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

This paper introduces F $^2$ STNet, a federated forecasting framework for graph-structured data that integrates spectral graph features, a lightweight state-space temporal encoder, and a fairness-aware aggregation mechanism to achieve accurate and equitable spatiotemporal predictions in decentralized, heterogeneous environments.

Original authors: Jiayi Zhang, Jinfeng Xu, Hewei Wang, Siyuan Cen, Haidong Huang, Yiyao Zhan, Zheyu Chen, Jinjiang You, Ai Jian, Edith C. H. Ngai

Published 2026-08-11

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Jiayi Zhang, Jinfeng Xu, Hewei Wang, Siyuan Cen, Haidong Huang, Yiyao Zhan, Zheyu Chen, Jinjiang You, Ai Jian, Edith C. H. Ngai

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to predict the future, but the clues are scattered across a giant, invisible web. Some clues are about where things are connected (like which subway stations are linked), and others are about when things happen (like the rush hour traffic). This is the world of "spatiotemporal forecasting," a fancy term for guessing how things move and change across space and time. It's the magic behind predicting traffic jams, air quality, or crowd flows. Usually, computers do this by gathering all the data into one giant brain. But what if that data is too private to share, or the computers holding it are too weak to handle a massive brain? That's where "Federated Learning" comes in. Think of it like a group project where students solve a problem together without ever showing their homework to each other; they just share their final answers to build a better group solution.

However, there's a catch. In a group project, if one student is struggling while another is a genius, the standard way of averaging their answers often leaves the struggling student behind. The "genius" answers dominate, and the group's overall solution might be great for the smart kids but terrible for the others. This paper tackles that exact problem: how to build a super-smart, shared prediction model that respects privacy, runs on weak computers, and makes sure everyone in the group gets a fair shot at a good result.

Enter F2STNet, a new framework designed to be the ultimate team player for graph-based predictions. The researchers built this system to handle three tricky challenges at once: understanding the shape of the data (the graph), remembering long-term patterns (the time), and treating every participant fairly.

First, let's look at how F2STNet "sees" the data. Imagine the graph (like a map of sensors) as a musical chord. Traditional methods try to listen to every single note individually, which is slow and messy. F2STNet, however, uses a "spectral" approach. It's like having a special pair of glasses that instantly breaks the chord down into its pure frequencies. This allows the model to understand the big picture of the connections without getting bogged down in the details. It's efficient, like knowing the key of a song rather than counting every beat.

Next, the model needs to remember what happened in the past to guess the future. Old methods used heavy, complex memory systems (like giant, slow-moving robots) to track time. F2STNet swaps this for a "lightweight state-space" layer. Think of this as a super-efficient, diagonal shortcut. Instead of walking every step of a long path, it takes a direct, linear slide. This keeps the model fast and light, perfect for devices that don't have supercomputers inside them.

But the real star of the show is the "Fairness-aware Federated Aggregation" (FFA). In a standard team effort, everyone's contribution is weighted by how much data they have. If one city has 1,000 sensors and another has 10, the big city's voice drowns out the small one. F2STNet changes the rules. It acts like a wise coach who notices when a team member is struggling. If a client (a city or sensor network) is making more mistakes than the average, the system gives their update more weight, not less. It uses a clever "reverse-annealing" schedule: at the start of training, it focuses on getting the basics right, but as the model gets smarter, it gradually shifts its focus to help the struggling members catch up. This ensures the final model works well for everyone, not just the data-rich giants.

The researchers tested F2STNet on three real-world datasets: traffic flow in California (PeMS04), subway flows in Hangzhou (HZMetro), and air quality across 184 Chinese cities (KnowAir). The results were promising. On the traffic and air quality datasets, F2STNet consistently beat the current top models (the "baselines") in accuracy, making smaller errors in its predictions. On the subway dataset, it achieved the lowest error rate for the average mistake (MAE).

Crucially, when they ran the experiment in a "federated" setting (where data stays local), F2STNet didn't just predict well; it was fair. On the California traffic data, it significantly improved the performance for the "worst-case" clients—the ones that usually get left behind in other systems. It also reduced the gap between the best and worst performers, proving that you can have a high-performing model that doesn't leave anyone behind.

The paper suggests that by combining these three ingredients—frequency-based graph understanding, a lightweight time-travel memory, and a fairness-first voting system—you can build a forecasting tool that is accurate, efficient, and equitable. While the authors note that their current fairness method uses a linear approach for stability and might need more complex tweaks for extreme situations, the results show that this balanced approach is a strong step forward for decentralized, privacy-safe prediction.

