Spatially continuous learning systems: artificial neural networks in a bulk material continuum

摘要

Artificial (and biological) neural networks are usually envisioned as a collection of massively connected discrete nonlinear processors. There is a finite number of neurons and each neuron can be individually identified and occupies a certainlocation in 2D or 3D space. There is also a numerous but finite number of interconnections between neurons. A major hurdle, when attempting to build neural networks in hardware is implementing the massive number of these physical interconnections required for all but the simplest applications. As an alternative, this paper describes the physical development of trainable computational devices implemented in bulk materials as Feedforward Continuum Artificial Neural Networks (CANNs). Nonlinear neuronprocessing and connectivity are a natural result of the linear and nonlinear physical processes inherent in the bulk material in which the network is implemented. These physical processes can be externally controlled and the control mechanism can betrained by an error backpropagation method based on gradient descent optimization. When trained, the physical systems can function as a feedforward artificial neural networks. An example is presented below where a feedforward artificial neural network isimplemented in a cube of Zinc Selenide, a bulk Kerr-type nonlinear optical material. Inputs are encoded as patterns on an information laser beam propagating through the material. Nonlinear neuron processing results from the 3rd order X{sup}3 opticalnonlinearity of the material. Connectivity and weighting results from optical paths created in the material by a trainable weight pattern imposed on an additional weighting laser beam which propagates through the material along with the input informationbeam. Numerical models and training simulations of this continuum artificial neural network are presented. Ongoing research involves simulations and experimental work toward implementing the same architecture, but with much lower optical power, usingscreening optical nonlinearies present in SBN photorefractive crystals under an applied electric field. Also described are proof of concept experimental results from an optical network built using very thin samples of Kerr-type optical material separatedby long distances for free space propagation of the light to allow detection of the network output.