Abstract: An initializer for circle distribution on a 2D surface using a polar coordinate system for image compression, video compression, motion detection, and posture detection. The initializer can also be used for sphere distribution in a 3D shape. The initializer uses a mixed deterministic and iterative/stochastic approach. Using the polar coordinate system for initialization enables coverage of the user space, and after parameters are initialized, the method transitions to a cartesian coordinate system. Methods for using the polar system in CPU units by applying an XNOR/AND architecture for neural network model compression are also described. The neural network includes a perceptron for supervised learning of binary classifiers. The unit responsible for multiplication in a MAC architecture can be replaced with a non-linear expressive function. Thus, a neural network having a non-linear expressive perceptron (quadtron) is described for solving circle distribution and other problems.