Diffusion Processes

Diffusion processes can be implemented by the spreading activation of neurons, and they can be used for important tasks, such as path planning (Steinbeck & al. 1995) and other kinds of optimization (Miller & al. 1991, Ting & Iltis 1994). In a diffusion process the rate of change of a field is directly proportional to the field, $\d\psi/\d t \propto \nabla^2\psi$. The Laplacian of the field can be approximated in terms of the convolution of a Gaussian with the field, which is implemented by a simple pattern of connections with nearby neurons: $\d\psi/\d t \propto \gamma\otimes\psi - \psi$, where $\gamma$ is a Gaussian field of appropriate dimension. (See MacLennan 1997 for more details.)