Firing Rate Models

Emergence of universal computations through neural manifold dynamics

“…In this section, we will present statements concerning the dynamics of the following mathematical models: The first one describes the time evolution of a filtered measure of the firing rate [37], while the second does so for the voltage of the cell when action potentials are removed [18]. Each F i models the relationship between the voltage and the spike frequency of each neuron, and they are going to be called transfer functions.…”

“…Nonetheless, restricting the neural manifold to be flat is a rather strong and unrealistic assumption, as even in the v-model the observed manifold is not Euclidian, since to obtain the firing rates we still must apply a non-linear transfer function, F [18]. Thus, the low-rank hypothesis turns out to be a plausible frame from which to make sense of the seemingly parsimonious correlations observed between individual neurons in the cortex.…”

“…In order to tackle this challenge, many researchers have used recurrent neural networks (RNN) as a model for neural dynamics, searching for a plausible yet tractable modelling capable to shed light on the neural machinery by which cortical computations are biologically implemented [12], [13]. These various types of networks describe the behavior of a neural circuit in terms of continuous population variables, primarily the passive somatic potential [14], synaptic conductance [15], [16], or an average of the firing rate of action potentials [17], [18], which is why they are commonly referred to as "firing rate models" in theoretical neuroscience [18]. Although they are crude approximations of neuronal dynamics that lack many nuances of the mechanisms of spike generation [16], their behavior exhibits many aspects of biological neuronal systems, such as recurrence, feedback, nonlinearity, and principal component activity [19], and thus they have appealed many neuroscientists who have found in them a way to simulate, interpret, and make sense of empirical data, showing that RNN setups are capable of replicating many experimental observations [10], [11], [19]- [25].…”

Collective irregular dynamics in balanced networks of leaky integrate-and-fire neurons

“…Starting from the Fokker-Planck equation (6), the firing rate ν(t) can be also expressed in terms of the probability current at v = v θ , i.e.…”

“…This is, indeed the philosophy adopted by many studies based on pulse coupled units, such as leaky integrate-and-fire (LIF) neurons [5]. Accordingly, a general question arises as to whether the two approaches are consistent with one another and, in particular, to what extent spiking neurons reproduce the scenario observed in rate models [6,7].…”