension by transporting a compact, receiver-anchored correction and letting validation evidence control its adoption.

  • Motivation: Graph subgraphs contain complementary evidence, but a global model can collapse incompatible knowledge and erase information represented by a local GNN.Federated learning collaborates without pooling raw records, while structural diversity creates both opportunity and risk.
  • Motivation: One-shot communication leaves no later round to repair a poor collaboration, so receivers must limit the influence of returned knowledge.The server must return useful information while preserving receiver control.
  • Design gap: Existing one-shot approaches may synthesize server data, optimize after aggregation, or return consolidated replacements, while compressed updates ignore propagation-dependent parameter relevance.These limitations leave the deployment problem of compact, graph-aware, receiver-controlled correction unresolved.
  • PACE: PACE adds a propagation-aware low-rank correction to the complete Local model instead of replacing it.A self-inclusive RegMean consensus and receiver-carrier subtraction construct the correction without server graph synthesis or post-download optimization.
  • Evaluation: PACE improves Accuracy and weighted-F1 over Local on five benchmarks, while ogbn-arxiv receivers select α = 0 and reproduce Local exactly.The matched one-shot evaluation spans six graph benchmarks.

Related Work

Related work spans personalized federated optimization, graph-aware collaboration, one-shot consolidation, compact communication, and selective adoption. PACE connects these strands by combining propagation-shaped correction transport with a complete Local predictor and validation-based external adoption.

  • Personalization under heterogeneous clients: Personalized federated methods modify objectives, separate shared and private parameters, or alter collaboration relations to address client heterogeneity.Examples include regularized objectives, personalized heads, local normalization, and graph-informed personalization.
  • Federated graph learning: Federated graph learning addresses structural heterogeneity and missing cross-client neighborhoods through methods operating on gradients, structural knowledge, or graph-specific representations.Graph structure adds shifts beyond ordinary federated statistical heterogeneity.
  • One-shot federated consolidation: One-shot federated consolidation combines independently trained client knowledge through distillation, parameter approximations, alignment, or graph-specific structural surrogates.These families commonly rely on surrogate inputs, posterior approximations, proxy models, or synthesized graph support.
  • Compact communication and model merging: Low-rank methods reduce exchanged state, whereas PACE factorizes a post-training update and selects rank as a performance–communication operating point.PACE differs from methods that directly parameterize compact federated models or compress gradients.
  • Selective adoption and confidence: PACE uses validation NLL to select one coefficient along the logit segment between a fixed Local model and a returned External model.Its contribution is a receiver-specific adoption rule rather than generic confidence scoring.

Problem Formulation

Each client trains a complete local GCN on a private community-structured subgraph, then communicates one compact upload for a personalized server return. The receiver keeps its Local model and uses validation labels only to calibrate how strongly the External candidate affects its logits.

  • Client setting: Client i owns a community-structured subgraph with local features, edges, and labels, while all clients share a GCN architecture and public initialization.Raw nodes, edges, features, and labels remain local.
  • Communication: The one-shot protocol permits one upload and one personalized return, containing a rank-r update carrier and compact propagation-moment information.Serialized communication is measured against dense model size, and no client performs another model update after download.
  • Transport and calibration: PACE constructs an External candidate around the receiver’s complete Local model because collaborative usefulness varies across receivers.Full-strength application of a shared candidate can introduce negative transfer.
  • Calibration: Validation labels solve a one-dimensional calibration problem without selecting checkpoints, updating parameters, or creating another message.Test labels are reserved for final evaluation.
  • Scope: The protocol reduces exchanged state but provides no formal privacy guarantee because model carriers and moment sketches can disclose information.A separate privacy analysis is required.

PACE: Transport and Calibrate

PACE transports external knowledge as a propagation-aware, low-rank correction while retaining each receiver’s complete Local model. Receiver-local CNLL then selects how much the correction affects logits without updating parameters or sending feedback.

  • Transport: PACE treats cross-client knowledge as a low-rank correction to the complete Local model rather than a replacement.The protocol uses one compact upload and one personalized return.
  • Transport: Rank-6 carriers are transmitted with low-rank factors, while vectors and other non-matrix parameters remain unfactorized or dense.The wire representation stores factors instead of reconstructed dense tensors.
  • Protocol: The complete protocol uses one upload, one server return, zero post-return parameter updates, and zero feedback uploads.The pipeline caption also excludes test-label selection and additional communication.
  • Transport: Propagation-aware sketches measure coordinate-wise second moments of propagated training-node messages and normalize them without using validation or test labels.The layerwise convention preserves relative propagation geometry while preventing activation scale from becoming an unintended donor weight.
  • Receiver-Anchored Correction: The server forms a uniform self-inclusive RegMean consensus, and each receiver’s correction arises by subtracting its own carrier from that shared consensus.Personalization comes from the receiver displacement and later coefficient selection, not receiver-dependent donor weights.
  • Convex NLL Logit Calibration: CNLL selects one scalar between Local and External logits using validation NLL, leaving model parameters fixed.The coefficient is not selected using dataset name, client count, seed, or test performance.

Experiments

Across six one-shot subgraph-FGL benchmarks, PACE evaluates whether a compact, receiver-anchored correction can augment or preserve a complete Local predictor. It improves both primary metrics on five datasets, preserves Local exactly on ogbn-arxiv, and remains compact under Rank-6 communication.

