Structured state-space models are deep Wiener models

The goal of this paper is to provide a system identification-friendly introduction to the Structured State-space Models (SSMs). These models have become recently popular in the machine learning community since, owing to their parallelizability, they can be efficiently and scalably trained to tackle extremely-long sequence classification and regression problems. Interestingly, SSMs appear as an effective way to learn deep Wiener models, which allows to reframe SSMs as an extension of a model class commonly used in system identification. In order to stimulate a fruitful exchange of ideas between the machine learning and system identification communities, we deem it useful to summarize the recent contributions on the topic in a structured and accessible form. At last, we highlight future research directions for which this community could provide impactful contributions.