Temporal-Aware Bidirectional Local Label Propagation for Semi-Supervised Time Series Forecasting Under Sparse Supervision

The rapid growth of time-series data collection has made large-scale observations readily available, yet labeled annotations remain inherently sparse due to practical and domain-specific constraints, such as costly, time-consuming, and expertise-intensive labeling processes. While semi-supervised learning (SSL) has shown promise in leveraging limited labeled data, its application to time-series forecasting remains underexplored due to the unique challenges of aligning sparse labels with complex temporal dependencies. In this work, we present bidirectional local label propagation (Bi-LLP), a scalable SSL method specifically designed for time series forecasting under extreme label sparsity. Bi-LLP employs a dual-branch transformer to model temporal dependencies in both forward and backward directions. The representations are then used to perform consistency-driven local label propagation (LP) that enforces agreement between the two temporal directions. To better capture temporal patterns, we incorporate a temporal proximity metric (TPM) and a temporal-refined attention mechanism, jointly preserving intrinsic temporal structures and enhancing the exploitation of unlabeled data. Extensive experiments conducted on broad benchmarks and a real-world industrial case confirm that Bi-LLP consistently outperforms state-of-the-art SSL methods, particularly under sparse labeling conditions.