Analog ANN as Co-processors: For decades signal processing was performed with analog electronics, including the era of analog computers. In the last decades, most analog circuits were substituted by digital electronic systems. Artificial Neural Networks (ANN) were originally inspired by analog systems, and implemented with analog electronics. Today they are computed by discretized digital computers.

A weighted analog electronics summer circuit requires l+1 resistors and a difference amplifier with about 4-8 transistors (at least 2).. An approximated non-linear transfer function, e.g., the sigmoid function, can be built from at least two transistors, and typically less than 20 transistors if the gradient of the function is computed, too. The tanh function can be implemented with only two diodes. Such small circuits are well suited for printed (organic) electronics replacing more and more silicon electronics, but still limiting circuits to a size of about 100 transistors.

In our work we address the following questions:

1. Can AANN be trained with a digital floating point arithmetic performing gradient-based error optimization and finally be converted into an analog circuit approximation (assuming ideal operational amplifiers)?
2. Can AANN be trained with an in-circuit model approach using a circuit simulator performing gradient-based error optimization, especially assuming transistor-reduced nodes?
3. If no traditional gradient-based error optimization can be applied (due to lack of gradient functions or too high computational times), can genetic algorithms used to a find a solution?
4. Are organic transistors are suitable?

The implementation and approximation error of simple non-linear activation functions using transistor electronics are investigated and discussed. Instead using real analog electronics, we will substitute the circuits by a simulation model using the spice3f simulator. We will consider different model abstraction levels, starting with ideal operational amplifier (voltage controlled voltage sources), then using approximated real OPAMP models, and finally introducing transistor circuits with models of organic transistors.