An Artificial Neural Network contains 2 neurons in the Input Layer (called neuron 0 and neuron 1), 2 neurons in the middle layer or hidden layer (called neuron 2 and neuron 3), and one neuron in the output layer (neuron 4). The depiction shows the structure of this Neural Network 5.9 46
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- The language must be in python. Neural Network Units weights of [-1.2, -1.1, 3.3, -2.1] two training examples:Example 1: [0.9, 10.0, 3.1, 1]Example 2: [0.9, 2.1, 3.7, 1] Note that you don't have to explicitly include a threshold or bias since the examples include a last element of 1 which means that the last weight effectively operates as a threshold. Create a single ReLU unit and provide the outputs for those examples. Calculate the derivative of the sigmoid with respect to net input for both examples Calculate the derivative of the ReLU with respect to net input for both examplesConsider the (directed) network in the attached document We could represent this network with the following Prolog statements: link(a,b). link(a,c). link(b,c). link(b,d). link(c,d). link(d,e). link(d,f). link(e,f). link(f,g). Now, given this network, we say that there is a "connection" from a node "X" to a node "y" if we can get from "X" to "Y" via a series of links, for example, in this network, there is a connection from "a" to "d", and a connection from "c" to "f", etc.Consider a fully-connected artificial neural network with one hidden layer, i.e., a multilayer perceptron (MLP), which has 5 inputs, 3 neurons in the hidden layer, and 1 output neuron. The relation between the output y and the inputs x = [x1, . . . , x5] is given by y(x) = f (w, φ(x)), where φ(x) = [φ1(x), φ2(x), φ3(x)] 1. Draw the diagram that shows the inputs, nuerons, connections, correspond-ing weight parameters, and activation functions. 2. Explain the relation y(x) = f (w, φ(x)): write the explicit relation, explainthe role of functions f and φ(x), and state examples of functions.
- Two layers neural networks consist of 3 input neurons and one output neuron. The input vector is (x1, x2, x3) where x3 is always =1.0. x1, x2 and the desired output d are given by the table below. When using the initial weight vector w = (1.0, 1.0, -3.0) there was an error as shown in the figure. The equation for the decision boundary was: x1*1 + x2*1 - 1*3=0. , (i.e. net = x1*w1+x2*w2+x3*w3), f(net) is the sign of net What are the new values of the vector w after the first input (1,1,1), note that input x3 is always 1.0? What are the new values of the vector w after the second input (9.4, 6.4, 1.0)? Suggest a vector w such that the total error is ZERO for the 10 points.Need Help with this code completion. class neural_network: def __init__(self,Nhidden,Ninput,Noutput,Nonlinearities): self.layer = [] # BUILD THE NETWORK # Add a linear layer with Ninput input features and Nhidden output features # YOUR CODE HERE # Add a non-linearity if(Nonlinearities[0]=='relu'): self.layer.append(relu()) else: self.layer.append(sigmoid()) # Add a linear layer # YOUR CODE HERE # Add a non-linearity def forward(self,X): # Forward propagation # YOUR CODE HERE return X def backward(self,dY): # Backward propagation # YOUR CODE HERE return def update(self, learning_rate): # Updating the parameters of the network according to algorithm # YOUR CODE HERE self.layer[0].W = self.layer[0].b =…Prolog Consider the (directed) network in the attached document. We could represent this network with the following Prolog statements: link(a,b). link(a,c). link(b,c). link(b,d). link(c,d). link(d,e). link(d,f). link(e,f). link(f,g). Now, given this network, we say that there is a "connection" from a node "X" to a node "Y" if we can get from "X" to "Y" via a series of links, for example, in this network, there is a connection from "a" to "d", and a connection from "c" to "f", etc. Formulate the appropriate Prolog rule "connection(X,Y)" which is true if (and only if) there is a "connection" from "X" to "Y" as described above --- note that this rule will be recursive. Test this rule out on the above network, to see if it is working correctly. Once it is working correctly, you will note that, e.g., the query "connection(a,e)." will give "true" multiple times. This means something, actually:
- link(a,b). link(a,c). link(b,c). link(b,d). link(c,d). link(d,e). link(d,f). link(e,f). link(f,g). Using the above Formulate the appropriate Prolog predicate "path(X,Y,N)" which is true if (and only if) there is a path of length "N" from node "X" to node "Y". For example, there is a path of length3. Assume a graph G = (V, E) represents a computer network where the vertices represent computers and the edges represent point-to-point network connections between the computers. Assume each edge (u, v) of G is associated with a real number f(u,v) between 0 and 1 which represents the probability that the corresponding network connection is faulty. Assume these probabilities are independent. a. Propose an algorithm that finds a path between two given vertices u and v with the smallest probability of being faulty (a path is faulty if at least one of its edges is faulty). b. Analyze the complexity of your algorithm.Consider a system that handles railway connections as it associates (source) cities to all their corresponding destinations. The requirements of the system are as follows: 1. A source city may have connections to possibly multiple destination cities. 2. Multiple source cities may share the same group of destination cities. We introduce type CITY . A possible state of the system is shown below as it is captured by variable connections:connections ={Montreal → {Ottawa, Kingston, Quebec, Halifax},Ottawa → {Montreal, Toronto},Toronto → {Montreal, Ottawa},Halifax → {Montreal, Quebec},Quebec → {Montreal, Halifax},Kingston → {Montreal}} 1. Is connections a binary relation? Explain why, and if so express this formally. 2. In the expression connections ∈ (...), what would the RHS be? 3. Is connections a function? If so, define the function formally, and reason about the properties of injectivity, surjectivity and bijectivity. 4. Describe the meaning and evaluate the following…
- This paper deals with Extended Huffman Codes. For instance, for a source emitting two symbols A and B, the second order extension involves coding messages AA, AB, BA and BB (2^2 in number). The third order extension involves messages such as AAA, AAB, etc. (2^3 in number). The probabilities of such strings are computed by multiplying the individual probabilities. Calculate third, fourth and fifth order extensions of a source message. 1. Choose an alphabet a set of at least six (6) symbols with assigned probabilities. It can be assigned as [ A=0.3; B= 0.7; C=0.1;D=0.2;E=0.5;F=0.15]. Compute the third, fourth and fifth order extension probabilities. Using the built-in algorithm, derive the Huffman Code for each extension. Compute the following quantities: (i) Average length of the codeword; (ii) The code efficiency; (iii) The Compression Ratio. Note: I am assuming but needs to be verified that if we need are using 6 symbols A to F. 6^3=216, the 6 to the third power comes…Define the neural network a fully connected network with two hidden layers with Nh1 and Nh2 features, respectively. The hidden layers should use relu activation and the final layer should not have any activation. a linear network with no hidden layer. We will use this network to study the benefit of depth, or equivalently using a non-linear network instead of a linear network. The final layer should not have any activation class NeuralNet(N.Module): # YOUR CODE HERE class LinearNet(N.Module): #YOUR CODE HEREConsider the following NFA (M1) over the alphabet Σ = {0, 1}: * Attached Image * Two automata M1 and M2 are said to be equivalent if L(M1) = L(M2). In other words, two machines are equivalent if they accept the same string and reject the same strings. Create a new NFA M2 that is equivalent to M1 but does not use any empty (?) transitions. Hint: Define the transition function by δ: Q x Σ -> ?(Q)