Visualisation of CNN dynamics

where u denotes the CNN input vector, x the state vector, y = f ( x ) the output vector, f (.) a nonlinear function, A the feedback template matrix, B the control template matrix, i the bias vector, and ∂ the contribution from the boundary. CNN cell capacitance and resistance are assumed to be normalised to unity. Existing simulators mostly aim to increase the computational efficiency. In fact, having an efficient simulator at our disposal is a prerequisite for research in CNN-related areas. However, most tools provide only the output of a CNN at the equilibrium point, without revealing information about its dynamics. From the user’s point of view, these simulators behave like black boxes. Forming an idea of how a CNN ‘works’ is left to the imagination, a severe shortcoming, especially for those people who are not yet experienced in CNN theory. This is where the simulator presented in this Letter becomes relevant. The basic idea is to create a visualising CNN simulator that allows us to track the way in which the state trajectories evolve, thus gaining an insight into the behaviour of CNN dynamics. The simulator permits the graphical creation of an input image, an easy change of template values, and instant visualisation of the resulting effect on the individual CNN cells. At the same time, since the simulator is also meant to be useful for those who are new to the CNN area, it is kept simple; the number of parameters to be entered by the user is minimal. Since the program is written in Java and is accessible through World Wide Web on http://www.isi.ee.ethz.ch/ ~ haenggi/CNNsim.html there is no need to download and compile it explicitly, and it is easily and publicly accessible. The source code is available under the same address.