Continuous Spatiotemporal Transformers
This work addresses a fundamental limitation in machine learning for continuous systems, offering a novel solution with potential applications in neuroscience and other domains.
The authors tackled the problem of modeling continuous spatiotemporal dynamical systems by introducing the Continuous Spatiotemporal Transformer (CST), which guarantees smooth outputs through Sobolev space optimization, achieving superior performance in tasks like learning brain dynamics from calcium imaging data.
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.