TS-Inverse: A Gradient Inversion Attack Tailored for Federated Time Series Forecasting Models

TL;DR

Federated time series forecasting (TSF) enables privacy-preserving collaborative learning but remains vulnerable to gradient inversion attacks. The authors first perform an empirical analysis showing existing GIAs struggle to reconstruct both observations and targets for TS data, then introduce TS-Inverse, a TS-specific gradient inversion framework that learns a gradient-to-quantile mapping via an auxiliary dataset and employs time-series–aware regularizations. TS-Inverse combines a gradient-inversion model with an L1 gradient-matching objective and periodicity, trend, and learned-quantile bounds regularizations, plus a one-shot target reconstruction for batch size one; this yields substantial reconstruction improvements (2x–10x lower sMAPE) over baselines. The work highlights tangible privacy risks in federated TSF and provides concrete methodological guidance for evaluating defenses, including the impact of architecture choices and TS-specific priors. Code is released to enable replication and further defense-oriented research.

Abstract

Federated learning (FL) for time series forecasting (TSF) enables clients with privacy-sensitive time series (TS) data to collaboratively learn accurate forecasting models, for example, in energy load prediction. Unfortunately, privacy risks in FL persist, as servers can potentially reconstruct clients' training data through gradient inversion attacks (GIA). Although GIA is demonstrated for image classification tasks, little is known about time series regression tasks. In this paper, we first conduct an extensive empirical study on inverting TS data across 4 TSF models and 4 datasets, identifying the unique challenges of reconstructing both observations and targets of TS data. We then propose TS-Inverse, a novel GIA that improves the inversion of TS data by (i) learning a gradient inversion model that outputs quantile predictions, (ii) a unique loss function that incorporates periodicity and trend regularization, and (iii) regularization according to the quantile predictions. Our evaluations demonstrate a remarkable performance of TS-Inverse, achieving at least a 2x-10x improvement in terms of the sMAPE metric over existing GIA methods on TS data. Code repository: https://github.com/Capsar/ts-inverse

Figures (11)

• Figure 1: Federated time series forecasting: a use case in energy demand forecasting with an honest-but-curious "watching" server. Each smart meter has a forecasting model and a sequence of energy data. The server distributes the global model parameters and retrieves the locally trained models.
• Figure 2: Example of univariate time series forecasting.
• Figure 3: Baseline reconstruction results with FCN, CNN, GRU-2-FCN, and TCN model architectures on the Electricity 370 dataset with seeds (10). In each graph, the blue and green lines are the ground truth observations and targets respectively. The orange and red lines are the respective reconstructed observations and targets.
• Figure 4: Key steps of TS-Inverse framework
• Figure 5: TS-Inverse reconstruction results with FCN, CNN, and TCN model architectures on a sample from each dataset.