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A Trust-Network-Based Federated Learning Framework for Multi-Center Aging Clock Prediction
Chunxu Zhang, Bo Li, Wenliang Wang, Yang Liu, Di Jiang, Yuan Huang, Yo-ichi Nabeshima, Akinori Yamamura, Bo Yang, Qiang Yang
TL;DR
Multi-center aging-clock modeling must learn from limited local data under partial, asymmetric trust while retaining discriminative, interpretable age prediction across heterogeneous centers. TNFL propagates a model through authorized cross-center relations with generative replay; across datasets, it lowers MAE versus local training and performs comparably to server-based FedAvg.
Problem
A central question is which proteins are relevant to aging-clock prediction and how their effects and interactions organize across orders; multi-center modeling also faces limited local data and partial, asymmetric trust.
Source: §2 · p. 16, §3.1 · p. 18Method
TNFL progressively propagates an evolving aging-clock model through authorized cross-center relations and uses generative replay to retain information from previously visited centers.
Source: §3.1 · p. 18Results
Across datasets, TNFL lowers MAE versus local training and performs comparably to FedAvg, while identified interactions organize into higher-order subnetworks spanning aging-related systems.
Source: §1.1.3 · p. 9, §1.2.1 · p. 11Takeaways & Limitations
Coherent higher-order aging-related protein patterns emerged without prior protein-interaction or pathway knowledge during training.
Source: §1.1.3 · p. 9The analysis treats each omics modality separately, capturing only part of aging’s molecular complexity.
Source: §2 · p. 17
Abstract
from arXiv · showhide
Aging clocks quantify biological aging and help characterize individual health status. What protein interactions are important for accurate aging clocks, and are they zeroth-order or higher-order? Addressing these questions requires learning from large molecular datasets distributed across medical centers, where privacy constraints prevent centralized data sharing. Federated learning offers a natural solution but faces four challenges in this setting: limited local sample sizes, sparse and directional inter-center trust, the need to retain discriminative age prediction while supporting interpretation, and model drift and forgetting under heterogeneous cross-center data. We propose TNFL, a trust-network-based federated learning framework that progressively propagates models along directed pairwise trust relations without centralized aggregation. TNFL combines an age-aware mixture-of-experts model with generative replay to preserve previously learned information and reduce forgetting and drift. Experiments across multiple molecular datasets show that TNFL enables effective aging-clock prediction with limited local data, provides interpretable age-dependent prediction patterns, and maintains stable performance across interaction orders. To investigate the biological questions, we analyze TNFL-identified pairwise protein interactions and their higher-order organization through functional and network analyses. The identified interactions repeatedly form coordinated higher-order subnetworks spanning multiple aging-related biological systems, with several proteins recurring across subnetworks. These findings suggest that TNFL captures molecular relationships beyond isolated pairwise associations and reveals coherent higher-order biological organization associated with aging.
1 Results
TNFL identifies age-associated protein patterns and coherent higher-order subnetworks, while supporting aging-clock prediction across limited-data centers and remaining robust to interaction order, measurement variability, and trust-network structure.
