Plasticity and Firing Rate Dynamics in Leaky Integrate-and-Fire Models of Cortical Circuits

Abstract

A very large part of computational neuroscience is to understand neuronal firing rates and how each neuron’s activity effects its neighbors. Detangling the complex patterns observed in neuronal activity is a challenging subject. Understanding how these patterns emerge from a single cell is even more daunting. In this body of work, we aim to shed some light on firing rate dynamics as well as on how plasticity may play a role in developing cortical circuits. In chapter 1, we describe how just a couple plasticity rules can together generate both feedforward and feedback connections in a model resembling cortical neurons. We use simulations of leaky integrate-and-fire neurons to explore the different outcomes. We find that a specific pattern of plasticity rules gives rise to synaptic connectivity patterns observed in cortex. In chapter 2, we develop a method for understanding higher order terms to the firing rate equation derived from leaky integrate-and-fire neurons. We equate the dynamics to those of electrical circuits and find the firing rate is equivalent to current. The analysis shows that oscillations in firing rate will necessarily exist when an inhibitory network is connected to a network of excitatory LIF neurons. Furthermore, the framework may provide new tools for analyzing weight changes. In chapter 3, we investigate learning in artificial neural networks. Specifically, we aimed to understand catastrophic forgetting as well as how to build spiking artificial neural networks. Results in chapter 3 are inconclusive.