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LR-XFL: Logical Reasoning-Based Explainable Federated Learning
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Proposes LR-XFL, a federated learning framework where clients send entropy-based logic rules and the server adaptively chooses AND/OR connectors, beam-searches rule combinations, and weights clients by rule contribution.
Problem
Federated learning models are hard to explain globally because the server cannot access raw client data, and naive logic-rule aggregation can create conflicts or reduce rule accuracy.
Approach
Clients generate local logic rules from an entropy-based logic network; the server selects AND or OR as the global connector using positive/negative co-occurrence matrices (diagonality and exclusivity), selects rules via beam search on server validation data, and weights clients by how many of their rules are selected.
Key results
- Outperforms FedAvg-Logic by 1.19% in model accuracy on average, 5.81% in rule accuracy, and 5.41% in rule fidelity.
- On CUB, LR-XFL reaches 89.49% model accuracy and 90.67% rule accuracy versus 88.64% and 74.89% for FedAvg-Logic.
- Ablating the adaptive connector on CUB (forcing OR) drops rule accuracy from 90.67% to 76.29%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use LR-XFL instead of FedAvg-Logic | Federated learning · Four benchmark datasets (average) | model accuracy: 1.19% | Helped |
| Use LR-XFL instead of FedAvg-Logic | Federated learning · Four benchmark datasets (average) | rule accuracy: 5.81% | Helped |
| Use LR-XFL instead of FedAvg-Logic | Federated learning · Four benchmark datasets (average) | rule fidelity: 5.41% | Helped |
| Use LR-XFL instead of DDT | Federated learning · Four benchmark datasets (average) | model accuracy: 3.58% | Helped |
| Use LR-XFL instead of DDT | Federated learning · Four benchmark datasets (average) | rule accuracy: 0.27% | Helped |
| Use OR rather than the automatically selected AND connector (ablation) | LR-XFL · CUB | model accuracy: 89.49% -> 87.96% | Hurt |
| Use OR rather than the automatically selected AND connector (ablation) | LR-XFL · CUB | rule accuracy: 90.67% -> 76.29% | Hurt |
| Use OR rather than the automatically selected AND connector (ablation) | LR-XFL · CUB | rule fidelity: 99.64% -> 98.83% | Hurt |
| Increase client noise level | LR-XFL, FedAvg-Logic, and DDT · CUB | model accuracy | Hurt |
| Increase client noise level | LR-XFL, FedAvg-Logic, and DDT · CUB | rule fidelity | No clear effect |
Surprising findings
- On MIMIC-II, LR-XFL has lower rule accuracy (65.15%) than FedAvg-Logic (68.27%) and DDT (67.80%).
- DDT achieves the best performance at 80% noise level, outperforming LR-XFL in that setting.
Limitations
- Connector selection depends on hyperparameter thresholds for diagonality and exclusivity (set to 0.9 and 0.8 by tuning).
- Rule accuracy is lower than baselines on MIMIC-II, and DDT is better at high noise (80%).
Experimental setup
Datasets: MNIST CUB V-Dem MIMIC-II
Benchmarks: MNIST (Even/Odd) CUB V-Dem MIMIC-II
Metrics: classification accuracy rule accuracy rule fidelity
Baselines: Centralised Learning Distributed Decision Tree (DDT) FedAvg-Logic
Builds on: entropy-based logic explanations of neural networks FedAvg beam search
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