Cortical multi-layered, multi-area networks as a substrate for stochastic computing

Classical studies on stochastic computing in neural networks have focused on symmetric networks of highly simplified neuron models (Hinton et al., 84; Hinton et al., 2006). While recent works have successfully introduced more complex single neurons dynamics (Buesing et al., 2011; Petrovici et al., 2013) and asymmetric connectivity of local cortical circuits (Habenschuss et al., 2013), the scale of these networks still lacks biological realism. In order to relate insights from theoretical considerations and modeling studies to experimental data, it is necessary to investigate stochastic computations in large-scale models of brain circuits with realistic layer-specific and inter-areal connectivity.We present two models combining simple, single-cell dynamics with complex connectivity based on anatomical and electro-physiological findings across different species and cortical regions. This approach allows the investigation of dynamical consequences of the connectivity while keeping the model analytically tractable. The microcircuit model (Potjans et al., 2014) represents a 1mm^2 patch of early sensory cortex composed of 4 layers, with one excitatory and one inhibitory population each. The model is full-scale in the sense that it represents the full neuron and synapse density leading to approx. 80,000 neurons with an average in-degree on the order of 10^{4} synapses. The network yields population-specific stationary firing rates resembling measured cortical activity, with inhibitory neurons showing higher rates than excitatory cells and a certain pattern of firing rates in the excitatory populations. Furthermore, the propagation of transient input follows a distinct sequence across populations and features a 'hand-shaking' mechanism between the different cortical layers. However, on this scale, 50% of the synapses to a neuron have to be replaced by noise (modeled as random spike trains drawn from a Poisson distribution), because they originate from outside of the 1mm^2 patch.The multi-area model of visual cortex (Schmidt et al., 2013) therefore extends the microcircuit model to multiple cortical areas and allows us to replace large parts of the Poissonian inputs by simulated spike trains. The cortico-cortical as well as the intra-areal connectivity is based on data of a large number of anatomical studies. Missing data is estimated using structural regularities derived from experimental findings. In addition, we use a method to systematically modify the network connectivity to bring the model to a realistic working point, while still fulfilling anatomical constraints. The network shows asynchronous, irregular spiking across populations and areas. The variety of firing rate patterns across areas reflects the rich connectivity structure.The firing rates in both models are well predicted by a mean-field theory based on (Fourcaud et al., 2002; Wong et al., 2006). The spectra and cross-correlations of the population firing rates can be derived by describing the interactions of the populations with a linear rate model. We identify the anatomical connections strongly involved in the generation of oscillations by decomposing the effective connectivity of the circuitry (Bos et al., 2014).These models provide a starting point to address the issue of probabilistic computations in large-scale cortical circuits. Emerging questions address the influence of the global, asymmetric connectivity on the properties of the stationary distributions of network states, e.g. convergence time, the exploration of computational profit given by the features of a layered network and the impact of intrisically generated oscillations. In the outlook we discuss the advantageousness of restricting the state space by mean-field theory to a regime in which computation is feasible