In this paper, we propose a new neural architecture for classification of visual patterns that is motivated by the two concepts of image pyramids and local receptive fields. The new architecture, called pyramidal neural network (PyraNet), has a hierarchical structure with two types of processing layers: Pyramidal layers and one-dimensional (1-D) layers. In the new network, nonlinear two-dimensional (2-D) neurons are trained to perform both image feature extraction and dimensionality reduction. We present and analyze five training methods for PyraNet [gradient descent (GD), gradient descent with momentum, resilient backpropagation (RPROP), Polak-Ribiere conjugate gradient (CG), and Levenberg-Marquadrt (LM)] and two choices of error functions [mean-square-error (mse) and cross-entropy (CE)]. In this paper, we apply PyraNet to determine gender from a facial image, and compare its performance on the standard facial recognition technology (FERET) database with three classifiers: The convolutional neural network (NN), the k-nearest neighbor (k-NN), and the support vector machine (SVM).