Design of coupling resistor networks for neural network hardware

The specification of an artificial neural network includes (1) the transformation relating each neuron's output voltage to its input voltage, and (2) a set of coupling weight factors expressing the input voltage of any neuron as a linear combination of the output voltages of other neurons. In analog VLSI chips for direct hardware implementation of these networks, neurons are often represented by amplifier elements (e.g. operational amplifiers or opamps), and resistors or active transconductances are used to couple signals from the outputs of certain neurons to the inputs of other neurons. Each coupling conductance is proportional to a single, corresponding coupling weight only under the following 'ideal' conditions: (1) each opamp has negligible output impedance, and (2) the input voltage of each opamp is developed across a low-resistance sampling resistor that is not loaded by the opamp itself. By contrast, the output impedance of a practical opamp may not be negligible in comparison to that of the high-fan network that it drives, and the sampling resistances on the opamp inputs cannot be arbitrarily low lest the input voltages be corrupted by unavoidable opamp input voltage offsets.