A new polarization-encoding scheme for a bipolar kth-order neural network based on inner-product representation is proposed. Bipolar data multiplication is achieved as the rotation of linearly polarized light. A compact architecture of the bipolar kth-order neural network is suggested. In the architecture, no subtractions are needed, and the threshold levels for the neurons are fixed. Also, we show that a liquid-crystal device such as a liquid-crystal television is acceptable as a polarization modulator in the proposed architecture by computer simulation.