A one-dimensional loss surface is given by
f(x)=3x4−4x3−12x2+5f(x) = 3x^4 - 4x^3 - 12x^2 + 5f(x)=3x4−4x3−12x2+5
You plan to minimise it with gradient descent, using a small learning rate, from various random initialisations.
Which statement about this loss surface is correct?
Select all that apply.
fff is convex, so gradient descent converges to the same point, x=2x = 2x=2, from every initialisation.
fff is not convex: x=−1x = -1x=−1 and x=2x = 2x=2 are both local minima, only x=2x = 2x=2 is global, and f(2)=−27f(2) = -27f(2)=−27.
fff is not convex: x=−1x = -1x=−1 and x=2x = 2x=2 are both local minima, and x=−1x = -1x=−1 is the global one because f(−1)=0f(-1) = 0f(−1)=0 is below f(0)=5f(0) = 5f(0)=5.
fff is not convex, but x=0x = 0x=0 is its only critical point, so gradient descent always ends up at x=0x = 0x=0, where f=5f = 5f=5.