Neural networks often have many parameters that need to be optimised. Suppose that in a simple...

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Neural networks often have many parameters that need to be optimised. Suppose that in a simple case a particular neural network has just two parameters z and y that satisfy y < 4 and a + y < 25. An analyst establishes that the performance function of the network is f(x,y) = (x + y)3/2-6(x + y)+9y. (a) Find Vf(x,y). (b) Find the Hessian matrix H(r. y) for f(x,y). (c) Locate and classify all stationary points of f(x, y). (d) At what values of r, y is the network performance maximised? (e) At what values of x, y is the network performance minimised? (f) In which direction if the function f decreasing most rapidly when (x, y)=(,1)? Neural networks often have many parameters that need to be optimised. Suppose that in a simple case a particular neural network has just two parameters z and y that satisfy y < 4 and a + y < 25. An analyst establishes that the performance function of the network is f(x,y) = (x + y)3/2-6(x + y)+9y. (a) Find Vf(x,y). (b) Find the Hessian matrix H(r. y) for f(x,y). (c) Locate and classify all stationary points of f(x, y). (d) At what values of r, y is the network performance maximised? (e) At what values of x, y is the network performance minimised? (f) In which direction if the function f decreasing most rapidly when (x, y)=(,1)?

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a To find Vfx y we need to take the gradient of fx y with respect to x and y Vfx y fx fy Taking the ... View the full answer