Related papers: Encoding certainty in bump attractors
We consider dynamical behavior of non-autonomous wave-type evolutionary equations with nonlinear damping, critical nonlinearity, and time-dependent external forcing which is translation bounded but not translation compact (i.e., external…
Neural coding is a key problem in neuroscience, which can promote people's understanding of the mechanism that brain processes information. Among the classical theories of neural coding, the population rate coding has been studied widely in…
Anatomical studies demonstrate that brain reformats input information to generate reliable responses for performing computations. However, it remains unclear how neural circuits encode complex spatio-temporal patterns. We show that neural…
We propose a network of oscillators to retrieve given patterns in which the oscillators keep a fixed phase relationship with one another. In this description, the phase and the amplitude of the oscillators can be regarded as the timing and…
It has been proposed that neural noise in the cortex arises from chaotic dynamics in the balanced state: in this model of cortical dynamics, the excitatory and inhibitory inputs to each neuron approximately cancel, and activity is driven by…
This study reports an unintuitive finding that positional encoding enhances learning of recurrent neural networks (RNNs). Positional encoding is a high-dimensional representation of time indices on input data. Most famously, positional…
The behavior of the network and its stability are governed by both dynamics of individual nodes as well as their topological interconnections. Attention mechanism as an integral part of neural network models was initially designed for…
In statistical mechanics, the Potts model is a model for interacting spins with more than two discrete states. Neural networks which exhibit features of learning and associative memory can also be modeled by a system of Potts spins. A…
Neuromorphic chips embody computational principles operating in the nervous system, into microelectronic devices. In this domain it is important to identify computational primitives that theory and experiments suggest as generic and…
Randomly connected networks of excitatory and inhibitory spiking neurons provide a parsimonious model of neural variability, but are notoriously unreliable for performing computations. We show that this difficulty is overcome by…
We study a model of spiking neurons, with recurrent connections that result from learning a set of spatio-temporal patterns with a spike-timing dependent plasticity rule and a global inhibition. We investigate the ability of the network to…
A neural correlate of parametric working memory is a stimulus specific rise in neuron firing rate that persists long after the stimulus is removed. Network models with local excitation and broad inhibition support persistent neural…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
In certain situations, neural networks are trained upon data that obey underlying symmetries. However, the predictions do not respect the symmetries exactly unless embedded in the network structure. In this work, we introduce architectures…
The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We…
Attractor models are simplified models used to describe the dynamics of firing rate profiles of a pool of neurons. The firing rate profile, or the neuronal activity, is thought to carry information. Continuous attractor neural networks…
Hippocampal place and time cells encode spatial and temporal aspects of experience. Both have the same neural substrate, but have been modeled as having different functions and mechanistic origins, place cells as continuous attractors, and…
Hopfield attractor networks are robust distributed models of human memory, but lack a general mechanism for effecting state-dependent attractor transitions in response to input. We propose construction rules such that an attractor network…
We study nonlinear dynamics in a system of two coupled oscillators, describing the motion of two interacting microbubble contrast agents. In the case of identical bubbles, the corresponding symmetry of the governing system of equations…
We continue the work of a series of previous studies of a mathematical model that describes the mean-field limit behavior of a homogeneous network of excitatory point spiking neurons. Contrary to other models, here noise is intrinsic to the…