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Formal Logic Enabled Personalized Federated Learning through Property Inference
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Proposes FedSTL, a personalized federated learning framework that automatically mines signal temporal logic properties per client, uses them as loss regularizers, and clusters clients by property alignment.
Problem
Federated learning with heterogeneous clients struggles to give symbolic reasoning guarantees: client predictions miss device-specific temporal logic properties, leading to suboptimal performance in AIoT settings like traffic prediction.
Approach
Automatically infer STL properties from each client's local data via specification mining with robustness-based tight bounds, enforce them through a property loss and a teacher-student correction, and cluster clients by how well cluster models satisfy their properties, with bi-level (shared cluster layers plus private client heads) updates.
Key results
- RNN MSE reduced by up to 54% versus baseline with FedSTL-based property enhancement on the traffic task (abstract reports up to 54% accuracy improvement).
- Teacher-corrected predictions (FedSTL-T) reach 100% property satisfaction across RNN, GRU, LSTM, and Transformer backbones.
- FedSTL-S cluster model with Transformer achieves MSE .025 vs .061 for IFCA-S on the intra-task SUMO task.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add inferred client logic properties and property-based prediction correction | FedSTL with RNN · Highway traffic volume, 15 states | MSE: .107$\pm$.032 -> .076$\pm$.022 | Helped |
| add inferred client logic properties and property-based prediction correction | FedSTL with GRU · Highway traffic volume, 15 states | MSE: .134$\pm$.033 -> .118$\pm$.027 | Helped |
| add inferred client logic properties and property-based prediction correction | FedSTL with LSTM · Highway traffic volume, 15 states | MSE: .110$\pm$.035 -> .099$\pm$.026 | Helped |
| add inferred client logic properties and property-based prediction correction | FedSTL with Transformer · Highway traffic volume, 15 states | MSE: .061$\pm$.004 -> .287$\pm$.013 | Hurt |
| add inferred client logic properties and prediction correction | FedSTL with RNN · Highway traffic volume, 15 states | satisfaction rate: 80.04$\pm$1.00 -> \textbf{100.0$\pm$0.00} | Helped |
| add inferred client logic properties and prediction correction | FedSTL with GRU · Highway traffic volume, 15 states | satisfaction rate: 80.51$\pm$0.75 -> \textbf{100.0$\pm$0.00} | Helped |
| add inferred client logic properties and prediction correction | FedSTL with LSTM · Highway traffic volume, 15 states | satisfaction rate: 81.93$\pm$0.89 -> \textbf{100.0$\pm$0.00} | Helped |
| add inferred client logic properties and prediction correction | FedSTL with Transformer · Highway traffic volume, 15 states | satisfaction rate: 78.05$\pm$0.63 -> \textbf{100.0$\pm$0.00} | Helped |
Surprising findings
- Promoting satisfaction of logic properties also reduced prediction error, per the authors' observation.
- The Transformer FedSTL-T variant had higher MSE (.287) than other FedSTL variants despite 100% satisfaction.
Limitations
- Theoretical convexity and convergence analysis relies on strong assumptions that do not hold for deep networks, as the authors acknowledge.
- Evaluation limited to two tasks with a single property family in the main traffic experiment and simulated data for the second.
- Compares against FL baselines but does not evaluate against other neuro-symbolic or STL-based learning methods.
Experimental setup
Datasets: U.S. Traffic Volume Data Tabulations (FHWA, 2019, 15 states) SUMO simulated Nashville, TN road traffic and pollution data (100 clients)
Benchmarks: U.S. Traffic Volume Data Tabulations SUMO smart city multivariate simulation
Metrics: MSE property satisfaction rate (rho %)
Baselines: FedAvg FedProx FedRep Ditto IFCA
Builds on: FedAvg IFCA Ditto FedRep FedProx
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