Estimating the CNN Steady State using Forward-Backward Recursions

We describe a technique by which the steady state solution of some CNN template operations can be approximated in a few passes over the input image. For digital implementations, this is much more efficient than numerical integration of the CNN differential equations. In particular, we show that the steady state solution to linear 1D CNN filtering operations can be found exactly in two passes over the input image using the forward-backward filtering technique commonly used in digital signal processing to obtain zero phase linear filters. We then show that this technique can be modified to find approximate solutions to some nonlinear CNN operations, using the example of a local winner-take-all network