b) Let an activation function be defined as
Show that What is the value of
at the origin? Also, find the value of
as v approaches
and
Let's go step by step to solve this numerically. ### 1. Given Activation Function \[ \Phi (V) = \frac{1}{1+e^{-aV}}, \quad a > 0 \] ### 2. Derivative of \(\Phi(V)\) We differentiate \(\Phi(V)\) with respect ___ _________ _____ _______ ________ _______ ________ ______ _____ ______ ___.
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b) Write the types of Neural Memory Models. Also, give one example of each.
Consider the set of pattern vectors P. Obtain the connectivity matrix (CM) for the patterns in P (four patterns).
Which of the following statements are true or false? Give a short proof or a counter example in support of your answers.
a) There is chance of occurrence of the premature convergence in Roulett-wheel selection shceme used in GA.
b) Gradient based optimization methods are used when the objective function is not smooth and one needs efficient local optimization.
c) The cut of a fuzzy set A in U is defined as A
d) A single perception with preprocessing is neither an auto associative network nor a multiple layer neural network.
e) If W then perception is non-linear separable.
a) Construct the α − cut at α = 4.0 for the fuzzy sets defined in Q. 1(b)
a) Define Kohonen networks with examples.
a) Consider the following travelling salesman problem involving 9 cities
| Parent 1 | G | J | H | F | E | D | B | I | C |
| Parent 2 | D | C | H | J | I | G | E | F | B |
i) Order crossover #1, assuming and
sites as the crossover sites
ii) Order crossover #2, assuming
and
as the key positions.
b) Let an activation function be defined as
Show that What is the value of
at the origin? Also, find the value of
as v approaches
and