Related papers: Associative memory and dead neurons
Recurrent neural networks (RNNs) with random, but sufficiently strong and balanced coupling display a well known high-dimensional chaotic dynamics. Here, we investigate if externally applied inputs to these RNNs can stabilize globally…
Classical autoassociative memory models have been central to understanding emergent computations in recurrent neural circuits across diverse biological contexts. However, they typically neglect neuromodulatory agents that are known to…
A new approach to describing correlation properties of complex dynamic systems with long-range memory based on a concept of additive Markov chains (Phys. Rev. E 68, 061107 (2003)) is developed. An equation connecting a memory function of…
Exactly solvable neural network models with asymmetric weights are rare, and exact solutions are available only in some mean-field approaches. In this article we find exact analytical solutions of an asymmetric spin-glass-like model of…
We construct an exactly solvable circuit of interacting memristors and study its dynamics and fixed points. This simple circuit model interpolates between decoupled circuits of isolated memristors, and memristors in series, for which exact…
We study a neural network model in which both neurons and synaptic interactions evolve in time simultaneously. The time evolution of synaptic interactions is described by a Langevin equation including a Hebbian learning term, and a bias…
A fundamental problem in neuroscience is understanding how working memory -- the ability to store information at intermediate timescales, like 10s of seconds -- is implemented in realistic neuronal networks. The most likely candidate…
Neural dynamical systems with stable attractor structures, such as point attractors and continuous attractors, are hypothesized to underlie meaningful temporal behavior that requires working memory. However, working memory may not support…
We introduce a three-dimensional vectorial extension of the Hopfield associative-memory model in which each neuron is a unit vector on $S^2$ and synaptic couplings are $3\times 3$ blocks generated through a vectorial Hebbian rule. The…
While modern representation learning relies heavily on global error signals, decentralized algorithms driven by local interactions offer a fundamental distributed alternative. However, the macroscopic convergence properties of these…
The modern Hopfield network, proposed by Krotov and Hopfield, is a mathematical generalization of the Hopfield network, which is a basic model of associative memory that employs higher-order interactions. This study introduces an open…
Active systems, which are driven out of equilibrium by local non-conservative forces, can adopt unique behaviors and configurations. An important challenge in the design of novel materials which utilize such properties is to precisely…
Brains need to predict how the body reacts to motor commands. It is an open question how networks of spiking neurons can learn to reproduce the non-linear body dynamics caused by motor commands, using local, online and stable learning…
The aim of the present paper is to study the effects of Hebbian learning in random recurrent neural networks with biological connectivity, i.e. sparse connections and separate populations of excitatory and inhibitory neurons. We furthermore…
The underdamped, non-linear, generalized Langevin equation is widely used to model coarse-grained dynamics of soft and biological materials. By means of a projection operator formalism, we show under which approximations this equation can…
When learning to perform motor tasks in a simulated environment, neural networks must be allowed to explore their action space to discover new potentially viable solutions. However, in an online learning scenario with physical hardware,…
The time elapsed model describes the firing activity of an homogeneous assembly of neurons thanks to the distribution of times elapsed since the last discharge. It gives a mathematical description of the probability density of neurons…
Priming is the ability of the brain to more quickly activate a target concept in response to a related stimulus (prime). Experiments point to the existence of an overlap between the populations of the neurons coding for different stimuli.…
The Hopfield associative memory model stores random patterns in synaptic couplings according to Hebb's rule and retrieves them through gradient descent on an energy function. This conventional setting, where neurons are assumed to have…
The distinct timescales of synaptic plasticity and neural activity dynamics play an important role in the brain's learning and memory systems. Activity-dependent plasticity reshapes neural circuit architecture, determining spontaneous and…