Suppose a 2x2 convolution kernel is used in the first layer, a 3x3 convolution kernel is used in the second layer and a 3x3 convolution kernel is used in the third layer. What are the receptive fields of the element of the output of the third layer?
Added by Scott B.
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The receptive field of an element in the output of the second layer is 5x5, since the 3x3 kernel can see a 5x5 region of the input (the output of the first layer). Show more…
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Kernel functions are the functions that map one space to a higher dimensional space. This question demonstrates the primary use of kernel functions in SVM. Consider four points: A = (-1, -1), B = (1, 1), C = (1, -1), D = (-1, 1) and two labels red, blue. Suppose A, B belong to the label red and C, D belong to the label blue. (a) Are labels red and blue linearly separable? Explain your reasoning. (b) Consider the kernel function: ϕ(x) = (x²₁, x²₂, √2x₁x₂, √2x₁, √2x₂, 1) where x = (x₁, x₂). We can observe that this kernel function maps 2-dimensional space to 6-dimensional space. What are the points A, B, C, D after transformation? (c) Are labels red and blue linearly separable after the transformation? Explain your reasoning.
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