  Transformer architectures have shown promising results in time series
processing. However, despite recent advances in subquadratic attention
mechanisms or state-space models, processing very long sequences still imposes
significant computational requirements. Token merging, which involves replacing
multiple tokens with a single one calculated as their linear combination, has
shown to considerably improve the throughput of vision transformer
architectures while maintaining accuracy. In this work, we go beyond computer
vision and perform the first investigations of token merging in time series
analysis on both time series transformers and state-space models. To
effectively scale token merging to long sequences, we introduce local merging,
a domain-specific token merging algorithm that selectively combines tokens
within a local neighborhood, adjusting the computational complexity from linear
to quadratic based on the neighborhood size. Our comprehensive empirical
evaluation demonstrates that token merging offers substantial computational
benefits with minimal impact on accuracy across various models and datasets. On
the recently proposed Chronos foundation model, we achieve accelerations up to
5400% with only minor accuracy degradations.
