An optical quadratic neural network utilizing four-wave mixing in barium titanate (BaTiO3) has been developed. This network implements a feedback loop using a CCD camera, a microcomputer, two monochrome liquid crystal televisions, and various optical elements. For training, the network employs the supervised quadratic perceptron algorithm to associate binary-valued input vectors with specified training vectors. Using a spatial multiplexing scheme for two bipolar neurons, the quadratic network was able to associate an input vector with various target vectors. In addition, the network successfully associated two input vectors with two corresponding target vectors in the same training session. Both analytical and experimental results are presented.