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Fig. 2 shows the activations in the three hidden units of a shallow network. The slopes in the hidden units are 1.0, 1.0, and -1.0, respectively, and the joints in the hidden units are at positions 1/6, 2/6, and 4/6. Find values of ϕ0, ϕ1, ϕ2, and ϕ3 that will combine the hidden unit activations as ϕ0+ϕ1h1+ϕ2h2+ϕ3h3 to create a function with four linear regions that oscillate between output values of zero and one. The slope of the leftmost region should be positive, the next one negative, and so on. How many linear regions will we create if we compose this network with itself? How many will we create if we compose it with itself K times?
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Fig. 2 shows the activations in the three hidden units of a shallow network. The slopes in the hidden units are
1.0, 1.0, and -1.0, respectively, and the joints in the hidden units are at positions 1/6, 2/6, and 4/6. Find values
of ϕ0, ϕ1, ϕ2, and ϕ3 that will combine the hidden unit activations as ϕ0+ϕ1h1+ϕ2h2+ϕ3h3 to create a function
with four linear regions that oscillate between output values of zero and one. The slope of the leftmost region
should be positive, the next one negative, and so on. How many linear regions will we create if we compose this
network with itself? How many will we create if we compose it with itself K times?
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