1.1.2 Pairwise Protein Interactions
- The top model-identified protein pairs showed known STRING associations for GIP–CGA, INSL3–CGA, and GIP–INSL3, while other pairs showed functional convergence without direct STRING links.GFAP-related pairs implicated neuroinflammatory and neuroendocrine processes; GFAP–NPPB reflected neural and cardiac stress signaling, while EDA2R–CGA and CCDC80-related pairs involved inflammatory, endocrine, and extracellular-matrix remodeling functions.Source: §1.1.2 · p. 7
1.1.3 Higher-Order Organization of Protein Interactions
- Model-identified interactions repeatedly organized into higher-order subnetworks spanning neural, vascular, endocrine, metabolic, inflammatory, and stress-related systems, without prior interaction or pathway knowledge in training.Recurrent proteins included GFAP, NEFL, GDF15, GIP, ELN, LTBP2, and CXCL17; subnetworks included neurovascular-endocrine coordination, hypothalamic and neuroendocrine regulators, and cardiometabolic stress signaling, consistent with broader aging-related coordination.Source: Figure 3 · p. 8, §1.1.3 · p. 9
1.2.1 Predictive Performance
- TNFL reduced MAE versus local training by 0.69 years on UKB-Center, matching FedAvg’s 0.70-year reduction, and beat FedAvg by 0.12 and 0.34 years on UKB-Imbalance and GEO-Methylation.Across backbones, TNFL improved over local training; the main AgeMoE implementation had the strongest overall performance and lower global-test variance, with median MAE reductions of 0.54 years on UKB-Center, 0.55 on UKB-Imbalance, and 2.55 on GEO-Methylation. Generative replay supported cross-center generalization, particularly under greater heterogeneity.Source: Figure 4 · p. 10, §1.2.1 · pp. 11–12
1.2.2 Robustness Evaluation
- Across sampled interaction orders, AgeMoE with generative replay kept client-level MAE ranges below 0.5 years and cumulative degradation below 0.2 years on UK Biobank datasets, with near-zero degradation on GEO-Methylation.On UKB-Center, later updates maintained or improved earlier-visited clients’ performance, and median step-wise forgetting rates were mostly below zero. Predictive performance also degraded only slightly under simulated measurement variability and remained comparable across feasible trust-network structures.Source: §1.2.2 · pp. 12, 14, 15, Figure 5 · p. 13
2 Discussion
TNFL supports multi-center aging-clock prediction with limited local data while revealing age-related protein effects and interactions from individual to higher orders. Its trust-directed propagation and generative replay address cross-center collaboration and knowledge retention, though the framework and analyses have several limitations.
Summary of Main Findings
- TNFL identifies age-associated proteins and coherent pairwise interactions that form higher-order subnetworks across multiple aging-related biological systems.Computationally, it predicts aging clocks with limited local data, supports different predictive backbones, benefits from generative replay, and remains stable across interaction orders and trust-network structures.Source: §2 · p. 15
Comparison with Existing Work
- Unlike standard federated learning’s central aggregation, TNFL propagates models along directed pairwise trust relations without a globally trusted server.Cumulative learning lets data-limited centers use previously accumulated information, while generative replay helps preserve knowledge across heterogeneous updates; Table 1 compares representative methods across four challenges.Source: §2 · p. 15, Table 1 · p. 16
- TNFL extends aging-clock interpretation from identifying relevant molecular features to examining individual protein effects and pairwise and higher-order protein organization.Earlier work examined feature importance, biological relevance, and variation across age stages or population subgroups.Source: §2 · p. 16
Limitations and Future Directions in Aging Clock Modeling
- TNFL assumes a predefined trust network and feasible propagation sequences, uses chronological age as its target, analyzes each omics modality separately, and has not been evaluated in real-world multi-center deployments.Future directions include adaptive routing and termination, targets such as healthspan or phenotypic age, multi-omics integration, and deployment studies under real institutional and communication constraints.Source: §2 · pp. 16–17
3 Methods
TNFL learns aging clocks by propagating models through pre-established directed trust relations between centers, combining age-aware prediction with generative replay to retain previously acquired information. Its methods define the multi-center setting, trust-constrained training protocol, AgeMoE predictor, and joint training with replay.
