Alert dont submit AI generated answer.data mining According to the Neural Network structure shown in the following figure, and assumethat:1. All weights are set as: 0.50.2*x, x < 02. Activation function is LeakyReLU: f(x) = {0.2 *n-x, x ≥03. Loss function is defined as: L = ½-½ 11(y; — ŷ;)², where y; is the ground truth and ŷiis the output of the Neural Network.W₁₁(Σ(Σx1ΣΣΣŷ(Σ(Σ)Given a dataset D = {(x1,y1), (x2, y2), (X3, Y3), (x4, Y4)}, and• x₁ = (1,3), y₁ = 5• x2 = (-1,2), y₂ = 3• x3 = (2,6), y3 = 7•x4 = (4,2), y = 2Q1: [15%] [Forward Propagation] calculate the corresponding output ŷ1, ŷ2, Ŷ3, ŷ4JLQ2: [20%] [Backward Propagation] calculate the loss function and gradient: (redweight in the structure)aw 1

Q1: For X₁ = (1,3): z₁ = (1 * 0.5) + (3 * 0.5) = 2 ŷ₁ = f(z₁) = f(2) = 2 For X₂ =…

Answered: According to the Neural Network…

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter12: Review Of Calculus And Probability

Section12.5: Random Variables, Mean, Variance, And Covariance

Problem 5P

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Computer Science A way to avoid overfitting in Deep Neural Networks is to add an additional term R to the loss function L (for example L can be the cross entropy loss) as follows: L(w) + λR(w). (1) You know that one choice for R is the L2 norm, i.e. R(w) = ||w||2 2 . One friend of yours from the School of Maths told you however that there’s no need to use squares (i.e. powers of two) and that you can achieve the same effect by using absolute values, i.e. the L1 norm: R(w) = ||w||1. Would you agree with him? i.e. is the use of the L2 norm equivalent to using the L1 norm for regularization purposes? Justify your answer
2: Back propagation: Consider the following neural network. Single-circled nodes denote variables (e.g. æ1 is an input variable, hy is an intermediate variable, y is an output variable), and double-circled nodes denote functions (e.g. Σ takes the sum of its inputs, and ♂ denotes the logistic function σ(x) = 1+e-x. In the network below, hi = l+e-T1w1T2W2 · 1 1 W1 = -1.7 Cloon Σ W2 = 0.1 1 h - 0.6 oblood Σ S2 W4 = - 1.8 W5 = ww 0.2 = 0.5 3
Q. Idempotency law isI. P Ú P = P.II. P Ù P = P.III. P + P = P.(a) Only (I) above(b) Only (II) above(c) Only (III) above(d) Both (I) and (II) above
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Let M be the PDA defined by Q = {q, q0 , q1 , q2}, Σ = {a,b}, Γ = {a}, F := {q , q1}.δ(q0 , a , Z0) = {(q, Z0 ) } δ(q , a, Z0) = {(q , aZ0)} δ(q , a, a) = {(q , aa)} δ(q , b , a) = {(q1 ,e)} δ(q1 , b , a) = {(q1 ,e)} δ(q1 , b, Z0 ) = {(q2 , e)} Describe the CFG and the language accepted by M
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A produce dealer has a warehouse that stores a variety of fruits. He wants a machine capable of sorting the fruit according to the type. There is a conveyor belt on which the fruit is loaded. It is then passed through a set of sensors which measure 3 properties of the fruit: shape, texture, and weight. The sensor system is somehow rather primitive: • Shape sensor : -1 if the fruit is round and 1 if it is more elliptical• Texture sensor : -1 if the surface is smooth, 1 if it is rough• Weight sensor : -1 if the fruit is > 500g, 1 if is < 500g The sensor output will then be input to a Neural Networks based classifying system. As an AI Engineer you are supposed to design (draw the architecture and determine the optimal weight W and bias b) a simple neural network (could be a single perceptron) that can be used to recognize the fruit so that it can be directed to the correct storage bin. As a startup case, the simple network will only be used for two type of fruit i.e. banana and…

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