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

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 certain location in 2D or 3D space. There are also numerous but a 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, the paper describes the physical development of trainable computational devices implemented in bulk materials as feedforward continuum artificial neural networks (CANNs). Nonlinear neuron processing 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 be trained 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 where a feedforward artificial neural network is implemented 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 3^rd order χ³ optical nonlinearity 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 information beam