Effect of Sensory Input on Trajectories Generated by Recurrent Neural Networks.

摘要

We show that the iterative signals generated by a simple recurrently connected network of only 3 sigmoidal nodes become stable, periodic or chaotic, depending on the magnitude of a global parameter (s) that controls the steepness of the node responses. High values of s produce chaotic signals, and low values lead to stable signals, i.e. unchanging from cycle to cycle. The transition from stability, through periodicity to chaos is shown to be consistent with Feigenbaum's model of critical nonlinear systems. For large networks that are recurrently connected, the stability also depends critically on the node connection weights and biases. When these are fixed randomly, it is possible to find large systems that also show a transition from stability to chaos by the adjustment of s. When the weights and biases are allowed to evolve by a modified Hebbian rule, which depends on the internal state of the network, we find that the system becomes stable or chaotic, again depending on s, but does not appear to exhibit periodicity. We have developed a software simulation of a machine whose motion in two dimensions is controlled entirely by the iterative activity of a recurrently connected neural network. The activities of some randomly chosen nodes drive motor responses that control the movement. In the absence of external input, the machine can be made to spiral into inactivity or to follow a chaotic trajectory. If the simulated environment contains one or more emitting sources, and the machine carries sensors whose responses are fed into the network, the motion is influenced by the sensory input.