TRACE: Parameter-Efficient Time Series Forecasting via Transient Chaotic System

Time series forecasting plays a pivotal role in numerous real-world domains, ranging from climate prediction to financial engineering. Over the past decades, neural networks, as a data-driven approach, have dominated the field and have yielded significant performance. However, how these black-box architectures internalize temporal structures within latent representations remains a fundamental mystery. In this work, we observe that trained time-series forecasters propagate input perturbations with positive finite-time sensitivity, reminiscent of transient chaos. These observations suggest that the transient chaos emerging in trained forecasters can be explicitly used as a fixed, non-trainable transient chaotic system to process information. Motivated by this insight, we propose a TRAnsient Chaotic Evolution network (TRACE), which embeds temporal representations into the phase space of continuous-time chaotic oscillators and constrains their evolution through a causal coupling topology among time steps. In TRACE, the nonlinear temporal transformation is therefore performed by the fixed autonomous flow rather than by additional learnable layers, substantially reducing the number of trainable parameters. We provide rigorous geometric derivations that theoretically substantiate TRACE's effectiveness, and extensive empirical analyses further confirm that this framework naturally satisfies the geometric proposition. Furthermore, TRACE delivers competitive forecasting performance against current state-of-the-art models while providing physical interpretability. The code is available at https://anonymous.4open.science/r/TRACE-6776.