When neuron operations are computed in parallel using a large number of arithmetic units, arithmetic units for neuron operations and arithmetic units for error signal operations need not be provided separately, and a neural network arithmetic apparatus that consumes the bus band less is provided for updating of synapse connection weights. Operation results of arithmetic units and setting information of a master node are exchanged between them through a local bus. During neuron operations, partial sums of neuron output values from the arithmetic units are accumulated by the master node to generate and output a neuron output value, and an arithmetic unit to which neuron operations of the specific neuron are assigned receives and stores the neuron output value outputted from the master node.

A pattern recognition system, comprising a neural network formed utilizing nanotechnology and a pattern input unit, which communicates with the neural network, wherein the neural network processes data input via the pattern input unit in order to recognize data patterns thereof. Such a pattern recognition system can be implemented in the context of a speech recognition system and/or other pattern recognition systems, such as visual and/or imaging recognition systems.

Fractal memory systems and methods include a fractal tree that includes one or more fractal trunks. One or more object circuits are associated with the fractal tree. The object circuit(s) is configured from a plurality of nanotechnology-based components to provide a scalable distributed computing architecture for fractal computing. Additionally, a plurality of router circuits is associated with the fractal tree, wherein one or more fractal addresses output from a recognition circuit can be provided at a fractal trunk by the router circuits.

A variable resistor apparatus includes a plurality of nanoparticles disposed between two terminals, wherein the plurality of nanoparticles provides an electrical resistance. An electric field applied to the plurality of nanoparticles across the two terminals results in an alignment of the nanoparticles over time and a decrease in the electrical resistance thereby providing a variable resistor apparatus. The electric or electrical field can be applied across the two terminals perpendicular to the plurality of nanoconnections. The nanoparticles can comprise nanoconductors, which can be formed as, for example, nanotubes and/or nanowires. The nanoparticles are generally disposed in a solution within a connection gap formed between the two terminals. The solution can comprise a solvent and/or a suspension of nanoparticles forming a mixture thereof. The solution can also be provided as a liquid, a gel, and or a gas. The solution may also comprise a dielectric.

Physical neural network systems and methods are disclosed. A physical neural network can be configured utilizing molecular technology, wherein said physical neural network comprises a plurality of molecular conductors, which form neural network connections thereof. A training mechanism can be provided for training said physical neural network to accomplish a particular neural network task based on a neural network training rule. The neural network connections are formed between pre-synaptic and post-synaptic components of said physical neural network. The neural network generally includes dynamic and modifiable connections for adaptive signal processing. The neural network training mechanism can be based, for example, on the Anti-Hebbian and Hebbian (AHAH) rule and/or other plasticity rules.