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We propose a biologically inspired model of spiking neurons based on the dynamics of a damped, driven pendulum. Unlike traditional models such as the Leaky Integrate-and-Fire (LIF) neurons, the pendulum neuron incorporates second-order,…
An intriguing interpretation of the time-evolution of dynamical systems is to view it as a computation that transforms an initial state to a final one. This paradigm has been explored in discrete systems such as cellular automata models,…
Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…
Objective. Precise control of neural systems is essential to experimental investigations of how the brain controls behavior and holds the potential for therapeutic manipulations to correct aberrant network states. Model predictive control,…
Processing long temporal sequences is a key challenge in deep learning. In recent years, Transformers have become state-of-the-art for this task, but suffer from excessive memory requirements due to the need to explicitly store the…
The highly irregular spiking activity of cortical neurons and behavioral variability suggest that the brain could operate in a fundamentally probabilistic way. Mimicking how the brain implements and learns probabilistic computation could be…
We present an account of neuroplasticity with respect to cell-internal processing pathways in relation to membrane and synaptic plasticity. We think traditional synapse-centric, weight-based models of memorization are not sufficient or…
Molecular dynamics simulations are an important tool for describing the evolution of a chemical system with time. However, these simulations are inherently held back either by the prohibitive cost of accurate electronic structure theory…
We propose a scalable neuromorphic architecture based on spiking dynamics emerging from the autonomous time-continuous evolution of clockless (asynchronous) digital circuits. Implemented on commercially available field-programmable gate…
We propose data-driven nonlinear smoother (DNS) to estimate a hidden state sequence of a complex dynamical process from a noisy, linear measurement sequence. The dynamical process is model-free, that is, we do not have any knowledge of the…
Continuous time recurrent neural networks (CTRNN) are systems of coupled ordinary differential equations that are simple enough to be insightful for describing learning and computation, from both biological and machine learning viewpoints.…
Neural mass models are used to simulate cortical dynamics and to explain the electrical and magnetic fields measured using electro- and magnetoencephalography. Simulations evince a complex phase-space structure for these kinds of models;…
We investigate discrete-time conewise linear systems (CLS) for which all the solutions exhibit a finite number of switches. By switches, we mean transitions of a solution from one cone to another. Our interest in this class of CLS comes…
The time evolution of an exactly solvable layered feedforward neural network with three-state neurons and optimizing the mutual information is studied for arbitrary synaptic noise (temperature). Detailed stationary temperature-capacity and…
We propose a new model based on the Ising model with the aim to study synaptic plasticity phenomena in neural networks. It is today well established in biology that the synapses or connections between certain types of neurons are…
In this review, we describe the singular success of attractor neural network models in describing how the brain maintains persistent activity states for working memory, error-corrects, and integrates noisy cues. We consider the mechanisms…
Can a scientific simulation system be physically consistent, interpretable by design, and scalable across regimes--all at once? Despite decades of progress, this trifecta remains elusive. Classical methods like Kinetic Monte Carlo ensure…
Thermodynamic-driven filament formation in redox-based resistive memory and the impact of thermal fluctuations on switching probability of emerging magnetic switches are probabilistic phenomena in nature, and thus, processes of binary…
Spatiotemporal flows of neural activity, such as traveling waves, have been observed throughout the brain since the earliest recordings; yet there is still little consensus on their functional role. Recent experiments and models have linked…
Neuro-inspired computing architectures are one of the leading candidates to solve complex, large-scale associative learning problems. The two key building blocks for neuromorphic computing are the synapse and the neuron, which form the…