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.

在处理非均匀间隔的时间序列数据时，传统的循环模型表现不佳，研究人员通常会使用基于神经常微分方程的模型和基于 Transformer 的模型来解决长程依赖和不规则采样数据的问题。为了解决这一挑战，本文引入了 Rough Transformer，一种在连续时间表示中操作的 Transformer 模型，大大降低了计算成本。我们提出了 “多视图签名注意力”，使用路径签名增强了原始注意力机制，捕捉了输入数据的本地和全局依赖关系，并对序列长度和采样频率的变化保持鲁棒性，并获得了空间处理的改进效果。我们发现，Rough Transformers 在各种时间序列相关任务中始终优于传统的注意力机制，同时获得了神经常微分方程模型的表征优势，并且仅消耗计算时间和内存资源的一小部分。