3.1 Problem Formulation and Multi-Center Challenges
- TNFL formulates chronological-age prediction from molecular features across locally held, heterogeneous center datasets, addressing limited local data, asymmetric trust, interpretability, and cross-center forgetting.Rather than using a globally trusted coordinator, the framework progressively propagates a model along authorized relations while replay helps retain information from previously visited centers.Source: §3.1 · pp. 17–18
3.2 Directed Trust Relations and Trust-Network Formulation
- TNFL defines communication through directed, pairwise, message-specific trust relations; protocol messages exclude raw data and local optimization information, and trust is non-transitive.The trust network is a pre-established collaboration structure that constrains feasible model-propagation sequences.Source: §3.2 · pp. 18–19
3.3.1 Framework Overview
- TNFL successively propagates and updates an evolving model across centers, using AgeMoE for age prediction and generative replay to retain information during heterogeneous adaptation.AgeMoE also exposes age-dependent routing behavior for interpretation.Source: §3.3.1 · p. 19
3.3.2 Trust-Constrained Training Sequence
- Training follows a finite sequence in which every consecutive center pair must have a pre-established directed trust relation; the sequence composes, but does not create or extend, trust.The route may revisit centers when permitted by the trust-network topology.Source: §3.3.2 · pp. 19–20
3.5.1 Joint Training of Aging Clock and Generative Model
- At subsequent centers, the generator synthesizes pseudo-samples, prediction-consistency filtering selects them, the aging clock updates on filtered samples plus local data, and the generator updates on local data.At the initial center, pseudo-sample generation and consistency filtering are omitted because no preceding-center model state is available.Source: Figure 6 · p. 20, §3.5.1 · p. 25
3.3.3 Sequential Training Protocol
- Each center updates the model state received from its predecessor using local data, and the protocol ends after the final update, with model release governed separately from training transmissions.Local data and optimization information remain at each center; final release does not require the terminal center to have direct trust relations with every participant.Source: §3.3.3 · p. 21, §3.3.4 · p. 21
3.4.1 AgeMoE Aging Clock Model
- AgeMoE uses a Transformer encoder and input-dependent expert routing for age prediction, with an age-aware regularizer encouraging similar routing distributions for samples of similar ages.The regularizer uses symmetric KL divergence between routing distributions of nearest neighbors in age space.Source: §3.4.1 · pp. 21–23
3.4.2 Generative Replay for Cross-Center Knowledge Preservation
- TNFL uses an age-conditioned CVAE to generate pseudo-samples representing information from preceding centers for replay alongside local data during later updates.Conditioning on age and an age-bin identifier captures coarse age-level information and finer variation within bins.Source: §3.4.2 · pp. 24–25
1. Pseudo-sample generation and prediction-consistency filtering
The procedure generates pseudo-samples to represent information from previously visited clients, then filters them using prediction consistency to provide more reliable supervision for subsequent training.
1. Pseudo-sample generation and prediction-consistency filtering
- Pseudo-samples are generated by drawing latent vectors from a standard normal distribution and decoding features conditioned on target ages and age-bin identifiers.The ages and bin identifiers are sampled from the age range maintained by the generator.Source: §1 · p. 25
- The aging clock received from the preceding center predicts each generated sample’s age as the reference for filtering.Generated samples can vary in quality.Source: §1 · p. 25
- Samples whose predicted ages are sufficiently consistent with their conditioning labels are retained, excluding inconsistent examples and improving the reliability of generated supervision.The retained samples form the filtered set used in subsequent training.Source: §1 · p. 25
2. Aging clock update
The aging clock is updated on filtered pseudo-samples combined with the current center’s data, using the AgeMoE objective to learn locally while retaining information from previously visited clients.
2. Aging clock update
- Filtered pseudo-samples are combined with the current center’s data to update the aging clock.This combined dataset lets the model learn from the current center while retaining information from previously encountered client distributions.Source: §2 · p. 26
- Aging clock parameters are optimized by minimizing the AgeMoE objective.Source: §2 · p. 26
- Generated samples provide complementary supervision that preserves information acquired from previously visited clients during sequential updates.Source: §2 · p. 26
3. Generative model update
TNFL sequentially updates its generative model with each center’s local data and passes it along with the aging clock. The paper also specifies replay-based optimization, directed-trust obligations, and the experimental settings used to evaluate the framework.
