Structurally Dynamic Spiking Neural Networks

The aim of the project is to design, implement, and analyse SNNs with dynamic size and connectivity analogous to the developing brain. It is hoped that this would aid in overcoming difficulties in training SNNs, and potentially mimic some of the adaptive processes of the brain.
Broadly speaking, in humans, brain development starts after the first two weeks following conception as the first neural progenitor cells appear in the embryo. Neural patterning - the formation of neural 'motifs' that account for the structure of the brain - occurs as a result of excitatory/inhibitory effects on gene expression resulting from the diffusion of signalling proteins (Turing Patterns). Although interesting, this is fantastically complicated and to implement reaction-diffusion reactions as they appear in the human brain to grow an SNN would, effectively, require simulating an entire brain.
Translating this to SNNs, our goal is not to simulate the human brain, but rather to use principles from it that are pertinent to artificial intelligence. In this vein, I would like to explore incorporating analogues for developmental neurogenesis and synaptogenesis for structural adaption, in addition to local synaptic plasticity rules. In order to achieve this, I would need to modify an existing SNN simulator (i.e. Brian) to allow for neurogenesis and the formation/pruning of synapses.
Synaptogenesis could be explored in a sim- ilar way; synaptic pruning and neuronal turnover could be applied where synapses/neurons are not making substantial contributions. Once the groundwork for replicating this behaviour is in place, I would begin both empirical tests of these networks. Tasks should be selected that demonstrate adaptive behaviour, something where deep learning networks tend to fail.
In addition to these empirical tests, I would also intend to mathematically analyse the behaviours of these networks. Dynamical systems analysis is the most common approach to modelling neurons - the membrane potential equations and parameter values for a given neuron would be known for a given time, and hence the change in its dynamics over time could be observed. However, it is more difficult to describe the collective dynamics for a large network of neurons.