Effect of Homeostatic Plasticity on Hebbian Learning: A Mathematical Investigation
Abstract
Synaptic plasticity refers to the neurobiological process by which specific patterns of activity at the synapses -- the junctions between neurons that allow them to communicate -- result in changes in synaptic strengths and enable the brain to adapt to new information over time. One of the most studied theories of synaptic plasticity is Hebbian learning, or Hebbian plasticity, named for Donald Hebb who proposed that when neuron A repeatedly participates in firing neuron B, the synaptic strength of A onto B increases. If we think of A as the presynaptic neuron and B as the postsynaptic neuron, Hebbian plasticity implies that changes in synaptic strengths in a network of neurons is a function of the pre- and postsynaptic neural activities. Just like many biological processes, synaptic plasticity requires a compensatory mechanism, commonly referred to as synaptic homeostasis, to help ensure that the nervous system is in a dynamic regime where it functions optimally. Synaptic homeostasis also changes and adapts to the activity of the brain. This process is called homeostatic plasticity. A review of the literature reveals a varied and somewhat paradoxical set of findings about homeostatic plasticity. While in most theoretical models, it needs to be fast Ð- in seconds or minutes Ð- and sometimes even instantaneous to achieve stability, experimentalists witness slower homeostatic plasticity -- in hours or days. It has, in fact, been suggested that both fast and slow homeostatic mechanisms exist and that learning and memory use an interplay of both forms of homeostasis: while fast homeostatic control mechanisms (also referred to as rapid compensatory processes or RCPs) help maintain the stability of synaptic plasticity, slower ones are important for fine-tuning neural circuits. The proposed work will use analytical, numerical, and data-driven machine learning methods to investigate and model the dynamical interactions between synaptic plasticity and homeostatic plasticity. The overall goal is made up three specific aims that come together to form a comprehensive body of research: (1) to develop and analyze a multistable learning rule, with multiple firing rate setpoints, that incorporates a slow homeostasis mechanism as well two RCPs to model learning and memory formation. (2) to analyze the dynamical interaction between synaptic plasticity and homeostatic plasticity during recurrent network activity, with focus on surround suppression. (3) to develop a data-driven theoretical framework in which the nonlinear evolution of synaptic activity dynamics can be approximated with a linear operator, with the secondary goal of extracting important timescale information. Investigation will be done at both single-neuron and network levels and will employ a combination of theoretical tools including Ð but not limited to Ð stability and bifurcation analysis, perturbation analysis, data-driven spectral decomposition and deep learning of recurrent artificial neural network. Hebbian plasticity is widely assumed to be the neural basis of associative long-term memory and developmental changes such as receptive field development. The proposed work will contribute to the shaping and fine-tuning of the widely held (though, state-of-the-art) view that both fast and slow homeostatic mechanisms exist and that learning and memory use an interplay of both forms of homeostasis; thereby adding to the understanding of how homeostatic plasticity interacts with Hebbian learning to stabilize the firing rates of neurons and help the nervous system function optimally. Furthermore, findings in theoretical neuroscience have directly benefited other STEM fields. To mention a couple instances, advances in the subject of artificial neural networks has benefited a great deal from studies on Hebbian plasticity; and surround suppression, even though a receptive field neurological process, has inspired computer vision algorithms such as efficient image representation.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jun 25, 2021
- Source ID
- W911NF2110192
Entities
People
- Lawrence Udeigwe
Organizations
- Army Contracting Command
- Manhattan University
- United States Army