Neural Networks - Algorithms, Applications,and ... - Csbdu.in

8.2 ART1 315In this case, the equilibrium activities are X = (-0.25, -0.25, -0.087. -0.25,0.051)' with only one positive activity. The new output pattern is (0,0,0,0, 1)',which exactly matches the input pattern, so no reset occurs.Even though unit 2 on F 2 had previously encoded an input pattern, it getsreceded now to match the new input pattern that is a subset of the originalpattern. The new weight matrices appear as follows. For F\,0 0 0.756 0.756 0.756 0.7560 0 0.756 0.756 0.756 0.7560 0 0.756 0.756 0.756 0.7561 0 0.756 0.756 0.756 0.7560 1 0.756 0.756 0.756 0.756For F 2 ,0 0 0 1 00 0 0 0 10.329 0.329 0.329 0.329 0.3290.329 0.329 0.329 0.329 0.3290.329 0.329 0.329 0.329 0.3290.329 0.329 0.329 0.329 0.329If we return to the superset vector, (0,0,1,0,1)', the initial forward propagationto F 2 yields activities of (0.000, 1.000,0.657,0.657,0.657,0.657)*, sounit 2 wins again. Going back to F\, V = (0,0,0,0,1)*, and the equilibriumactivities are (-0.25, -0.25, -0.071, -0.25,0.051)'. The new outputs are(0,0,0,0,1)'. This time, we get a reset signal, since |S|/|I 2 = 0.5 < p. Thus,unit 2 on F 2 is removed from competition, and the matching cycle is repeatedwith the original input vector restored on F\.Propagating forward a second time results in activities on F 2 of (0.000,0.000,0.657, 0.657,0.657,0.657)*, where we have forced unit 2's activity tozero as a result of sustained inhibition from the orienting subsystem. We chooseunit 3 as the winner this time, and it codes the input vector. On subsequentpresentations of subset and superset vectors, each will access the appropriate F 2unit directly without the need of a search. This result can be verified by directcalculation with the example presented in this section.Exercise 8.6: Verify the statement made in the previous paragraph that thepresentation of (0,0,1,0, 1)' and (0,0,0,0,1)' result in immediate access tothe corresponding nodes on F 2 without reset by performing the appropriatecalculations.Exercise 8.7: What does the weight matrix on F 2 look like after unit 3 encodesthe superset vector given in the example in this section?Exercise 8.8: What do you expect will happen if we apply (0, 1, 1,0, 1)' to theexample network? Note that the pattern is a superset to one already encoded.Verify your hypothesis by direct calculation.