Title :
A geometric view of neural networks using homotopy
Author :
Coetzee, Frans M. ; Stonick, Virginia L.
Author_Institution :
Dept. of Electr. & Comput. Eng. Carnegie Mellon Univ., Pittsburgh, PA, USA
Abstract :
A homotopy approach is formulated for solving for the weights of a network. It is shown how this leads simply to a geometric interpretation of the weight optimization problem. The homotopy approach accounts for distinct sets of weights and infinite weights. The geometric interpretation further aids in explaining the appearance of local minima in the network, the appearance of infinite weights, and the similarities and differences between optimizing the weights in a nonlinear network, and the weights in a linear network
Keywords :
geometry; neural nets; homotopy; local minima; neural network geometry; weight optimization problem; Adaptive signal processing; Computer networks; Linear systems; Neural networks; Nonlinear equations; Parameter estimation; Polynomials; Signal mapping; Signal processing; Signal processing algorithms;
Conference_Titel :
Neural Networks for Processing [1993] III. Proceedings of the 1993 IEEE-SP Workshop
Conference_Location :
Linthicum Heights, MD
Print_ISBN :
0-7803-0928-6
DOI :
10.1109/NNSP.1993.471877
