Nonlinear, local and highly parallel algorithms can perform several simple but important visual computations. Specific classes of algorithms can be considered in an abstract way. I study here the class of polynomial algorithms to exemplify some of the important issues for visual processing like linear vs. nonlinear and local vs. global. Polynomial algorithms are a natural extension of Perceptrons to time dependent grey level images.. Although they share most of the limitations of Perceptrons, they are powerful parallel computational devices. Several of their properties are characterized and especially (a) their equivalence with Perceptrons for geometrical figures and (b) the synthesis of non-linear algorithms (mappings) via associative learning. Finally, the paper considers how algorithms of this type could be implemented in nervous hardware, in terms of synaptic interactions strategically located in a dendritic tree.

Neural networks present a fundamentally different model of computation from the conventional sequential digital model. Dedicated hardware may thus be more suitable for executing them. Given that there is no clear consensus on the model of computation in the brain, model flexibility is at least as important a characteristic of neural hardware as is performance acceleration. The SpiNNaker chip is an example of the emerging 'neuromimetic' architecture, a universal platform that specialises the hardware for neural networks but allows flexibility in model choice. It integrates four key attributes: native parallelism, event-driven processing, incoherent memory and incremental reconfiguration, in a system combining an array of general-purpose processors with a configurable asynchronous interconnect. Making such a device usable in practice requires an environment for instantiating neural models on the chip that allows the user to focus on model characteristics rather than on hardware details. The central part of this system is a library of predesigned, 'drop-in' event-driven neural components that specify their specific implementation on SpiNNaker. Three exemplar models: two spiking networks and a multilayer perceptron network, illustrate techniques that provide a basis for the library and demonstrate a reference methodology that can be extended to support third-party library components not only on SpiNNaker but on any configurable neuromimetic platform. Experiments demonstrate the capability of the library model to implement efficient on-chip neural networks, but also reveal important hardware limitations, particularly with respect to communications, that require careful design. The ultimate goal is the creation of a library-based development system that allows neural modellers to work in the high-level environment of their choice, using an automated tool chain to create the appropriate SpiNNaker instantiation. Such a system would enable the use of the hardware to explore abstractions of biological neurodynamics that underpin a functional model of neural computation.