Synaptic plasticity controls the emergence of population-wide invariant representations in balanced network models
The intensity and features of sensory stimuli are encoded in the activity of neurons in the cortex. In the visual and piriform cortices, the stimulus intensity re-scales the activity of the population without changing its selectivity for the stimulus features. The cortical representation of the stimulus is therefore intensity-invariant. This emergence of network invariant representations appears robust to local changes in synaptic strength induced by synaptic plasticity, even though: i) synaptic plasticity can potentiate or depress connections between neurons in a feature-dependent manner, and ii) in networks with balanced excitation and inhibition, synaptic plasticity determines the non-linear network behavior. In this study, we investigate the consistency of invariant representations with a variety of synaptic states in balanced networks. By using mean-field models and spiking network simulations, we show how the synaptic state controls the emergence of intensity-invariant or intensity-dependent selectivity by inducing changes in the network response to intensity. In particular, we demonstrate how facilitating synaptic states can sharpen the network selectivity while depressing states broaden it. We also show how power-law-type synapses permit the emergence of invariant network selectivity and how this plasticity can be generated by a mix of different plasticity rules. Our results explain how the physiology of individual synapses is linked to the emergence of invariant representations of sensory stimuli at the network level.
Mean-field models for finite-size populations of spiking neurons
Firing-rate (FR) or neural-mass models are widely used for studying computations performed by neural populations. Despite their success, classical firing-rate models do not capture spike timing effects on the microscopic level such as spike synchronization and are difficult to link to spiking data in experimental recordings. For large neuronal populations, the gap between the spiking neuron dynamics on the microscopic level and coarse-grained FR models on the population level can be bridged by mean-field theory formally valid for infinitely many neurons. It remains however challenging to extend the resulting mean-field models to finite-size populations with biologically realistic neuron numbers per cell type (mesoscopic scale). In this talk, I present a mathematical framework for mesoscopic populations of generalized integrate-and-fire neuron models that accounts for fluctuations caused by the finite number of neurons. To this end, I will introduce the refractory density method for quasi-renewal processes and show how this method can be generalized to finite-size populations. To demonstrate the flexibility of this approach, I will show how synaptic short-term plasticity can be incorporated in the mesoscopic mean-field framework. On the other hand, the framework permits a systematic reduction to low-dimensional FR equations using the eigenfunction method. Our modeling framework enables a re-examination of classical FR models in computational neuroscience under biophysically more realistic conditions.