3. Generative model update
- Each center updates the received generator using its local data, then passes the updated generator along with the aging clock for subsequent interactions.The generator is optimized with a CVAE objective; sequential updates incorporate each center’s data distribution.Source: §3 · p. 26
3.5.2 Sequential Optimization Formulation
- At each step, TNFL initializes from protocol-authorized parameters, filters generated pseudo-samples for replay, and updates the aging clock and generator; the first center has no replay set.The final aging-clock model is output after the last update.Source: §3.5.2 · pp. 26–27
3.6.2 Security Properties along Trust Sequences
- Along a valid trust sequence, downstream centers do not use received messages to infer the private information of upstream centers.The proposition composes receiver-side confidentiality across successive transmissions.Source: §3.6.2 · p. 29
3.7.1 Datasets and Multi-Center Construction
- Evaluation uses UK Biobank proteomics (46,988 samples, 2,920 proteins) and GEO methylation (6,392 samples, 485,514 CpG sites), partitioned into 18, 10, and 4 clients across three settings.UKB-Imbalance has 10 clients and a smallest client of 300 samples; GEO clients are markedly imbalanced.Source: §3.7.1 · pp. 30–31
3.7.2 Model Configurations
- AgeMoE combines a Transformer encoder and mixture-of-experts regression head with a CVAE that generates age-conditioned replay samples filtered by prediction consistency.For UK Biobank the tolerance is 1 year; configurations differ between the UK Biobank and GEO experiments.Source: §3.7.2 · pp. 32–33
3.7.3 Evaluation Setup
- TNFL is compared with local training and FedAvg using MAE on client-level and global test sets; interaction-order robustness is assessed across sampled valid trust sequences.The study evaluates 500 sequences for UKB-Center, 50 for UKB-Imbalance, and all 24 permutations for GEO-Methylation.Source: §3.7.3 · p. 33
4 Declarations •
The authors report multiple institutional and project funding sources, no competing interests, and distinct access conditions for the study’s datasets. The declarations also provide code and consent information and describe author contributions.
Funding
- Funding came from PolyU funds and institutes, the Joint Research Centre for AI Aging Science and Medicine, and industry support for the endowed department.The endowed Department of Aging Science and Medicine is supported by GAKKEN HOLDINGS CO., LTD. and Medical Care Service Inc.Source: §4 · p. 34
Competing interests and data availability
- The authors declare no competing interests; DNA methylation data came from public GEO-derived resources, while UK Biobank data require an approved application.UK Biobank data are not publicly available because of access restrictions.Source: §4 · p. 34
Code availability and consent for publication
- The complete study code is provided in the Supplementary Materials, and consent for publication is not applicable because no identifiable individual-level information is reported.Source: §4 · p. 34
Author contribution
- Qiang Yang conceived and supervised the study; Chunxu Zhang and Bo Li designed the method, developed the model, conducted experiments, analyzed results, and drafted the manuscript.Other authors contributed methodological suggestions, revisions, biological analysis and interpretation, expert aging-biology review, and all authors reviewed and approved the manuscript.Source: §4 · p. 34
Appendix A Details About Biological Analysis of Key Molecular Features · A.1 Selection of Key Omics Features via Age-Dependent Expert Sensitivity · A.2 Pathway–Gene Composition of Enriched Functional Clusters
The appendix describes an age-dependent expert-sensitivity procedure for ranking molecular features and provides gene-level compositions for enriched functional clusters. These analyses support inspection of feature contributions and protein mappings to biological processes.
A.1 Selection of Key Omics Features via Age-Dependent Expert Sensitivity
- An expert whose routing weight increases with age provides the aging-related reference representation for identifying molecular features associated with aging.Its age-dependent behavior serves as a data-driven basis for assessing feature contributions to aging-related model behavior.Source: §A.1 · pp. 34–35
- Each protein or methylation CpG site was independently varied across ten empirical quantile levels to measure changes in expert routing weight.All other features were held fixed during each perturbation.Source: §A.1 · p. 35
- Feature influence was quantified as the routing-weight difference between its highest and lowest quantile levels, and features were ranked by this score.Source: §A.1 · p. 35
A.2 Pathway–Gene Composition of Enriched Functional Clusters
- For the UKB-Center proteomic dataset, the appendix provides the full gene-level composition of all significantly enriched ontology clusters.This complements the pathway enrichment analysis of top-ranked proteins.Source: §A.2 · p. 35
- The 20 pathways identified in the main text are decomposed to list the constituent proteins contributing to each functional module.Source: §A.2 · p. 35
- The listed protein compositions enable direct inspection of how individual proteins map onto biologically coherent processes.Source: §A.2 · p. 35
A.3 Model-based Identification of Synergistic Protein Pairs · A.4 Model-based Discovery of Higher-Order Protein Interactions
The analysis ranked model-derived protein pairs by synergy and examined higher-order protein coordination using complementary analytical settings. A beam-search-style procedure expanded synergistic pairs into representative protein groups.
