Geometry of neural networks with asymmetric weight matrices

Dynamics of Hopfield neural networks with asymmetric weights are elucidated from the geometrical viewpoint which is based on the eigenspace analysis of weight matrices. As the examples of asymmetric networks, cross-correlational associative memory and random networks are discussed. Complex dynamical behaviors of asymmetric networks such as spurious memory of cross-correlational associative memory and state transitions of random networks are explained geometrically. Also neuro-window method of asymmetric networks is proposed, which realizes capacity expansion and selective retrieval in cross-correlational associative memory.