To optimise a neural network can require selecting the best combination of a large set of parameters. For a simple case, suppose that a neural network has just two parameters x and y. The network is only feasible if y ≥ −1, x ≤ 3 and y ≤ x. An analyst establishes that the performance function of the network is f(x,y) = xy² + x² - 4xy. (a) Find Vf(x, y). (b) Find the Hessian matrix H(x, y) for f. (c) Locate and classify all stationary points of f(x, y). (d) Draw a rough sketch showing the feasible region of parameters, along with the locations of the stationary points. (e) For what values of x and y is the maximum performance of the network achieved, and for what values is the minimum achieved?
To optimise a neural network can require selecting the best combination of a large set of parameters. For a simple case, suppose that a neural network has just two parameters x and y. The network is only feasible if y ≥ −1, x ≤ 3 and y ≤ x. An analyst establishes that the performance function of the network is f(x,y) = xy² + x² - 4xy. (a) Find Vf(x, y). (b) Find the Hessian matrix H(x, y) for f. (c) Locate and classify all stationary points of f(x, y). (d) Draw a rough sketch showing the feasible region of parameters, along with the locations of the stationary points. (e) For what values of x and y is the maximum performance of the network achieved, and for what values is the minimum achieved?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. To optimise a neural network can require selecting the best combination of a large set of
parameters. For a simple case, suppose that a neural network has just two parameters x
and y. The network is only feasible if y ≥ −1, x ≤ 3 and y ≤ x. An analyst establishes
that the performance function of the network is
f(x,y) = xy² + x² − 4xy.
(a) Find Vf(x, y).
(b) Find the Hessian matrix H(x, y) for f.
(c) Locate and classify all stationary points of f(x, y).
(d) Draw a rough sketch showing the feasible region of parameters, along with the
locations of the stationary points.
(e) For what values of x and y is the maximum performance of the network achieved,
and for what values is the minimum achieved?
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