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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 identification and modeling of time-varying systems is a fundamental challenge in signal processing and system identification. To address this challenge, we propose a class of time-varying state-space model (SSM) based neural networks…
Over the past few years, research on deep graph learning has shifted from static graphs to temporal graphs in response to real-world complex systems that exhibit dynamic behaviors. In practice, temporal graphs are formalized as an ordered…
A pervasive challenge in neuroscience is testing whether neuronal connectivity changes over time due to specific causes, such as stimuli, events, or clinical interventions. Recent hardware innovations and falling data storage costs enable…
To maximize future rewards in this ever-changing world, animals must be able to discover the temporal structure of stimuli and then anticipate or act correctly at the right time. How the animals perceive, maintain, and use time intervals…
State-space models effectively model multivariate time series by updating over time a representation of the system state from which predictions are made. The state representation is usually a vector without any explicit structure.…
Today's deep learning architectures are primarily based on perceptron models, which do not capture the oscillatory dynamics characteristic of biological neurons. Although oscillatory systems have recently gained attention for their closer…
Parameterized state space models in the form of recurrent networks are often used in machine learning to learn from data streams exhibiting temporal dependencies. To break the black box nature of such models it is important to understand…
State space models (SSMs) have shown remarkable empirical performance on many long sequence modeling tasks, but a theoretical understanding of these models is still lacking. In this work, we study the learning dynamics of linear SSMs to…
This paper introduces novel deep dynamical models designed to represent continuous-time sequences. Our approach employs a neural emission model to generate each data point in the time series through a non-linear transformation of a latent…
Deep state-space models (Deep SSMs) are becoming popular as effective approaches to model sequence data. They have also been shown to be capable of in-context learning, much like transformers. However, a complete picture of how SSMs might…
A diverse white matter network and finely tuned neuronal membrane properties allow the brain to transition seamlessly between cognitive states. However, it remains unclear how static structural connections guide the temporal progression of…
State space models (SSMs) have gained attention by showing potential to outperform Transformers. However, previous studies have not sufficiently addressed the mechanisms underlying their high performance owing to a lack of theoretical…
Recent works exploring deep learning application to dynamical systems modeling have demonstrated that embedding physical priors into neural networks can yield more effective, physically-realistic, and data-efficient models. However, in the…
Learning requires the traversal of inherently distinct cognitive states to produce behavioral adaptation. Yet, tools to explicitly measure these states with non-invasive imaging -- and to assess their dynamics during learning -- remain…
Recent advances at the intersection of control theory, neuroscience, and machine learning have revealed novel mechanisms by which dynamical systems perform computation. These advances encompass a wide range of conceptual, mathematical, and…
Variational inference has had great success in scaling approximate Bayesian inference to big data by exploiting mini-batch training. To date, however, this strategy has been most applicable to models of independent data. We propose an…
Modeling the time-series of high-dimensional, longitudinal data is important for predicting patient disease progression. However, existing neural network based approaches that learn representations of patient state, while very flexible, are…
We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…
This paper studies an input-driven one-state differential equation model initially developed for an experimentally demonstrated dynamic molecular switch that switches like synapses in the brain do. The linear-in-the-state and…