A.3 Model-based Identification of Synergistic Protein Pairs
- Candidate pairs exhaustively combined important proteins and were evaluated for their joint influence on estimated biological age in the global test population.The important proteins were identified in the previous section.Source: §A.3 · p. 35
- Pairwise synergy was quantified by comparing model outputs across four perturbation states: both proteins suppressed, either one retained, or both retained.Suppression set a protein’s values to zero across all samples while leaving other proteins unchanged.Source: §A.3 · p. 35
- The analysis focused on the top 10 synergistic protein pairs; positive scores indicate effects exceeding the sum of individual contributions, while negative scores suggest redundancy or antagonism.Pairs were ranked by their synergy scores.Source: §A.3 · p. 35
A.4 Model-based Discovery of Higher-Order Protein Interactions
- For higher-order analysis, candidate protein sets were constructed from model-identified important proteins to assess their collective effects.Source: §A.4 · p. 36
- Higher-order synergy was analyzed across four settings combining biological-age prediction or latent expert routing with full-population or young-subset data.Full-population analysis prioritized globally stable coordination; young subsets were intended to reveal early-stage or age-dependent signals potentially diluted overall.Source: §A.4 · p. 36
- A beam-search-style process expanded strongly synergistic seed pairs one protein at a time, retaining promising groups and yielding 16 representative protein groups across the four settings.Candidate groups were evaluated by their overall collective effect under the model at each expansion step.Source: §A.4 · p. 36
A.5 Biological Analysis on Methylation Data
Analysis of GEO DNA methylation features identified aging-related biological signals, suggesting TNFL captures meaningful molecular patterns across methylation and proteomic data.
A.5 Biological Analysis on Methylation Data
- The analysis selected the top 300 CpG sites by the magnitude of expert-routing-weight changes under systematic perturbations.These features were selected for downstream analysis as the most influential methylation features associated with expert routing behavior.Source: §A.5 · p. 36
- Methylation-derived signals mapped to approximately 245 genes enriched for cell adhesion, developmental, cell-cycle, MAPK, and immune functions, with blood-cell trait links and FOXO3-target enrichment.DisGeNET associations included neutrophil and basophil counts; FOXO3 has previously been implicated in longevity and aging-related regulation.Source: §A.5 · pp. 36–37, Figure A1 · p. 37
- All selected CpGs mapped successfully and were predominantly located in gene-associated regions and CpG islands.The authors describe this distribution across genomic elements as non-random.Source: §A.5 · p. 36
Appendix B Analysis of the Generative Component
Generative replay improves AgeMoE’s global predictive performance, with larger gains on datasets showing stronger cross-client distributional differences. It preserves information from earlier clients and augments local updates with pseudo-samples.
Appendix B Analysis of the Generative Component
- Generative replay preserves information from previously visited clients and augments local training with pseudo-samples, supporting improved global generalization during cross-client updates.The comparison removes the generative module while keeping all other training settings unchanged.Source: Appendix B · pp. 37–38
- Experiments cover UKB-Center, UKB-Imbalance, GEO-Methylation, and UKB-AgeSplit, whose six clients are partitioned into five-year age intervals to simulate stronger distributional differences.Age-based client partitions model settings where centers serve systematically different patient populations.Source: Appendix B · p. 38
- AgeMoE with the generative component improves global predictive performance across datasets, with larger gains on GEO-Methylation and age-partitioned UK Biobank, where client distributions differ more strongly.The global test comparison covers all clients; the generative model helps retain representative information from previously visited clients and maintain coverage of the overall data distribution.Source: Figure B2 · p. 38, Appendix B · p. 38
Appendix C Details on Robustness Metrics … C.3 Forgetting Rate
Appendix C defines three robustness metrics for evaluating how TNFL’s predictive performance varies across sequences of client interactions: client-level MAE range, cumulative MAE degradation, and forgetting rate.
