Related papers: Replica-mean-field limits for intensity-based neur…
We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random…
Residual deep neural networks (ResNets) are mathematically described as interacting particle systems. In the case of infinitely many layers the ResNet leads to a system of coupled system of ordinary differential equations known as neural…
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…
The replicated field theory of the random field Ising model involves the couplings of replicas of different indices. The resulting correlation functions involve a superposition of different types of long distance behaviours. However the…
The replica method is applied to a neural network model with state-dependent synapses built from those patterns having a correlation with the state of the system greater than a certain threshold. Replica-symmetric and first-step…
The characterization of network and biophysical properties from neural spiking activity is an important goal in neuroscience. A framework that provides unbiased inference on causal synaptic interaction and single neural properties has been…
We establish mean-field limits for large-scale random-access networks with buffer dynamics and arbitrary interference graphs. While saturated-buffer scenarios have been widely investigated and yield useful throughput estimates for…
We study large but finite neural networks that, in the thermodynamic limit, admit an exact low-dimensional mean-field description. We assume that the governing mean-field equations describing macroscopic quantities such as the mean firing…
In the last five decades, mean-field neural-networks have played a crucial role in modelling associative memories and, in particular, the Hopfield model has been extensively studied using tools borrowed from the statistical mechanics of…
We discuss the effects of common synaptic inputs in a recurrent neural network. Because of the effects of these common synaptic inputs, the correlation between neural inputs cannot be ignored, and thus the network exhibits sample…
In this paper we address the question of statistical model selection for a class of stochastic models of biological neural nets. Models in this class are systems of interacting chains with memory of variable length. Each chain describes the…
The continuous integration of experimental data into coherent models of the brain is an increasing challenge of modern neuroscience. Such models provide a bridge between structure and activity, and identify the mechanisms giving rise to…
Recurrent neural networks are powerful tools for understanding and modeling computation and representation by populations of neurons. Continuous-variable or "rate" model networks have been analyzed and applied extensively for these…
The thermodynamic and retrieval properties of fully connected Blume-Emery-Griffiths networks, storing ternary patterns, are studied using replica mean-field theory. Capacity-temperature phase diagrams are derived for several values of the…
Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small population sizes. This makes it necessary to favor…
The mean-field limit of a Markovian model describing the interaction of several classes of permanent connections in a network is analyzed. Each of the connections has a self-adaptive behavior in that its transmission rate along its route…
The experimental study of neural networks requires simultaneous measurements of a massive number of neurons, while monitoring properties of the connectivity, synaptic strengths and delays. Current technological barriers make such a mission…
The bio-inspired integrate-fire-reset mechanism of spiking neurons constitutes the foundation for efficient processing in Spiking Neural Networks (SNNs). Recent progress in large models demands that spiking neurons support highly parallel…
Recurrent neural networks have been extensively studied in the context of neuroscience and machine learning due to their ability to implement complex computations. While substantial progress in designing effective learning algorithms has…
We study finite-size fluctuations in a network of spiking deterministic neurons coupled with non-uniform synaptic coupling. We generalize a previously developed theory of finite size effects for uniform globally coupled neurons. In the…