Related papers: L2RU: a Structured State Space Model with prescrib…
A proper parametrization of state transition matrices of linear state-space models (SSMs) followed by standard nonlinearities enables them to efficiently learn representations from sequential data, establishing the state-of-the-art on a…
Accurate modeling of nonlinear systems is essential for reliable control, yet conventional identification methods often struggle to capture latent dynamics while maintaining stability. We propose a \textit{stable-by-design LPV neural…
State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex time series…
Linear recurrent networks (LRNNs) and linear state space models (SSMs) promise computational and memory efficiency on long-sequence modeling tasks, yet their diagonal state transitions limit expressivity. Dense and nonlinear architectures…
Liquid State Machine (LSM) is a brain-inspired architecture used for solving problems like speech recognition and time series prediction. LSM comprises of a randomly connected recurrent network of spiking neurons. This network propagates…
State Space Models (SSMs) have emerged as powerful components for sequence modeling, enabling efficient handling of long-range dependencies via linear recurrence and convolutional computation. However, their effectiveness depends heavily on…
State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the…
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…
State-space models (SSMs) have recently attention as an efficient alternative to computationally expensive attention-based models for sequence modeling. They rely on linear recurrences to integrate information over time, enabling fast…
Linear time-periodic (LTP) dynamical systems frequently appear in the modeling of phenomena related to fluid dynamics, electronic circuits, and structural mechanics via linearization centered around known periodic orbits of nonlinear…
We consider linear time invariant systems with exogenous stochastic disturbances, and in feedback with structured stochastic uncertainties. This setting encompasses linear systems with both additive and multiplicative noise. Our concern is…
Linear recurrent neural networks, such as State Space Models (SSMs) and Linear Recurrent Units (LRUs), have recently shown state-of-the-art performance on long sequence modelling benchmarks. Despite their success, their empirical…
Deep state space models (SSMs) are an actively researched model class for temporal models developed in the deep learning community which have a close connection to classic SSMs. The use of deep SSMs as a black-box identification model can…
State-space models (SSMs) that utilize linear, time-invariant (LTI) systems are known for their effectiveness in learning long sequences. To achieve state-of-the-art performance, an SSM often needs a specifically designed initialization,…
Structured State Space Models (SSMs), which are at the heart of the recently popular Mamba architecture, are powerful tools for sequence modeling. However, their theoretical foundation relies on a complex, multi-stage process of…
Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs)…
Modelling long-term dependencies is a challenge for recurrent neural networks. This is primarily due to the fact that gradients vanish during training, as the sequence length increases. Gradients can be attenuated by transition operators…
This paper presents a system identification framework -- inspired by multi-task learning -- to estimate the dynamics of a given number of linear time-invariant (LTI) systems jointly by leveraging structural similarities across the systems.…
State space models (SSMs) leverage linear, time-invariant (LTI) systems to effectively learn sequences with long-range dependencies. By analyzing the transfer functions of LTI systems, we find that SSMs exhibit an implicit bias toward…
Linear time-invariant state space models (SSM) are a classical model from engineering and statistics, that have recently been shown to be very promising in machine learning through the Structured State Space sequence model (S4). A core…