Appendix C Details on Robustness Metrics
- The appendix formalizes three metrics to assess predictive-performance sensitivity to different client-interaction sequences over the trust network.The metrics are client-level MAE range, cumulative MAE degradation, and forgetting rate.Source: Appendix C · p. 39
C.1 Client-level MAE Range
- For each client, client-level MAE range measures the spread of local-test MAE values across all interaction orders.A smaller range indicates more stable performance across interaction sequences.Source: §C.1 · p. 39
- Boxplots of per-client MAE ranges compare the distribution of client-level performance variability among models.Each box represents the spread of client ranges across clients.Source: §C.1 · p. 39
C.2 Cumulative MAE Degradation
- Cumulative MAE degradation tracks global-test MAE across sequential client updates within each interaction order.The measure aggregates effects across clients rather than capturing only individual local behavior.Source: §C.2 · p. 39
- Lower cumulative degradation indicates sequential updates do not substantially increase error; boxplots compare degradation distributions across interaction sequences and models.Degradation is accumulated across the T update steps in each order.Source: §C.2 · p. 39
C.3 Forgetting Rate
- Forgetting rate compares a client’s MAE immediately after its update with its MAE under the final model in that propagation sequence.The comparison applies to the client appearing at position j in interaction order i.Source: §C.3 · pp. 39–40
- Positive forgetting rates indicate later performance deterioration, while negative values indicate improvement or knowledge retention.The metric is calculated only for the first half of clients in each sequence to focus on early-stage effects.Source: §C.3 · p. 40
- Boxplots of first-half clients’ forgetting rates show their distribution across sequences for comparing models’ client-level performance retention.The plotted rates are collected across sequences.Source: §C.3 · p. 40
Appendix D Details About Performance Under Simulated Measurement Variability
In a UKB-Center perturbation study, TNFL showed minimal predictive-performance decline under simulated inter- and intra-center measurement variability, with global mean MAE increasing from 2.33 to 2.40.
Appendix D Details About Performance Under Simulated Measurement Variability
- The perturbation study modeled center-shared client-level feature shifts and independent sample-level noise to represent inter- and intra-center measurement variability.The shifts represented systematic center biases, while sample noise represented sample-processing, measurement-precision, or local technical variability.Source: Appendix D · p. 40
- Perturbation magnitudes were set to client shifts of approximately 35% and sample noise of approximately 12% of the global feature standard deviation.These magnitudes were chosen to introduce controlled deviations representing plausible inter- and intra-center differences.Source: Appendix D · p. 40
- Global mean MAE increased by only 0.07, from 2.33 on original data to 2.40 on perturbed data, with performance evaluated on individual-client and global test sets.Results are summarized in Table D1.Source: Appendix D · p. 40
Appendix E Details About Performance Across Trust-Network Structures
Under trust-network-derived interaction sequences, TNFL showed predictive performance and robustness trends broadly consistent with those under random-permutation sequences. It retained its relative advantage over local training while remaining competitive with FedAvg.
Appendix E Details About Performance Across Trust-Network Structures
- Experiments on UKB-Center used random directed trust networks with sparsity from 0.1 to 0.5 and variable-length sequences covering all clients, including repeated visits when needed.The underlying sequential update mechanism and training protocol were unchanged; backbone compatibility experiments were not repeated, and UKB-Center was selected for its many clients and heterogeneous center data.Source: Appendix E · p. 41
- TNFL achieved similar predictive performance under trust-network-derived and random interaction sequences, outperforming local training relatively and remaining competitive with FedAvg.Performance patterns were consistent across independent local training, FedAvg, TNFL with random orders, and TNFL with trust-network-derived sequences.Source: Appendix E · p. 41, Figure E3 · p. 42
- Under trust-network-derived sequences, TNFL maintained low variability, limited cumulative degradation, and no observable increase in forgetting; median cumulative degradation remained below 0.5.Absolute cumulative-degradation magnitudes are not directly comparable with random-order results because trust-network-derived sequences can be longer due to repeated client visits.Source: Appendix E · p. 41, Figure E3 · p. 42