Suppose that we use sigmod activation function and square loss function: (t- o)2. The learning rate is a. Derive the formulae for updating Vij and Wij using the gradient descent learning strategy in the backward propagation. For simplicity, we don't have bias in our neural network.

B. Suppose we wish to animate a bouncing ball. We are given keyframes for the ball's motion. The key frames are at times T = {0, 3, 9, 15} with associated height values of H = {1, 6, 8, 3}. 1. Plot the graph of height versus time using linear interpolation between key frames. 2. Since the ball's speed changes as it falls and as it bounces, linear interpolation will not give a realistic result. Which method would create the most realistic bounce? And how would the graph look like? H 16- 14- 12- 10- 8- 6- 4- 2- 0- →T 4 6 8. 10 12 14 16

Implement a Convolutional Neural Network (CNN) using the structure provided in the image. Use the given MNIST dataset located in the "dataset" folder, and refer to the "read-mnist-dataset.ipynb" notebook for loading the data. Include Dropout and Batch Normalization in the network: Use Cross-Entropy Loss for classification. Select filter sizes, numbers, strides, and paddings. Avoid excessive parameters to keep training efficient. Analyze the following for each layer: Number of parameters Number of multiplications Sizes of input and output tensors Train the CNN on the MNIST training set and evaluate on the test set. The model must achieve at least 95% accuracy on the test set; adjust hyperparameters if necessary. Plot the cross-entropy loss for both the training and test sets over epochs, with the x-axis as iterations/epochs and y-axis as loss. Use PyTorch for all implementation. Dataset loading code: import numpy as npimport structfrom array import arrayfrom os.path import join #…

Trace the Perceptron algorithm for the following input. Suppose the actual labels are with respect to a line in 4-dimensional space passing through the origin with normal vector w* = (-1, 2, -3, 2); for example, the true label of (1, 1, 0, 1) is '+1' and that of (0, 0, 1, 1) is '-1' Assume the current weight function at time t is w₁ = (2, 1, -1, 1), and the next point is x₁ = (1, 0, 2, 2). What is the updated weight function w++ 1 at the end of round t? You must follow the same assumptions as in the example of Module 10. In particular, you need to normalize. the example. a. None of the other answers are correct. O b. (7/3,1,-1/3,5/3) ○ c. (-7/3, 1, -5/3, 1/3) d. (-5/3, 1, -1/3, 5/3) e. (5/3, 1, -5/3, 1/3) f. (-2, 4/3, -5/3, 1/3) g. (-2, 1, −1, 1) Oh. (-2, 2/3, -1/3, 5/3)

(1) Draw a transition graph for the dfa M={ Q,E, 8.q..F), where Q={g,.g1-42}. E= {a, b}, F = {q1} and ô is defined as S(q0, a) = q1- 8(q0, b) = q0, 8(q1, b) = q1. 8(q1, a) = q2, 8(q2, b) = q2, ô(q2, a) = q2 (2) Give the language accepted by the above dfa.

Suppose we are fitting a neural network with three hidden layers to a training set. It is found that the cross validation error Jcv(0) is much larger than the training error Jtrain (0). Should we increase the number of hidden layers?

dont dont answer if you are not sure dont post

Choose one answer. In deep neural networks, the vanishing gradient problem occurs because Select one: a. the gradient of the sigmoid is close to zero in the saturated regions. b. the error term of neurons close to the output is computed by multiplying the gradient several times. c. the error term of neurons close to the input is computed by multiplying the gradient several times. d. a and b e. a and c f. b and c

We know that in analogy with the response properties of V1 in the primary visual cortex, simple and complex cells are simulated in the HMAX model. The computation for simple cells is to take the sum over the inputs, while for complex cells is to take max over its inputs. We denote the two operations as S-filter and C-filter, respectively. Given a 3-by-3 array A, it is firstly passed through a layer of C-filters then a layer of S-filters. Compute the output array in the end. Assume the receptive field size of both S- and C-filters is 3-by-3, they move pixel-wisely on their input. The array is padded with zeros if necessary for the filtering. 6.0 10.0 10.0 A = 10.0 7.0 5.0 9.0 5.0 3.0 ANSWER: The output array B =

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.