Fig. 1: A super-Turing synstor circuit for an intelligent morphing wing.

a A crossbar circuit is depicted, featuring synstors connecting presynaptic and postsynaptic neuron circuits. The input voltage pulses applied to the input electrode are represented by the vector x. The output voltage pulses from the postsynaptic neuron form the vector y, while the voltage pulses applied to the output electrode are given by the vector \({{\bf{z}}}\). The resulting current at the nth output electrode is represented by the vector i with elements in, which induces y and v from the postsynaptic neuron circuit. \({{\bf{I}}}\) induces \({{\bf{y}}}\) and \({{\bf{z}}}\) from the postsynaptic neuron circuit. b System states (\({{\bf{s}}}\)) are detected by sensors and converted into input voltage pulses (x) through the presynaptic neuron circuit. These input pulses drive the synstor circuit, which operates in super-Turing mode, concurrently executing an inference algorithm (\({{\bf{I}}}={{\bf{Wx}}}\)) and modifying its conductance matrix (\({{\bf{W}}}\)) according to a learning rule (\(\dot{{{\bf{W}}}}=\alpha \,{{\bf{z}}}\,\bigotimes \,{{\bf{x}}}\)). The output (\({{\bf{y}}}\)) from the synstor circuit controls actuators that modify the system states (\({{\bf{s}}}\)). The goal is to minimize an objective function (\(E=\frac{1}{2}{{{\bf{s}}}}^{2}\)). When \(E\) reaches its minimum, \({{\bf{W}}}=\hat{{{\bf{W}}}}\) and \(\dot{{{\bf{W}}}}=0\). Under this condition, the circuit only executes the inference algorithm \({{\bf{I}}}=\hat{{{\bf{W}}}}{{\bf{x}}}\) in Turing mode.