High-Dimensional NN

There have been several attempts to extend the parameters (weights and biases) of the usual real-valued neural networks to higher dimensions (complex numbers, 3-dimensional vectors, quaterninons, etc.). We call such neural networks with high-dimensional parameters high-dimensional neural networks. High-dimensional neural networks can deal with a cluster of something (for example, 4-dimensional vector consisting of height, width, breadth and time, and a N-dimensional vector consisting of N particles and so on) and will extend the applicable domains of artificial neural networks.

We already proposed the following high-dimensional neural networks:

• Complex-valued neural networks （１９９１）

• 3-dimensional vector neural networks （１９９２）

• 3-dimensional vector product neural networks （１９９３）

• Quaternay neural networks （１９９５）
  
  Related papers：
  1. Kobayashi, M., Muramatsu, J. and Yamazaki, H., "High Dimensional Neural Network by Linear Connections of Matrix"，IEICE Trans. Fundamentals, Vol.J85-A, No.7, pp.763-770, 2002 (in Japanese).
  Content: The authors discussed high-dimensional neural networks from the point of view of the vector representation.
  
  2. Kobayashi, M.., "Three-Dimensional Associative Memory Using Exterior Product"，IEE Trans. EIS, Vol.124, No.1, pp.150-156, 2004 (in Japanese).
  Content: The author proposed a mutually connected three-dimensional neural network model with exterior product calculations and investigated its performance.
  
  
  Back to the home page of T. Nitta