RAP: Reconstruction-Augmented Predictors for Robust Time-series Forecasting

Long-term time-series forecasting (LTSF) supports applications in energy, traffic, and healthcare, yet state-of-the-art models remain brittle when inputs are corrupted by sensor or preprocessing noise. To resolve this problem, we introduce a reconstruction-augmented predictor (RAP) that improves robustness without corrupting or filtering training inputs by coupling the standard forecasting loss with a self-reconstruction objective on the history window. A single encoder feeds two linear heads—reconstruction and prediction—so the shared representation is explicitly regularized to preserve fine-grained, multi-scale structure. For small input noise, we relate the predictor’s Jacobian energy to noisy forecasting risk and bound the residual Jacobian of a fitted full-sequence map under explicit distributional and curvature assumptions. Controlled ablations measure the effect of reconstruction on the fitted predictor. Across representative LTSF benchmarks in high-dimensional datasets, RAP remains competitive with strong baselines in clean forecasting and degrades more gracefully under synthetic corruptions, and its advantage grows with the length of the observed context. Our measurement confirms that the reconstruction term lowers the predictor's Jacobian energy, and controlled comparisons against Gaussian-noise training, low-pass filtering and an explicit Jacobian penalty on the same backbone isolate the effect of the objective.