2,593 research outputs found
Memristors for the Curious Outsiders
We present both an overview and a perspective of recent experimental advances
and proposed new approaches to performing computation using memristors. A
memristor is a 2-terminal passive component with a dynamic resistance depending
on an internal parameter. We provide an brief historical introduction, as well
as an overview over the physical mechanism that lead to memristive behavior.
This review is meant to guide nonpractitioners in the field of memristive
circuits and their connection to machine learning and neural computation.Comment: Perpective paper for MDPI Technologies; 43 page
The Neural Particle Filter
The robust estimation of dynamically changing features, such as the position
of prey, is one of the hallmarks of perception. On an abstract, algorithmic
level, nonlinear Bayesian filtering, i.e. the estimation of temporally changing
signals based on the history of observations, provides a mathematical framework
for dynamic perception in real time. Since the general, nonlinear filtering
problem is analytically intractable, particle filters are considered among the
most powerful approaches to approximating the solution numerically. Yet, these
algorithms prevalently rely on importance weights, and thus it remains an
unresolved question how the brain could implement such an inference strategy
with a neuronal population. Here, we propose the Neural Particle Filter (NPF),
a weight-less particle filter that can be interpreted as the neuronal dynamics
of a recurrently connected neural network that receives feed-forward input from
sensory neurons and represents the posterior probability distribution in terms
of samples. Specifically, this algorithm bridges the gap between the
computational task of online state estimation and an implementation that allows
networks of neurons in the brain to perform nonlinear Bayesian filtering. The
model captures not only the properties of temporal and multisensory integration
according to Bayesian statistics, but also allows online learning with a
maximum likelihood approach. With an example from multisensory integration, we
demonstrate that the numerical performance of the model is adequate to account
for both filtering and identification problems. Due to the weightless approach,
our algorithm alleviates the 'curse of dimensionality' and thus outperforms
conventional, weighted particle filters in higher dimensions for a limited
number of particles
Statistical Physics and Representations in Real and Artificial Neural Networks
This document presents the material of two lectures on statistical physics
and neural representations, delivered by one of us (R.M.) at the Fundamental
Problems in Statistical Physics XIV summer school in July 2017. In a first
part, we consider the neural representations of space (maps) in the
hippocampus. We introduce an extension of the Hopfield model, able to store
multiple spatial maps as continuous, finite-dimensional attractors. The phase
diagram and dynamical properties of the model are analyzed. We then show how
spatial representations can be dynamically decoded using an effective Ising
model capturing the correlation structure in the neural data, and compare
applications to data obtained from hippocampal multi-electrode recordings and
by (sub)sampling our attractor model. In a second part, we focus on the problem
of learning data representations in machine learning, in particular with
artificial neural networks. We start by introducing data representations
through some illustrations. We then analyze two important algorithms, Principal
Component Analysis and Restricted Boltzmann Machines, with tools from
statistical physics
Isochronal synchrony and bidirectional communication with delay-coupled nonlinear oscillators
We propose a basic mechanism for isochronal synchrony and communication with
mutually delay-coupled chaotic systems. We show that two Ikeda ring oscillators
(IROs), mutually coupled with a propagation delay, synchronize isochronally
when both are symmetrically driven by a third Ikeda oscillator. This
synchronous operation, unstable in the two delay-coupled oscillators alone,
facilitates simultaneous, bidirectional communication of messages with chaotic
carrier waveforms. This approach to combine both bidirectional and
unidirectional coupling represents an application of generalized
synchronization using a mediating drive signal for a spatially distributed and
internally synchronized multi-component system
Oscillatory dynamics with applications to cognitive tasks
Oscillations are ubiquitous in the brain and robustly correlate with distinct cognitive tasks. A specific type of oscillatory signals allows robust switching between states in networks involved in memorizing tasks. In particular, slow oscillations lead to an activation of the neuronal populations whereas oscillations in the beta range are effective in clearing the memory states. In this master thesis, previous works are revisited in order to provide a detailed analysis of the mechanisms underlying the states switching and their dependence on the network parameters. The model studied is a macroscopic description of the network recently derived due to mean-field theory advances. The role of spiking synchrony in the switching off of the active states is identified by means of bifurcation analysis and the study of the fixed points under the stroboscopic map. Finally, we propose an application of the effect of oscillations in a context of working memory
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