The reliability of our memories is nothing short of remarkable. Thousands of neurons die every day, synaptic connections appear and disappear, and the networks formed by these neurons constantly change due to various forms of synaptic plasticity. How can the brain develop a reliable representation of the world, learn and retain memories despite, or perhaps due to, such complex dynamics? Answering such questions is the natural evolution of recent work by the Dabaghian lab, which has been studying spatial cognition by modeling mechanisms of learning, based on algebraic topology methods developed by the Memoli group. This approach rests on the insight that the animal brain must first construct a rough-and-ready map of the environment before being able to fill it in with geometric details, which would be too computationally costly in light of typical navigational goals such as evading predators, returning to a nest, or finding a cafe. This basic map pays particular attention to the connectivity between places in the environment and is thus based on spatial topology; as such, the investigators hypothesized, it would be amenable to analysis by topological methods.
By simulating exploratory movements through different environments Dabaghian and Memoli will study how stable topological features arise in assemblies of simulated neurons operating under a wide range of conditions, including variations in firing rate, the size of the space each cell "senses," the number of cells in the population, and electrical oscillations in the brain that alter the behavior of the ensemble. They will use several novel methods from Persistent Homology Theory to understand how connections between cells (synapses) influence the speed and reliability of spatial learning. One might assume that learning would be enhanced if synapses never disappeared, but biology has clearly evolved to favor great synaptic plasticity. One reason may be that the loss of certain connections allows more room for mistakes to be unlearned. The objectives of this project are to study synaptic plasticity in a computational model, which will allow the influences of different parameters on the outcome of learning to be studied in detail. Principles that emerge on spatial learning in the hippocampus should be translatable to spatial cognition in machines.
