Neurons With Paraboloid Decision Boundaries for Improved Neural Network Classification Performance

In mathematical terms, an artificial neuron computes the inner product of a d-dimensional input vector x with its weight vector w, compares it with a bias value w₀ and fires based on the result of this comparison. Therefore, its decision boundary is given by the equation w^T x + w₀ = 0. In this paper, we propose replacing the linear hyperplane decision boundary of a neuron with a curved, paraboloid decision boundary. Thus, the decision boundary of the proposed paraboloid neuron is given by the equation (h^T x + h₀)² - ||x - p||₂² = 0, where h and h₀ denote the parameters of the directrix and p denotes the coordinates of the focus. Such paraboloid neural networks are proven to have superior recognition accuracy in a number of applications.