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。

粗糙变压器：轻量级连续时间序列建模与路径特征

Rough Transformers: Lightweight Continuous-Time Sequence Modelling with  Path Signatures

Time-series data in real-world medical settings typically exhibit long-range
dependencies and are observed at non-uniform intervals. In such contexts,
traditional sequence-based recurrent models struggle. To overcome this,
researchers replace recurrent architectures with Neural ODE-based models to
model 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
moderate lengths and greater. To mitigate this, we introduce the Rough
Transformer, a variation of the Transformer model which operates on
continuous-time representations of input sequences and incurs significantly
reduced computational costs, critical for addressing long-range dependencies
common in medical contexts. In particular, we propose multi-view signature
attention, which uses path signatures to augment vanilla attention and to
capture both local and global dependencies in input data, while remaining
robust to changes in the sequence length and sampling frequency. We find that
Rough Transformers consistently outperform their vanilla attention counterparts
while obtaining the benefits of Neural ODE-based models using a fraction of the
computational time and memory resources on synthetic and real-world time-series
tasks.

在医学背景下，基于时间序列的数据通常具有长程依赖并且在非均匀时间间隔下进行观察。为了解决这个问题，研究者们用基于神经 ODE 的模型取代了传统的基于序列的循环模型，来对不规则采样的数据进行建模，并使用基于 Transformer 的架构解决长程依赖的问题。尽管这两种方法都取得了成功，但是对于中等长度的输入序列而言，它们都需要非常高的计算代价。为了缓解这个问题，我们引入了 Rough Transformer，这是 Transformer 模型的一种变体，它能够对连续时间表示的输入序列进行操作，并且具有显著减少的计算代价，这对于处理医疗背景下的长程依赖是至关重要的。具体而言，我们提出了多视角签名注意力，它利用路径签名来增强原始注意力，并在输入数据中捕捉局部和全局依赖关系，同时对序列长度和采样频率的变化保持稳健性。我们发现，Rough Transformers 在合成和真实的时间序列任务中，始终优于其原始注意力对照组，并且只需要部分计算时间和存储资源，就能够获得基于神经 ODE 模型的好处。