Description
Q1. ADS Fundamentals [
1a. A vehicle is equipped with a stop-and-go pilot, which can fully operate a vehicle on a highway in traffic jams, but with a fallback-ready user. Which level(s) of driving automation is this driving automation system operating at? [1 mark]
Q2. Computer Vision Fundamentals
2a. Compute 1-D cross-correlation by applying the following filter [0 2 1] to the following signal [0 1 3 0] (assume enough zero padding to show all non-zero output). [2 marks]
2b. Assume that the output of cross-correlating the 1-D filter [2 3 2] with some input signal resulted in the following output signal [7 10 7]. What would be the output signal have we used convolution instead of cross-correlation and why? [1 mark]
. What is the name of the following filter and what is it computing? [1 mark]
. Why is the Canny filter using double thresholding? [1 mark]
g.1 What is each of the individual sinusoids corresponding to in the input image?
Consider the following representation in Hough space (polar coordinates).
| 2h. Which of the following value profiles represent black in HSV? (select all that apply) [1 mark]
1. 0,high,high 2. any,low,low 3. any,low,high 4. 60,high,high 5. any,high,low 6. any,any,low |
Starting with the probabilistic model for linear regression (assume single input x and single out y), show that maximizing the likelihood for a dataset (x, y) (with i.i.d. datapoints) is equivalent to minimizing the sum of squared errors. Hint: go via negative log likelihood [5 marks]
3b. What is the regression loss (as used in class) for a data point with label 0.4 and predicted output 0.7? [1 mark]
Apply what you’ve learned in lecture and Assignment 2) Given the following set of input vector X, ground truth vector Y, and weight matrices W1, W2, B1, and B2 of a 2 layer fully connected neural network, what is the inference probability of the correct class? What is the cross-entropy loss value? Assume ReLU activation on the first hidden layer and softmax activation on the output layer. Show each step of the computation. Hint: Use numerically stable softmax and assume e−1 ≈ 0.37 and e−7 ≈ 0.00 [5 marks]
3d. Consider the computational graph below for the following function
f(x1, x2) = ln(3x1 + e2x2) (8)
Draw the computational graph and annotate it with the forward pass (above the arrows) and backward pass (below the arrows) for x1 = 1 and x2 = 0 (propagate the gradient back to each function input). Recall
dex = ex (9) dx
dln(x) 1
= (10) dx x
Assume ln(4) ≈ 1.39 [5 marks]
Consider a convolutional layer with an input volume of depth 4 and output volume of depth 128. How many convolutional filters does the layer contain? What is the depth of each filter? [2 marks]
