Steven Pinker -- How the Mind Works - Hampshire High Italian ...

110 I HOW THE MIND WORKSup its inputs and get the right answer. Here is how it can be done forexclusive-or:Cy) AxorB.6/ NO 2(AorB) (5), Y5) (AandB).6 >v -4The two hidden units between the input and the output calculateuseful intermediate products. The one on the left computes the simplecase of "A or B," which in turn simply excites the output node. The oneon the right computes the vexing case of "A and B," and it inhibits theoutput node. The output node can simply compute "(A or B) and not (Aand B)," which is well within its feeble powers. Note that even at themicroscopic level of building the simplest demons out of toy neurons,internal representations are indispensable; stimulus-response connectionsare not enough.Even better, a hidden-layer network can be trained to set its ownweights, using a fancier version of the perceptron learning procedure. Asbefore, a teacher gives the network the correct output for every input, andthe network adjusts the connection weights up or down to try to reducethe difference. But that poses a problem the perceptron did not have toworry about: how to adjust the connections from the input units to thehidden units. It is problematic because the teacher, unless it is 1 a mindreader, has no way of knowing the "correct" states for the hidden units,which are sealed inside the network. The psychologists David Rumelhart,Geoffrey Hinton, and Ronald Williams hit on a clever solution. The outputunits propagate back to each hidden unit a signal that represents thesum of the hidden unit's errors across all the output units it connects to("you're sending too much activation," or "you're sending too little activation,"and by what amount). That signal can serve as a surrogate teachingsignal which may be used to adjust the hidden layer's inputs. The connectionsfrom the input layer to each hidden unit can be nudged up or downto reduce the hidden unit's tendency to overshoot or undershoot, giventhe current input pattern. This procedure, called "error back-propagation"or simply "backprop," can be iterated backwards to any number of layers.