Related papers: Evolutionary State-Space Model and Its Application…

Modeling the relationship between natural speech and a recorded electroencephalogram (EEG) helps us understand how the brain processes speech and has various applications in neuroscience and brain-computer interfaces. In this context, so…

Kalman filtering has proven to be effective for estimating brain activity using EEG recordings. In particular, the introduced post hoc standardization step of the algorithm, inspired by the sLORETA time-invariant method, reduces the depth…

Dynamic inference problems in autoregressive (AR/ARMA/ARIMA), exponential smoothing, and navigation are often formulated and solved using state-space models (SSM), which allow a range of statistical distributions to inform innovations and…

Electron spin resonance (ESR) spectroscopy in scanning tunneling microscopy (STM) has enabled probing the electronic structure of single magnetic atoms and molecules on surfaces with unprecedented energy resolution, as well as demonstrating…

Recent advances in deep learning have had a methodological and practical impact on brain-computer interface research. Among the various deep network architectures, convolutional neural networks have been well suited for…

Decoding speech from brain signals is a challenging research problem that holds significant importance for studying speech processing in the brain. Although breakthroughs have been made in reconstructing the mel spectrograms of audio…

We propose the *State Space Neural Operator* (SS-NO), a compact architecture for learning solution operators of time-dependent partial differential equations (PDEs). Our formulation extends structured state space models (SSMs) to joint…

Among the various architectures of Recurrent Neural Networks, Echo State Networks (ESNs) emerged due to their simplified and inexpensive training procedure. These networks are known to be sensitive to the setting of hyper-parameters, which…

Many real-world dynamical systems can be described as State-Space Models (SSMs). In this formulation, each observation is emitted by a latent state, which follows first-order Markovian dynamics. A Probabilistic Deep SSM (ProDSSM)…

The spectral content of macroscopic neural activity evolves throughout development, yet how this maturation relates to underlying brain network formation and dynamics remains unknown. Here, we assess the developmental maturation of…

This work explores the relationship between state space methods and Koopman operator-based methods for predicting the time-evolution of nonlinear dynamical systems. We demonstrate that extended dynamic mode decomposition with dictionary…

Electroencephalography (EEG) is a critical, non-invasive method to monitor electrical brain activity. EEGs can span anywhere from a couple seconds to multiple hours, posing a major hurdle for existing deep learning methods due to two major…

A major tenet in theoretical neuroscience is that cognitive and behavioral processes are ultimately implemented in terms of the neural system dynamics. Accordingly, a major aim for the analysis of neurophysiological measurements should lie…

While electroencephalogram (EEG) has been a crucial tool for monitoring the brain and diagnosing neurological disorders (e.g., epilepsy), learning meaningful representations from raw EEG signals remains challenging due to limited…

Mathematical models of cognition are often memoryless and ignore potential fluctuations of their parameters. However, human cognition is inherently dynamic. Thus, we propose to augment mechanistic cognitive models with a temporal dimension…

In the post-deep learning era, the Transformer architecture has demonstrated its powerful performance across pre-trained big models and various downstream tasks. However, the enormous computational demands of this architecture have deterred…

Selective state-space models (SSMs) are an emerging alternative to the Transformer, offering the unique advantage of parallel training and sequential inference. Although these models have shown promising performance on a variety of tasks,…

We present a method for incremental modeling and time-varying control of unknown nonlinear systems. The method combines elements of evolving intelligence, granular machine learning, and multi-variable control. We propose a State-Space…

Transformer models have achieved superior performance in various natural language processing tasks. However, the quadratic computational cost of the attention mechanism limits its practicality for long sequences. There are existing…

This paper presents a new filter for state-space models based on Bellman's dynamic-programming principle, allowing for nonlinearity, non-Gaussianity and degeneracy in the observation and/or state-transition equations. The resulting Bellman…