According to the Neural Network structure shown in the following figure, and assume that: 1. All weights are set as: 0.5 0.2*x, x < 0 2. Activation function is LeakyReLU: f(x) = {0.2 * n - x, x ≥0 3. Loss function is defined as: L = ½-½ 11(y; — ŷ;)², where y; is the ground truth and ŷi is the output of the Neural Network. W₁₁ (Σ (Σ x1 Σ Σ Σ ŷ (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 = 2 Q1: [15%] [Forward Propagation] calculate the corresponding output ŷ1, ŷ2, Ŷ3, ŷ4 JL Q2: [20%] [Backward Propagation] calculate the loss function and gradient: (red weight in the structure) aw 1
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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 answerThe following Boolean function: f(x1, x2, x3) = 1 if and only if exactly one of x1, x2 and x3 is 1. Construct by hand a neural network that computes f, using the minimal number of units. Make sure to specify what sort of units you are using. Prove that the function f defined in (i) is not implementable with a single perceptron.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
- For (∃ x)(P(x,b)) Would an example of this being true if the domain was all the Avengers and x was green skin, then "b" being the Hulk would make this true. Am example of this being false would be: If the domain was all integers and x was positive, even integers and "b" was integers greater than zero.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 MTraining neural networks requires two steps. In the forward pass we compute the output of the network and the loss given the input, and in the backward pass we compute the derivatives for all the parameters given the loss, and the values computed in the forward pass. Assume some instance, some target value and, and that you are using squared error loss. Write pseudocode for the forward and backward pass. You may use a separate variable for each node in the network, or store all the values of one layer in a list or similar datastructure.
- Write python code for this : Prepare a Dataset of 300 samples of Random Values of two Variables in range(1-1000). Let’s call these variables as X and Y such that X > Y. The Values of Remainder and Quotient is to be calculated for each sample (X, Y) pair such that Remainder = X % Y and Quotient = X / Y. Design a Neural Network Architecture and Pipeline that can take X and Y as input as input and Predict the values of Remainder and Quotient. You are to choose which Error Function you should be using. Derive the weight update Equations. Train the model for above generated Dataset for 10 epochs for all weights of the network using Python code from scratch and show the weight updates. Also, verify if this reduces the error or not.Consider a perceptron that has two real- valued inputs and an output unit that uses a Sigmoid function as its output function. All the initial weights and the output unit's threshold equal 0.2 Assume that the output should be 0 for the input in1 = 2 and .in2 = 5 Let (the learning rate) be 0.5 %3D Show the value of the all weights and the .output after 2 iteration the new weights the output isUsing R codes 3.6 Let X be a random variable with pmf given by p(x) = 1/10 for a = 1,..., 10 and p(x) = 0 for all other values of x. Find E[X] and confirm your answer using a simulation.
- In deep learning models, the activation function refers to a function in an artificial neuron (node) that delivers an output based on inputs. Activation functions in artificial neurons (nodes) are an important part of the role that the artificial neurons (nodes) play in modern artificial neural networks. One of the most popular activation functions for regression tasks is the rectified linear unit, or ReLU. Mathematically, the ReLU is defined as: х, x >0 0, x<0 Write a function called relu(x) that will perform the ReLU activation function on a given vector x. The function should return the output of the activation function. If X = -4:1:3, what is relu(X)?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…Algorithm: JP in algebra G(V, E), a directed or undirected network, as an input for algorithm 12: Results3: s=0, 4: wt 0, 5: s(1)=, 6: , 7: d = D(1,:), and 8: while s =10: s(i) = ; 11: w, p >=d; 9: i=argmins+d; (i)12: d(u) = wt Plus wt;13: π(i) = pd = d.min A(i,:); 14; 15; The aforementioned Python version of the algebraic algorithm