Autonomous learning of novel patterns by utilizing chaotic dynamics
Kazuhiro Kojima, Kenichiro Ito · 2003
We propose an autonomous dynamical pattern recognition and learning system which can learn new patterns without any external observer. For realizing the "I don't know" state as a filter, we constructed the network from Lorenz systems. First, we find a parameter which affects the network dynamics from the evolution equation. A series of computer simulations show the dependence of the network dynamics on the parameter. Then we find a critical region of the network dynamics. In this critical region, when the embedded pattern is given to the network, the output pattern of the network immediately goes to the relevant embedded pattern and the state of network reduces to the oscillatory state at once. On the other hand, when no embedded pattern is given to the network, the network state oscillates chaotically. It is considered to be the "I don't know" state. Second, we find a transition rule of the output pattern, that is, the pattern dynamics. This dynamics is approximated with a circle map. Further, we find a power law as a statistical property. It means that the pattern dynamics is intermittent chaos type II or III. Finally, when a Hebb rule is applied to the network under the external stimuli that are unknown patterns, the internal state of the network is inversely bifurcated from the chaotic state to the periodic state according to the progress of learning. By utilizing this bifurcation as an index of the progress of learning, the network can learn new patterns without any external observer. Further the network can learn new patterns without destroying the previous embedded patterns.