Related papers: Encoding certainty in bump attractors
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…
Cortical networks can maintain memories for decades despite the short lifetime of synaptic strength. Can a neural network store long-lasting memories in unstable synapses? Here, we study the effects of random noise on the stability of…
Encoding models are used for predicting brain activity in response to sensory stimuli with the objective of elucidating how sensory information is represented in the brain. Encoding models typically comprise a nonlinear transformation of…
Recordings of increasingly large neural populations have revealed that the firing of individual neurons is highly coordinated. When viewed in the space of all possible patterns, the collective activity forms non-linear structures called…
A stochastic model of excitatory and inhibitory interactions which bears universality traits is introduced and studied. The endogenous component of noise, stemming from finite size corrections, drives robust inter-nodes correlations, that…
We analyze the effects of spatiotemporal noise on stationary pulse solutions (bumps) in neural field equations on planar domains. Neural fields are integrodifferential equations whose integral kernel describes the strength and polarity of…
While cognitive representations of an environment can last for days and even months, the synaptic architecture of the neuronal networks that underlie these representations constantly changes due to various forms of synaptic and structural…
We analyze a multilayer neural field model of spatial working memory, focusing on the impact of interlaminar connectivity, spatial heterogeneity, and velocity inputs. Models of spatial working memory typically employ networks that generate…
We provide an empirical study of the stability of recurrent neural networks trained to recognize regular languages. When a small amount of noise is introduced into the activation function, the neurons in the recurrent layer tend to saturate…
We identify stable regions in the residual stream of Transformers, where the model's output remains insensitive to small activation changes, but exhibits high sensitivity at region boundaries. These regions emerge during training and become…
What is the physiological basis of long-term memory? The prevailing view in neuroscience attributes changes in synaptic efficacy to memory acquisition. This view implies that stable memories correspond to stable connectivity patterns.…
Problems with artificial neural networks originate from their deterministic nature and inevitable prior learnings, resulting in inadequate adaptability against unpredictable, abrupt environmental change. Here we show that a stochastically…
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. We here derive an expression for the number of attractors in…
The activity of ensembles of simultaneously recorded neurons can be represented as a set of points in the space of firing rates. Even though the dimension of this space is equal to the ensemble size, neural activity can be effectively…
We propose a method, based on persistent homology, to uncover topological properties of a priori unknown covariates of neuron activity. Our input data consist of spike train measurements of a set of neurons of interest, a candidate list of…
Biological systems rely on robust internal information processing: Survival depends on highly reproducible dynamics of regulatory processes. Biological information processing elements, however, are intrinsically noisy (genetic switches,…
Neural field models are commonly used to describe wave propagation and bump attractors at a tissue level in the brain. Although motivated by biology, these models are phenomenological in nature. They are built on the assumption that the…
We study the stable attractors of a class of continuous dynamical systems that may be idealized as networks of Boolean elements, with the goal of determining which Boolean attractors, if any, are good approximations of the attractors of…
Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which \textit{unstable…
Throughout the literature on Neural Cellular Automata (NCAs), it is often taken for granted that the systems learn attractors. This is shown through evolving the system for many timesteps and noting visual similarity to the goal state.…