Fisher Information Matrix of Unipolar Activation Function-Based Multilayer Perceptrons

• Published in: IEEE transactions on cybernetics Vol. 49; no. 8; pp. 3088 - 3098
• Main Authors: Guo, Weili, Ong, Yew-Soon, Zhou, Yingjiang, Hervas, Jaime Rubio, Song, Aiguo, Wei, Haikun
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.08.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Analytical form; Covariance matrices; Covariance matrix; Cybernetics; Error functions; Fisher information; Fisher information matrix (FIM); Gaussian distribution; Gradient methods; Indexes; Learning; learning dynamics; Mathematical model; Multilayer perceptrons; multilayer perceptrons (MLPs); Normal distribution; Parameters; Simulation; Singularities; singularity; Subspaces
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2018.2838680

The multilayer perceptrons (MLPs) are widely used in many fields, however, singularities in the parameter space may seriously influence the learning dynamics of MLPs and cause strange learning behaviors. Given that the singularities are the subspaces of the parameter space where the Fisher information matrix (FIM) degenerates, the FIM plays a key role in the study of the singular learning dynamics of the MLPs. In this paper, we obtain the analytical form of the FIM for unipolar activation function-based MLPs where the input subjects to the Gaussian distribution with general covariance matrix and the unipolar error function is chosen as the activation function. Then three simulation experiments are taken to verify the validity of the obtained results.