Neural Network Methods for Solving Strassen's Algorithm

Open Access
Author:
Chicoine, Kaley M
Area of Honors:
Computer Science
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Dr. John Sustersic, Thesis Supervisor
  • Dr. Jesse Barlow, Honors Advisor
Keywords:
  • Neural Networks
  • Strassen's Algorithm
  • Matrix Multiplication
Abstract:
Neural networks are a machine learning technique modeled after clusters of biological neurons. They have shown great capacity in solving computing problems of an imprecise nature, and have led to large advances in the areas such as image and facial recognition. However, neural networks also have their limits. When applied to a problem that has a numerically precise answer, neural networks are likely a suboptimal technique. As an exercise in the limits of neural network capabilities, neural network methods of learning were applied to learn Strassen's algorithm for 2x2 matrix multiplication. However, even with the state space extremely restricted, the network failed to converge on the correct answer. This suggests that problems with precise solutions should be approached with more symbolic methods. Neural networks are good tools for abstracting concepts, but more complex learning will require multiple layers of abstraction and careful selection of error function to produce meaningful results.