  • Evaluation setup: PACE evaluates six Louvain-partitioned benchmarks with 10 clients under matched one-round collaborative protocols.The evaluation covers citation, coauthor, product co-purchase, and large-scale OGB graphs.
  • Main results: PACE improves Accuracy and weighted-F1 over Local on five datasets, while ogbn-arxiv selects α = 0 and reproduces Local exactly.The correction receives nonzero External weight on the other five datasets.
  • Main results: 27 of 30 fixed receivers have nonnegative five-seed means, but the worst receiver averages −1.43 points, precluding a worst-client safety claim.The worst single run is −3.64 points.
  • Efficiency: At Rank-6, personalized returns occupy 9.6–17.6% of dense tensor bytes across all six datasets.Across the three rank-study benchmarks, Rank-6 averages 79.65% Accuracy with 12.38% upload and 10.47% personalized-return bytes relative to dense tensors.
  • Transport and resolver analysis: RegMean improves Accuracy over ordinary Mean by 1.13, 1.61, and 0.42 points on Cora, CiteSeer, and PubMed, respectively, winning all 15 paired comparisons.Propagation-aware moments add 0.44 points on CiteSeer while matching the raw-moment variant on Cora and PubMed.
  • Matched calibration fairness: PACE remains ahead of matched baselines after applying the same CNLL calibration on all three controlled citation datasets.The comparison tests whether scalar calibration alone accounts for PACE’s gains.

Conclusion

PACE uses a compact propagation-aware correction to augment a complete Local predictor rather than replace it. CNLL selectively admits the correction, preserving Local predictions when receiver evidence rejects it.

  • 9.6–17.6% of dense tensor bytes are occupied by Rank-6 personalized returns.
  • CNLL assigns nonzero correction weight on five datasets and zero on ogbn-arxiv, exactly preserving Local predictions there.
  • Matched controls show that applying CNLL to baselines does not account for the citation gains.
  • PACE’s main contribution is a receiver-dependent compact-correction interface, not universal performance dominance.

A Seed-Paired and Receiver-Level Diagnostics

The diagnostics organize transfer effects by seed and receiver while fixing Rank-6 globally for the reported experiments.

  • Figure 4 reports mean PACE-minus-Local differences with 95% paired t intervals over five matched seeds.
  • Win/Tie/Loss counts use a 0.01-point tolerance, while panel (c) separates helped, tied, and harmed citation receiver–seed units.
  • Rank-6 is fixed globally for both low-rank uploads and personalized returns rather than selected per dataset.
  • Rank-6 upload and personalized downlink ratios are measured relative to dense tensor bytes across three datasets.

C Complete Resolver Ablation

The complete shared-transport ablation evaluates receiver-local CNLL while holding the transported correction fixed across all dataset–client settings.

  • Table 6 changes only receiver-local CNLL calibration while holding the transported correction fixed.
  • ∆Accuracy is defined as Transport+CNLL minus Transport in percentage points.

D Matched CNLL Fairness Controls

Matched fairness controls apply the same receiver-local CNLL calibration to each baseline’s own External predictor, testing whether calibration alone explains PACE’s result.

  • These controls test whether PACE’s result can be explained by calibration alone without replacing native baseline identities.
  • Table 7 compares every baseline in native form with the same receiver-local CNLL logit calibration.
  • PACE uses its Rank-6 transported External predictor in the matched controls.

E Complete Louvain Results

The supplementary results report complete Louvain matrices for additional client counts and evaluate matched METIS and Dirichlet partitions under controlled protocols.

  • Complete Louvain Results: The reported metrics include Accuracy, weighted-F1, and Macro-F1, with values given as five-seed mean ± sample standard deviation in percent.
  • Complete Louvain Results: Tables 8 and 9 extend the Louvain results to C = 20 and C = 30 using the main-paper C = 10 layout.
  • Complete Louvain Results: Table 10 provides fixed-class Macro-F1 baseline matrices for C = 10, 20, and 30, with datasets as columns and methods as rows.
  • Partition Robustness: METIS and Dirichlet label-skew evaluations retain the model, optimization, client count, seeds, metrics, and one-round protocol while changing the partition.
  • Partition Robustness: Tables 11 and 12 report C = 10 results for METIS and Dirichlet partitions, respectively, using five-seed mean±sample standard deviation and marking the best and second-best displayed means.

F Information-Geometric Interpretation of CNLL

CNLL is a receiver-local scalar gate that interpolates Local and External logits through a normalized geometric opinion pool. Its validation objective is convex, enabling endpoint tests or bisection, while its guarantee remains limited to aggregate validation NLL rather than test accuracy or per-node improvement.

  • CNLL calibration: CNLL is a one-dimensional receiver-local gate, not a second learned model.The released resolver uses the same scalar computation without updating model parameters.
  • Information-geometric interpretation: For α ∈ [0, 1], logit interpolation equals a normalized geometric opinion pool and a weighted reverse-KL barycenter.The equivalence follows by substituting the Local and External softmax distributions and normalizing across classes.
  • Information-geometric interpretation: Class-independent shifts of Local logits leave the gate unchanged because they multiply the numerator and denominator by the same factor.Thus the gate depends on predictive beliefs rather than an arbitrary softmax logit origin.
  • CNLL calibration: CNLL validation risk is globally convex, so endpoint tests identify a boundary optimum and bisection locates an interior root when needed.Strict convexity is unnecessary; a degenerate flat segment can yield multiple minimizers.
  • CNLL calibration: The resolver performs 64 bisection iterations on the scalar problem without updating model parameters or consulting test labels.The derivative compares model-implied collaborative displacement with label-observed displacement.
  • Guarantee and scope: The validation-NLL result is a receiver-local aggregate guarantee, not a guarantee of test accuracy, per-node improvement, or worst-client performance.A zero cumulative validation log-evidence difference is handled directly.
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