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Say that a function f : R" → R is convex if and only if f((1 t)x+ty) ≤ (1 – t)f(x) + tf(y) for t = [0, 1] and all x, y € R¹. Select all that are true.

Say that a function f : R" → R is convex if and only if f((1 t)x+ty) ≤ (1 – t)f(x) + tf(y) for t = [0, 1] and all x, y € R¹. Select all that are true.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Let us analyze the linearity and convexity of deep neural networks. Recall that a function g: R" → Rm is linear if for all a, b € R, and x, y € R", g(ax +by) = ag(x) + bg(y). Say that a function f: R" → R is convex if and only if f((1 t)x+ty) ≤ (1 – t)f(x) + tf(y) for t = [0, 1] and all x, y € R". Select all that are true. The following fully connected network without activation functions is linear: g3 (92(91(x))), where gi(x) = Wix and W; are matrices Leaky ReLU = max{0.01x, x} is convex A combination of ReLUs such as ReLU(x) – ReLU(x - 1) is convex ResNet-50, which has ReLU activations, is nonlinear and convex (assume only 1 output activation).
Transcribed Image Text:Let us analyze the linearity and convexity of deep neural networks. Recall that a function g: R" → Rm is linear if for all a, b € R, and x, y € R", g(ax +by) = ag(x) + bg(y). Say that a function f: R" → R is convex if and only if f((1 t)x+ty) ≤ (1 – t)f(x) + tf(y) for t = [0, 1] and all x, y € R". Select all that are true. The following fully connected network without activation functions is linear: g3 (92(91(x))), where gi(x) = Wix and W; are matrices Leaky ReLU = max{0.01x, x} is convex A combination of ReLUs such as ReLU(x) – ReLU(x - 1) is convex ResNet-50, which has ReLU activations, is nonlinear and convex (assume only 1 output activation).
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The following fully connected network without activation functions is linear: g3(g2(g1(x))), where gi(x) = Wi x, and Wi are matrices.

  • True. This is because the output of each layer is simply a linear combination of the inputs.
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