Related papers: Dynamical stability for dense patterns in discrete…
Recent empirical studies have identified fixed point iteration phenomena in deep neural networks, where the hidden state tends to stabilize after several layers, showing minimal change in subsequent layers. This observation has spurred the…
We study the stationary states of networks consisting of weakly coupled bistable units. We prove the existence of a high multiplicity of stable steady states in networks with very general inter-unit dynamics. We present a method for…
Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of…
Recent studies point to the potential storage of a large number of patterns in the celebrated Hopfield associative memory model, well beyond the limits obtained previously. We investigate the properties of new fixed points to discover that…
The dynamics of a multiplex heterogeneous network of oscillators is studied. Two types of similar models based on the Hodgkin-Huxley formalism are used as the basic elements of the networks. The first type model demonstrates bursting…
Learning a task induces connectivity changes in neural circuits, thereby changing their dynamics. To elucidate task related neural dynamics we study trained Recurrent Neural Networks. We develop a Mean Field Theory for Reservoir Computing…
This paper deals with the global stability of time-delayed dynamical networks. We show that for a time-delayed dynamical network with non-distributed delays the network and the corresponding non-delayed network are both either globally…
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…
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…
Information coding by precise timing of spikes can be faster and more energy-efficient than traditional rate coding. However, spike-timing codes are often brittle, which has limited their use in theoretical neuroscience and computing…
Many natural and man-made network systems need to maintain certain patterns, such as working at equilibria or limit cycles, to function properly. Thus, the ability to stabilize such patterns is crucial. Most of the existing studies on…
Uncertainty estimation for unlabeled data is crucial to active learning. With a deep neural network employed as the backbone model, the data selection process is highly challenging due to the potential over-confidence of the model…
Stochastic neural networks are a prototypical computational device able to build a probabilistic representation of an ensemble of external stimuli. Building on the relationship between inference and learning, we derive a synaptic plasticity…
We study the dynamics of coupled oscillator networks with higher-order interactions and their ability to store information. In particular, the fixed points of these oscillator systems consist of two clusters of oscillators that become…
Collective rhythmic dynamics from neurons is vital for cognitive functions such as memory formation but how neurons self-organize to produce such activity is not well understood. Attractor-based models have been successfully implemented as…
We derive conditions for the existence of fixed points of cone mappings without assuming scalability of functions. Monotonicity and scalability are often inseparable in the literature in the context of searching for fixed points of…
The brain forms and stores distributed representations from sparse external input that compete for neuronal resources with already stored memory traces. It is unclear what dynamical properties of neural systems allow formation and…
The subject of study is a neural network with binary neurons, randomly diluted synapses and variable pattern activity. We look at the system with parallel updating using a probabilistic approach to solve the one step dynamics with one…
The existence of instabilities, for example in the form of adversarial examples, has given rise to a highly active area of research concerning itself with understanding and enhancing the stability of neural networks. We focus on a popular…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…