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

Problem Statement
Spatiotemporal prediction on graph-structured data is critical for applications such as traffic forecasting and environmental monitoring. However, existing approaches face two primary limitations in real-world deployment:

Data Privacy and Heterogeneity: Real-world data is often decentralized (e.g., distributed sensors) and heterogeneous across clients. Centralized training is infeasible due to privacy constraints, while standard Federated Learning (FL) methods struggle with statistical heterogeneity, leading to biased global models.
Model Efficiency and Fairness: Current state-of-the-art spatiotemporal models often rely on resource-heavy recurrent or attention-based modules. Furthermore, standard aggregation strategies like FedAvg prioritize data volume over client performance, causing unfair degradation for clients with difficult or underrepresented data distributions.

Methodology
The authors propose F2STNet, a federated forecasting framework designed to address these challenges through three core components:

Spectral-Temporal Architecture:
- Spectral Projection: Instead of relying solely on spatial message passing, F2STNet utilizes a truncated graph-Fourier basis derived from the normalized graph Laplacian. This allows the model to encode node-level graph-frequency contributions. A shared Multi-Layer Perceptron (MLP) projects these frequency vectors into embeddings, exposing the graph-frequency structure to the model.
- Lightweight Temporal Modeling: To avoid the computational cost of recurrent neural networks (RNNs) or heavy attention mechanisms, the framework employs a diagonal linear state-space layer. This module models long-range temporal dependencies with linear complexity relative to the sequence length, utilizing zero-order-hold discretization.
- Spatial Modeling: The model integrates graph convolution using an augmented adjacency matrix to capture spatial dependencies on the temporal embeddings.
Fairness-Aware Federated Aggregation (FFA):
- Unlike FedAvg, which weights updates strictly by local sample size, FFA dynamically adjusts client weights based on their predictive performance.
- Mechanism: Clients evaluate their models on a held-out local validation set. The aggregation weight for a client is adjusted based on the deviation of their validation loss from the average client loss. Clients with higher-than-average losses (indicating difficulty) receive increased weight relative to their data-size prior, while high-performing clients receive slightly less.
- Dynamic Scheduling: The influence of this fairness adjustment is controlled by a hyperparameter $\lambda_t$ , which follows a reverse-annealing schedule. Initially, $\lambda$ is low to prioritize global convergence; as training progresses, $\lambda$ increases to place greater emphasis on improving equity across heterogeneous clients.

Key Contributions

Unified Framework: The proposal of F2STNet, which integrates spectral encoding, linear state-space modeling, and fairness-aware aggregation into a single federated spatiotemporal framework.
Novel Aggregation Strategy: The design of FFA, a loss-based reweighting scheme that improves equity among heterogeneous participants without requiring demographic attributes.
Empirical Validation: Extensive experiments on three real-world datasets (PeMS04, HZMetro, and KnowAir) demonstrating the framework's efficacy.

Experimental Results

Centralized Performance: On all three datasets, F2STNet consistently outperforms state-of-the-art baselines (including STG-NCDE, PDFormer, STG-Mamba, and others) in terms of RMSE, MAE, and MAPE. Notably, it achieves the lowest MAE on the HZMetro dataset.
Federated Performance: In federated settings on PeMS04, F2STNet demonstrates superior performance compared to standard FL baselines (FedAvg, FedProx, MOON, etc.). Crucially, it improves worst-client performance and reduces client-dispersion metrics, indicating that the fairness-aware aggregation successfully mitigates performance degradation for disadvantaged clients.
Efficiency: The model achieves these results with a lower parameter count compared to many heavy attention-based baselines, as illustrated in the performance-efficiency trade-off analysis.

Significance
The paper claims that F2STNet provides a holistic solution for spatiotemporal forecasting in resource-constrained and privacy-sensitive environments. By combining spectral frequency analysis with efficient state-space modeling, it addresses the complexity of capturing both spatial and temporal dynamics. Simultaneously, the FFA mechanism addresses the critical issue of fairness in federated learning, ensuring that the global model performs reasonably well across all clients rather than favoring those with larger or cleaner datasets. This work highlights the necessity of integrating frequency encoding, lightweight temporal modeling, and fairness-aware aggregation to enable robust and scalable deployment of graph forecasting models.

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