Hamiltonian dynamics of neural networks

✍ Scribed by Ulrich Ramacher

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 874 KB
• Volume: 6
• Category: Article
• ISSN: 0893-6080
• DOI: 10.1016/s0893-6080(05)80058-9

✦ Synopsis

The activation and weight dynamics of Artificial Neural Networks are derived from a partial differential equation (PDE) that may incorporate weights either as parameters or variables. It is shown that a single first-order Hamilton-Jacobi "parametricai" PDE suffices to derive the various neurodynamical paradigms used today. In the case that weights are taken as variables, a new type of neurodynamics is discovered: A Hamilton function is derived so that the weights obey a second-order ordinary differential equation (ODE). As this ODE models the forces, experienced by the weights in the presence of some generalized error potential, it is called a learning law Results obtained for the association of time-varying patterns, using parametrical as well as dynamical weights, show that learning rules can be replaced by learning laws at equal performance.