Figure 3.

The XOR gate. (a) Schematic of the XOR logic gate; the orange and purple cells are the inputs, and the green cell is the output; the grey cells are intermediate cells offering computational support. (b) The XOR rule table: output is depolarized only when one of its inputs, but not both, is depolarized. Table specifies the output V_mem for various combinations of input V_mem levels; this is known as the “truth table” in the Boolean logic literature, where the “hyperpolarized” state (around −80 mV) is indicated as “0”, “False” or “OFF” and the “depolarized” state (around +80 mV) as “1”, “True” or “ON”. (c) Pareto front of training errors over time (one unit is equal to a single training epoch) for the XOR gate. This plot depicts the “front” with the best errors achieved over time. This figure demonstrates that the training does indeed result in learning, but fewer networks are successful compared to AND (Fig. 2). (d) Behavior of the best XOR gate. Shown here are the time series of the input and output nodes of the gate, shown for all four input-output conditions generated in a random sequence. The red and blue lines represent the states of the two input nodes, and green represents the output. The grey triangles mark the time points at which the inputs are switched to a different state. (e) The dynamical phase space of the gate: a depiction of a set of trajectories in the input-output space, illustrated in a time-lapse style. This dynamical system has two attractors in the output space, highlighted in filled red (depolarized state) and blue (hyperpolarized state) circles. The trajectories look straight because the inputs are fixed, and only the output changes.