Beyond Extrapolation: Knowledge Utilization with Bidirectional Inference for Time Series Forecasting

Liu Chong, Yingjie Zhou, Hao Li, Pengyang Wang, Qingsong Wen, Ce Zhu

Keywords: Time-series forecasting, Bidirectional inference, Structural future prior

Abstract:

Time-series forecasting is critical in application areas such as energy, transportation, and public health.
Most existing forecasters, however, are designed primarily around unidirectional inference from \textbf{history} to \textbf{target}.
While this formulation has achieved strong performance in many practical scenarios, it focuses solely on the history–target link and leaves unused the structured information in how trajectories continue after the target, even though such post-target behaviour can provide a valuable inductive bias for forecasting.
In a typical time series, each training example naturally forms a chain of three segments: ``\textbf{history} (model input), \textbf{target} (ground-truth output), \textbf{post-target continuation}''.
In this work, we explicitly use the third segment as a source of auxiliary features and propose KUP-BI (Knowledge Utilization Paradigm with a Bidirectionally Inspired Auxiliary Stream), a simple non-parametric mechanism that distils continuation-style information from a train-only historical library and injects it into standard forecasting backbones.
For each training chain, we extract an equal-length history window and post-target continuation window, apply a simple ratio-style operator that encodes how the continuation changes relative to its history, and store the resulting transformation together with its history in the library.
Given a current input window, we extract similar historical segments from this library, aggregate their associated transformations, and apply the aggregated transformation to the current input to obtain a deterministic continuation-style auxiliary feature that summarises how similar histories tended to evolve in the training data.
The input and auxiliary streams are encoded separately and fused through a lightweight feature-level gating module.
This design does not introduce information beyond what is already contained in the training trajectories, but provides a structured inductive bias that helps backbones exploit typical continuation patterns rather than relying solely on parametric extrapolation.
Across six benchmarks and several state-of-the-art models, KUP-BI consistently improves forecasting performance with small additional overhead.

Primary Area: learning on time series and dynamical systems

Submission Number: 10160