StretchTime: Adaptive Time Series Forecasting via Symplectic Attention

Transformer architectures have established strong baselines in time series forecasting, yet they typically rely on positional encodings that assume uniform, index-based temporal progression. However, real-world systems, from shifting financial cycles to elastic biological rhythms, frequently exhibit ``time-warped'' dynamics where the effective flow of time decouples from the sampling index. In this work, we first formalize this misalignment and prove that rotary position embedding (RoPE) is mathematically incapable of representing non-affine temporal warping. To address this, we propose Symplectic Positional Embeddings (SyPE), a learnable encoding framework derived from Hamiltonian mechanics. SyPE strictly generalizes RoPE by extending the rotation group $\mathrm{SO}(2)$ to the symplectic group $\mathrm{Sp}(2,\mathbb{R})$, modulated by a novel input-dependent adaptive warp module. By allowing the attention mechanism to adaptively dilate or contract temporal coordinates end-to-end, our approach captures locally varying periodicities without requiring pre-defined warping functions. We implement this mechanism in StretchTime, a multivariate forecasting architecture that achieves state-of-the-art performance on standard benchmarks, demonstrating superior robustness on datasets exhibiting non-stationary temporal dynamics.

Predicting the future from historical data is a critical task across many domains, from forecasting financial markets to monitoring climate change. While modern artificial intelligence models are highly effective at making these predictions, they typically rely on a rigid internal clock, assuming that time always progresses at a perfectly steady, uniform rate. However, real-world events are rarely so uniform; natural and human cycles often speed up or slow down, creating "time-warped" patterns. In this paper, we demonstrate that standard AI models mathematically struggle to adapt to these shifting rhythms. To solve this, we introduce StretchTime, a new forecasting model equipped with a flexible, adaptive clock. By allowing the system to dynamically stretch or compress its perception of time to match the underlying data, it can accurately track non-uniform real-world patterns. Our approach significantly improves prediction accuracy across various complex domains, such as traffic and solar energy forecasting, while requiring far less computing power than existing models.