Abstract
Modeling spatiotemporal dynamical systems is a fundamental challenge in machine learning. Transformer models have been very successful in NLP and computer vision where they provide interpretable representations of data. However, a limitation of transformers in modeling continuous dynamical systems is that they are fundamentally discrete time and space models and thus have no guarantees regarding continuous sampling. To address this challenge, we present the Continuous Spatiotemporal Transformer (CST), a new transformer architecture that is designed for the modeling of continuous systems. This new framework guarantees a continuous and smooth output via optimization in Sobolev space. We benchmark CST against traditional transformers as well as other spatiotemporal dynamics modeling methods and achieve superior performance in a number of tasks on synthetic and real systems, including learning brain dynamics from calcium imaging data.
Abstract (translated)
建模时间空间动态系统是机器学习中的 fundamental 挑战。Transformer 模型在自然语言处理和计算机视觉中非常成功,因为它们提供了可解释的数据表示。然而,Transformer 在建模连续动态系统方面的一个限制是,它们本质上是离散时间和空间模型,因此没有关于连续采样的保证。为了解决这个挑战,我们提出了 Continuous Spatiotemporal Transformer (CST),它是一种专门用于建模连续系统的Transformer 架构。这个新框架通过在欧几里得范数空间中的优化来保证连续和平滑的输出。我们与其他时间空间动态建模方法进行了基准比较,并在模拟和真实系统上的许多任务中取得了更好的表现,包括从钙成像数据学习大脑动态。
URL
https://arxiv.org/abs/2301.13338