  Time-series data in real-world settings typically exhibit long-range
dependencies and are observed at non-uniform intervals. In these settings,
traditional sequence-based recurrent models struggle. To overcome this,
researchers often replace recurrent architectures with Neural ODE-based models
to account for irregularly sampled data and use Transformer-based architectures
to account for long-range dependencies. Despite the success of these two
approaches, both incur very high computational costs for input sequences of
even moderate length. To address this challenge, we introduce the Rough
Transformer, a variation of the Transformer model that operates on
continuous-time representations of input sequences and incurs significantly
lower computational costs. In particular, we propose \textit{multi-view
signature attention}, which uses path signatures to augment vanilla attention
and to capture both local and global (multi-scale) dependencies in the input
data, while remaining robust to changes in the sequence length and sampling
frequency and yielding improved spatial processing. We find that, on a variety
of time-series-related tasks, Rough Transformers consistently outperform their
vanilla attention counterparts while obtaining the representational benefits of
Neural ODE-based models, all at a fraction of the computational time and memory
resources.
