Related papers: Inference in neural networks using conditional mea…
The neural dynamics generating sensory, motor, and cognitive functions are commonly understood through field theories for neural population activity. Classic neural field theories are derived from highly simplified models of individual…
The mean field algorithm is a widely used approximate inference algorithm for graphical models whose exact inference is intractable. In each iteration of mean field, the approximate marginals for each variable are updated by getting…
A recent dynamic mean-field theory for sequence processing in fully connected neural networks of Hopfield-type (During, Coolen and Sherrington, 1998) is extended and analized here for a symmetrically diluted network with finite connectivity…
We review a recent approach to the mean-field limits in neural networks that takes into account the stochastic nature of input current and the uncertainty in synaptic coupling. This approach was proved to be a rigorous limit of the network…
The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or…
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…
Studying neural connectivity is considered one of the most promising and challenging areas of modern neuroscience. The underpinnings of cognition are hidden in the way neurons interact with each other. However, our experimental methods of…
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…
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…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
The construction of transfer functions in theoretical neuroscience plays an important role in determining the spiking rate behavior of neurons in networks. These functions can be obtained through various fitting methods, but the biological…
Low-dimensional descriptions of neural network dynamics are an effective tool for bridging different scales of organization of brain structure and function. Recent advances in deriving mean-field descriptions for networks of coupled…
Neurons subject to a common non-stationary input may exhibit a correlated firing behavior. Correlations in the statistics of neural spike trains also arise as the effect of interaction between neurons. Here we show that these two situations…
We analyze the emergent regimes and the stimulus-response relationship of a population of noisy map neurons by means of a mean-field model, derived within the framework of cumulant approach complemented by the Gaussian closure hypothesis.…
Linear regression on network-linked observations has been an essential tool in modeling the relationship between response and covariates with additional network structures. Previous methods either lack inference tools or rely on restrictive…
Understanding the relationship between the heterogeneous structure of complex networks and cooperative phenomena occurring on them remains a key problem in network science. Mean-field theories of spin models on networks constitute a…
Mean-field models provide a link between microscopic neuronal activity and macroscopic brain dynamics. Their derivation depends on simplifying assumptions, such as all-to-all connectivity, limiting their biological realism. To overcome…
In order to assess the short-term memory performance of non-linear random neural networks, we introduce a measure to quantify the dependence of a neural representation upon the past context. We study this measure both numerically and…
Mean-field variational methods are widely used for approximate posterior inference in many probabilistic models. In a typical application, mean-field methods approximately compute the posterior with a coordinate-ascent optimization…
In this work, we investigate the use of normalizing flows to model conditional distributions. In particular, we use our proposed method to analyze inverse problems with invertible neural networks by maximizing the posterior likelihood. Our…