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Networks in the brain consist of different types of neurons. Here we investigate the influence of neuron diversity on the dynamics, phase space structure and computational capabilities of spiking neural networks. We find that already a…
How the information microscopically processed by individual neurons is integrated and used in organizing the behavior of an animal is a central question in neuroscience. The coherence of neuronal dynamics over different scales has been…
A collective chaotic phase with power law scaling of activity events is observed in a disordered mean field network of purely excitatory leaky integrate-and-fire neurons with short-term synaptic plasticity. The dynamical phase diagram…
This essay, derived from a lecture at "The Physics Modeling of Thought" workshop in Berlin in winter 2023, explores the mutually beneficial relationship between theoretical neuroscience and statistical physics through the lens of efficient…
Spatial and temporal resource constraints are critical for both biological and artificial intelligent systems. Here we define differentiable cost terms for breadth, depth, and time within a recurrent convolutional neural network conceived…
Simulation code for conventional supercomputers serves as a reference for neuromorphic computing systems. The present bottleneck of distributed large-scale spiking neuronal network simulations is the communication between compute nodes.…
The ability of discrete-time nonlinear recurrent neural networks to store time-varying small input signals is investigated by mean-field theory. The combination of a small input strength and mean-field assumptions makes it possible to…
Understanding how deep neural networks learn remains a fundamental challenge in modern machine learning. A growing body of evidence suggests that training dynamics undergo a distinct phase transition, yet our understanding of this…
Statistical mechanics determines the abundance of different arrangements of matter depending on cost-benefit balances. Its formalism and phenomenology percolate throughout biological processes and set limits to effective computation. Under…
The phenomenon of Stochastic Resonance (SR) is reported in a completely noise-free situation, with the role of thermal noise being taken by low-dimensional chaos. A one-dimensional, piecewise linear map and a pair of coupled…
Activity in the human brain moves between diverse functional states to meet the demands of our dynamic environment, but fundamental principles guiding these transitions remain poorly understood. Here, we capitalize on recent advances in…
We train an artificial neural network which distinguishes chaotic and regular dynamics of the two-dimensional Chirikov standard map. We use finite length trajectories and compare the performance with traditional numerical methods which need…
We study statistical properties of the irregular bursting arising in a class of neuronal models close to the transition from spiking to bursting. Prior to the transition to bursting, the systems in this class develop chaotic attractors,…
For infinitely large sparse networks of spiking neurons mean field theory shows that a balanced state of highly irregular activity arises under various conditions. Here we analytically investigate the microscopic irregular dynamics in…
Synaptic interactions structure the phase space of the dynamics of neural circuits and constrain neural computation. Understanding how requires methods that handle those discrete interactions, yet few exist. Recently, it was discovered that…
Collective chaos is shown to emerge, via a period-doubling cascade, from quasiperiodic partial synchronization in a population of identical inhibitory neurons with delayed global coupling. This system is thoroughly investigated by means of…
Nonlinear time series analyses have suggested that the human electroencephalogram (EEG) may share statistical and dynamical properties with chaotic systems. During slow-wave sleep or pathological states like epilepsy, correlation dimension…
Recurrent neural networks (RNNs) are machine learning models widely used for learning temporal relationships. Current state-of-the-art RNNs use integrating or spiking neurons -- two classes of computing units whose outputs depend directly…
We study a family of binary state, socially-inspired contagion models which incorporate imitation limited by an aversion to complete conformity. We uncover rich behavior in our models whether operating with either probabilistic or…
The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same…