An all-optical implementation of a feed-forward artificial neural network is presented that uses self-lensing materials in which the index of refraction is irradiance dependent. Many of these types of material have ultrafast response times and permit both weighted connections and nonlinear neuron processing to be implemented with only thin material layers separated by free space. Both neuron processing and weighted interconnections emerge directly from the physical optics of the device. One creates virtual neurons and their connections simply by applying patterns of irradiance to thin layers of the nonlinear media. This is a result of a variation of the refractive-index profile of the self-lensing nonlinear media in response to the applied irradiance. An optical-backpropagation training method for this network is presented. The optical backpropagation is a training method that can be implemented potentially within the same optical device as the forward calculations, although several issues crucial to this po sibility remain to be addressed. Such a network was numerically simulated and trained to solve many benchmark classification problems, and some of these results are presented. To demonstrate the feasibility of building such a network, we also describe experimental work in the construction of an optical network trained to perform a logic XNOR function. This network, as a proof of concept, uses a relatively slow thermal nonlinear material with ~1-s response time.