DyWPE: Signal-Aware Dynamic Wavelet Positional Encoding for Time Series Transformers

Existing positional encoding methods in transformers are fundamentally signal-agnostic, deriving positional information solely from sequence indices while ignoring the underlying signal characteristics. This limitation is particularly problematic for time series analysis, where signals exhibit complex, non-stationary dynamics across multiple temporal scales. We introduce Dynamic Wavelet Positional Encoding (DyWPE), a novel signal-aware framework that generates positional embeddings directly from input time series using the Discrete Wavelet Transform (DWT). Comprehensive experiments on ten diverse time series datasets demonstrate that DyWPE consistently outperforms state-of-the-art positional encoding methods, with particularly significant improvements on longer sequences and complex biomedical signals.