Stochastic Neural Algorithms

• Main Author: Engler, Gary Ronald
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01.01.2018
• Subjects: Applied Mathematics; Artificial intelligence; Neurosciences
• ISBN: 0438836979; 9780438836976

Computation in the brain has long been of interest and is responsible for the way human beings and other animals interact with the world. One particular area of interest for neural computation is spatial reasoning, which has been shown to involve the hippocampus in mammalian brains. The recent focus on this area is due to the relative simplicity of the structure, the ability to correlate brain activity with the location of the test subjects, and the 2014 award of the Nobel Prize in Medicine and Physiology for the discovery of place and grid cells, which function as a sort of 'GPS system' in the brain. With spatial reasoning in mind it is investigated how networks of stochastic spiking neurons solve problems on graphs, focusing on the shortest path problem in particular. An algorithm which generates a network of stochastic spiking neurons from a weighted graph whose network state can be interpreted as an induced subgraph of the initial graph which solves the shortest path problem on the initial graph is introduced. It is proven that the shortest path corresponds to the lowest energy path in the space of network states for the induced network. By constructing a network to solve a particular optimization problem we are better able to explore the relationship between structure and computation in neural systems. The effects of biologically inspired inhibitory subnetworks are then explored with different connection schemes and how they affect the overall behavior of the network. Two significant classes of network behavior are investigated and the implications towards biological networks is discussed; slower smoother convergence to the network state representing a solution, and oscillations in network activity that reach the solution faster but tend to 'overshoot' the minimal induced subgraph containing the shortest path.