4 Backpropagation Consider the following network with sigmoid activation functions in the hidden and output neurons, and binary cross entropy loss function. Assume we initialize the weights as follows: W11 = 1, W12 = 0.5, W21 = 0.1, W 22 = 0.2, W 13 = 1, W23 = 0.5. The biases for the hidden nodes are initialized as bl = 0.1, 62 = 0.1, and for the the output node is initialized as 63 = 0.5. Backward pass: Calculate the derivative of the loss w.r.t W11. What's the value of the derivative for the initialized weights, input 1 = 0.1, input 2 = 0.2, and label = 1? How do you update W11 using gradient descent, based on the derivative you derived in the previous part and learning rate ŋ = 0.1? What is the value of the loss using the updated W11? How did it change after the update?

4 Backpropagation Consider the following network with sigmoid activation functions in the hidden and output neurons, and binary cross entropy loss function. Assume we initialize the weights as follows: W11 = 1, W12 = 0.5, W21 = 0.1, W 22 = 0.2, W 13 = 1, W23 = 0.5. The biases for the hidden nodes are initialized as bl = 0.1, 62 = 0.1, and for the the output node is initialized as 63 = 0.5. Backward pass: Calculate the derivative of the loss w.r.t W11. What's the value of the derivative for the initialized weights, input 1 = 0.1, input 2 = 0.2, and label = 1? How do you update W11 using gradient descent, based on the derivative you derived in the previous part and learning rate ŋ = 0.1? What is the value of the loss using the updated W11? How did it change after the update?

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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A neuron j receives inputs from four other neurons whose activity levels are 10, -20, 4 and -2. The respective synaptic weights of neuron j are 0.8, 0.2, -1.0 and -0.9. Calculate the output of neuron j for the following two situations: i. The neuron is linear. ii The neuron is represented by a McCulloch-Pitts model. Assume that the bias applied to the neuron is zero.
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Consider the following procedure for initializing the parameters of a neural network: 1. Pick a random number r r = rand(1,1) * (2 + INIT_EPSILON ) – INIT_EPSILON 2. Set e =r for all i, j,l Does this work? No, because the procedure fails to break symmetry. O b. Yes, unless we are unlucky and get r = 0 (up to numerical precision). O. Yes or no, depending on the training set inputs x(i). d. Yes, because the parameters are chosen randomly.
Consider the diagram below showing a 2-input, one-output neural network. Let the loss function be 76058 a loss function and the output node have sigmoid activation with zero bias. Calculate the loss function L for the AND dataset as a function of wl and w2, and compute the direction of maximum decrease in the loss function. w1 w2 x1 x2
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Draw a feed forward neural network with 3 input neurons, 1 hidden layer including 2 neurons and 2 output neurons. Consider all the weights as -1 and thresholds 0. Run your network to find the output for the vector [1 -1 1]. Use activation function as hard limiter.
Subject: Machine Learning Given the neural network below, calculate and show the weight changes that would be made by one step of BACKPROPAGATION for the training instance (X1,X2)=(0,05,0.10) and (Y1, Y2)=(0.01,0.99). Assume that the hidden (H1 & H2) and output (Y1 & Y2) units use sigmoid functions, the network is being trained to minimize squared error, and the learning rate is 1. Edges from constant b1 and b2 on the side indicate bias parameters.
Please help step by step with explanation for tensorflow code with a final code for understanding thank you.
202F- Consider the following neural network. Assume that outputs 01, 02 are outputs of sigmoid activation functions. Targetl and Target2 are the ground truth for the outputs O1 and 02. Mean Squared Errors is our loss function. Calculate the derivative of the loss with respect to w5. w1 w5 i1 h1 01 w2 w6 w3 w7 i2 h2 02 w4 w8 b1 b2 1 1
Algebraic The Preis AlgorithmThe Preis algorithm solves the maximal weighted matching issue in a weighted network in a novel way. The algorithm is made up of the following phases. 1. Input: A weighted graph G = (V, E, w)2. Output: A maximal weighted matching M of G3. M ← Ø4. E ← E5. V ← V6. while E = Ø7. select at random any v ∈ V8. let e ∈ E be the heaviest edge incident to v9. M ← M ∪ e10. V ← V {v}11. E ← E \ {e and all adjacent edges to e} We will demonstrate two Python implementations of this technique.
Consider the following training set input values x' = (1, x? = (0, х3 (- 1, -0.5, -1)" No. desired output value 1. 0, - 1, 1)" - 1)" -1 2. 1 3. 1 Assume the learning rate is 0.1 and the initial weight vector is w, = (1, -1, 0)". After training draw the neural network.