Recent developments in neurodynamics and their impact on the design of neuro-chips

Neurons can be modeled either by equations or differential equations. For the latter, a low-pass filter must be added to the analog function blocks associated with the McCullogh and Pitts type of static neuron in order to provide the time-dependent neuron solution. The low-pass filter enhances stability and enables a time-continuous analog implementation much more compact than that attained with time-discrete analog or pure digital design. A few examples of equations as well as differential equations are known for that part of learning. However, much less than for the recall mode, it is clear how to design learning neuro-chips for temporal pattern processing. It is shown here that a partial differential equation can be used to provide a unified description of both the recall and learning dynamics of a neural network as well as to investigate systematically the VLSI potential for analog time-continuous neuro-chips. It turns out that the recall and learning dynamics can be divided into causal as well as noncausal solutions. The first type of solution includes oscillating or spiking neurons. The second type of solution allows for a much simpler signal representation but leads to the problem of storing the temporal signal of each neuron for as long a time as a single pattern lasts. As this is prohibitive for larger networks and time-varying patterns, the analog VLSI implementation of causal neuron models is suggested.