Title: Harnessing Untrained Dynamics: A Reservoir Computing Approach to State-Space Models
Primary area: learning on time series and dynamical systems
Keywords: echo state networks, reservoir computing, recurrent neural networks

Abstract: We introduce the Reservoir State Space Model (RSSM), a novel neural architecture that integrates the structured dynamics of State Space Models (SSMs) with the efficiency of reservoir computing to address long-term dependencies in sequence modeling. Leveraging the linear structure of SSMs, RSSMs implement efficient convolutional operations that maintain a latent internal state, akin to Recurrent Neural Networks (RNNs), while enabling fast and parallelizable computation. We conduct a stability analysis of the underlying SSMs to extend the memory capacity of the model, ensuring rich and expressive hidden representations.
A key innovation of RSSM is its use of untrained, structured convolutional dynamics as a fixed reservoir, with learning confined to a lightweight feed-forward readout layer. This design drastically reduces training complexity and computational overhead, making RSSMs well-suited for low-resource or real-time applications.
Empirical evaluations on standard sequence modeling benchmarks demonstrate that RSSMs achieve competitive accuracy while offering significant efficiency gains compared to traditional trainable architectures. 
Our results establish RSSMs as a new class of sequence models that combines the strengths of structured, fixed dynamics with the flexibility of learned representations, offering a compelling trade-off between performance and efficiency.