Many qualitative features of the emerging collective dynamics in neuronal networks, such as
correlated activity, stability, response to inputs, and chaotic and regular behavior, can be …

Autonomous, randomly coupled, neural networks display a transition to chaos at a critical
coupling strength. Here, we investigate the effect of a time-varying input on the onset of …

Attractor networks are an influential theory for memory storage in brain systems. This theory
has recently been challenged by the observation of strong temporal variability in neuronal …

Training recurrent neural networks (RNNs) remains a challenge due to the instability of
gradients across long time horizons, which can lead to exploding and vanishing gradients …

Understanding the functional principles of information processing in deep neural networks
continues to be a challenge, in particular for networks with trained and thus nonrandom …

Understanding capabilities and limitations of different network architectures is of
fundamental importance to machine learning. Bayesian inference on Gaussian processes …

The Thermodynamic Formalism provides a rigorous mathematical framework for studying
quantitative and qualitative aspects of dynamical systems. At its core, there is a variational …

Multidimensional stochastic integrate-and-fire (IF) models are a standard spike-generator
model in studies of firing variability, neural information transmission, and neural network …

Contemporary modeling approaches to the dynamics of neural networks include two
important classes of models: biologically grounded spiking neuron models and functionally …

It has been proposed that random wide neural networks near Gaussian process are
quantum field theories around Gaussian fixed points. In this paper, we provide a novel map …