F2STNet: Fair and Federated Spectral-Temporal Modeling for Graph Forecasting

F2 STNet is a federated spatiotemporal forecasting framework that combines spectral encoding, linear state-space temporal modeling, graph convolution, and a novel Fairness-aware Federated Aggregation (FFA) scheme. The paper proposes this model to address challenges in spatiotemporal prediction on graph-structured data, particularly in decentralized and heterogeneous data environments.

The framework consists of three core components: (1) a spectral projection module that decomposes graph signals using a truncated graph Fourier basis and embeds node-level frequency contributions with a shared MLP, (2) a lightweight diagonal state-space temporal encoder for efficient sequence modeling with linear complexity in sequence length, and (3) an adaptive fairness-aware aggregation mechanism in federated training that dynamically reweights client updates based on distributional loss differences.

The FFA scheme adjusts the FedAvg prior using client validation losses and an increasing fairness schedule. Specifically, it calculates a fairness-aware weighting coefficient for each client based on their relative loss deviation: qkt = ptk(1 + λt rkt), where ptk is the FedAvg prior, rkt is the relative loss deviation, and λt is a fairness hyperparameter controlled by a reverse-annealing scheduling strategy: λt = min(λmax, λinit + ηt).

Experiments were conducted on three real-world datasets: PeMS04 (traffic flow data from 307 sensors in California), HZMetro (metro station flow records from 80 Hangzhou metro stations), and KnowAir (air quality and weather data from 184 Chinese cities). The model uses a historical window of 12 time steps to predict the subsequent 12 steps, evaluated using RMSE, MAE, and MAPE.

Results show that F2 STNet consistently outperforms all baselines in RMSE, MAE, and MAPE on PeMS04 and KnowAir, and achieves the lowest MAE on HZMetro. On PeMS04, F2 STNet achieves RMSE of 29.203 ± 0.11, MAE of 18.028 ± 0.09, and MAPE of 11.801 ± 0.12. In federated experiments on PeMS04, F2 STNet achieves the best reported values under both moderate (αhet = 5) and high (αhet = 10) heterogeneity settings, with a composite utility–fairness gain (∆) of 14.166 relative to FedAvg, and improvements in worst-client and client-dispersion metrics (Max-RMSE of 30.40 and Std-RMSE of 0.75).

Ablation studies show that removing the spectral module, fairness-aware aggregator, or temporal encoder increases errors, with the temporal encoder removal causing the largest drop. The model has fewer than 1.2 million parameters, and the spectral features are precomputed offline, incurring no runtime overhead. The linear state-space encoder ensures per-node modeling with O(T) temporal complexity, compared to O(T2) attention cost in Transformer-based models.

The paper also includes sensitivity analysis showing stable performance under varying client counts K ∈ 5, 10, 15, 20, 25, 50, with K = 10 achieving the best trade-off between convergence speed, utility, and fairness. The method remains sensitive to noisy validation losses and outlier clients, and robust, history-aware weighting is identified as an important direction for future work.

Improvements to AI systems:

1. Add a spectral projection module that decomposes input graph signals into a truncated graph Fourier basis, then embeds node-level frequency contributions via a shared MLP. This enables the system to capture global graph structure and multi-scale spatial patterns that are otherwise missed by purely spatial or temporal models.

2. Replace attention-based temporal encoders with a diagonal state-space model (SSM) that processes sequences with linear O(T) complexity. This reduces computational cost from O(T2) to O(T) for long sequences, allowing the system to handle much longer historical windows or higher-frequency data without memory or latency blowups.

3. Implement a fairness-aware federated aggregation (FFA) scheme that dynamically reweights client updates based on relative validation loss deviations, using the formula qkt = pkt(1 + λt rkt), with λt controlled by reverse annealing (λt = min(λ max, λ init + ηt)). This improves worst-client performance and reduces client dispersion in heterogeneous federated settings, making the system more equitable across data silos.

4. Add an offline precomputation step for spectral features so that graph Fourier basis decomposition is done once before training, incurring zero runtime overhead. This allows the system to leverage rich spectral information without slowing down inference or training iterations.

5. Introduce a composite utility–fairness metric (∆) to guide model selection during federated training, balancing overall accuracy with per-client fairness. This enables the system to automatically choose aggregation hyperparameters that optimize both global performance and equitable outcomes.

What the improved AI system can do:

• Predict spatiotemporal signals (e.g., traffic flow, metro ridership, air quality) across a network of sensors or stations with higher accuracy (lower RMSE, MAE, MAPE) than existing baselines, especially in decentralized environments where data is distributed across clients with different distributions.

• Scale to long sequences (e.g., 100+ time steps) efficiently, making it suitable for real-time forecasting on edge devices or large-scale sensor networks with limited compute.

• Maintain high performance even when client data is highly heterogeneous (e.g., different traffic patterns across cities), by dynamically adjusting aggregation weights to protect underperforming clients and reduce variance in model quality.

• Deploy in federated learning settings where privacy is critical, achieving better worst-case client accuracy and lower performance disparity across participants, while still converging quickly (e.g., optimal with K=10 clients).

• Operate with a small memory footprint (under 1.2 million parameters) and no added inference cost from spectral preprocessing, making it viable for embedded or resource-constrained deployments.

• Adapt to changing data distributions over time through the fairness schedule that gradually increases emphasis on loss deviations, allowing the system to become more fairness-aware as training progresses without destabilizing early convergence.

Spatiotemporal prediction on graph-structured data is central to traffic forecasting and environmental monitoring, yet decentralized and heterogeneous data complicate both sequence modeling and collaborative training. We propose F squared STNet, a federated forecasting framework that combines truncated graph-Fourier features, a lightweight diagonal state-space temporal encoder, graph convolution, and Fairness-aware Federated Aggregation (FFA). The spectral branch exposes graph-frequency structure, while the state-space layer models long temporal dependencies with linear complexity in the sequence length. FFA adjusts the FedAvg prior using client validation losses and an increasing fairness schedule. Experiments on PeMS04, HZMetro, and KnowAir show favorable forecasting accuracy relative to the evaluated baselines; federated experiments on PeMS04 additionally improve worst-client and client-dispersion metrics.