Gauged neural network: Phase structure, learning, and associative memory

✍ Scribed by Motohiro Kemuriyama; Tetsuo Matsui; Kazuhiko Sakakibara

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 579 KB
• Volume: 356
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2005.05.083

✦ Synopsis

A gauge model of neural network is introduced, which resembles the Z(2) Higgs lattice gauge theory of high-energy physics. It contains a neuron variable S x ¼ AE1 on each site x of a 3D lattice and a synaptic-connection variable J xm ¼ AE1 on each link ðx; x þ mÞðm ¼ 1; 2; 3Þ. The model is regarded as a generalization of the Hopfield model of associative memory to a model of learning by converting the synaptic weight between x and x þ m to a dynamical Z(2) gauge variable J xm . The local Z(2) gauge symmetry is inherited from the Hopfield model and assures us the locality of time evolutions of S x and J xm and a generalized Hebbian learning rule. At finite ''temperatures'', numerical simulations show that the model exhibits the Higgs, confinement, and Coulomb phases. We simulate dynamical processes of learning a pattern of S x and recalling it, and classify the parameter space according to the performance. At some parameter regions, stable column-layer structures in signal propagations are spontaneously generated. Mutual interactions between S x and J xm induce partial memory loss as expected.