CS7015 (Deep Learning) : Lecture 11 Convolutional Neural Networks, LeNet, AlexNet, ZF-Net, VGGNet, GoogLeNet and ResNet Mitesh M. Khapra Department of Computer Science and Engineering Indian Institute of Technology Madras 1/68 Mitesh M. Khapra CS7015 (Deep Learning) : Lecture 11 Module 11.1 : The convolution operation 2/68 Mitesh M. Khapra CS7015 (Deep Learning) : Lecture 11 1 X xt−aw−a (x∗w)t a=0 input filter convolution Now suppose our sensor is noisy x1 x2 To obtain a less noisy estimate we would like to average several measure- ments st = = More recent measurements are more important so we would like to take a weighted average Suppose we are tracking the position of an aeroplane using a laser sensor at discrete time intervals x0 3/68 Mitesh M. Khapra CS7015 (Deep Learning) : Lecture 11 1 X xt−aw−a (x∗w)t a=0 input filter convolution Now suppose our sensor is noisy x2 To obtain a less noisy estimate we would like to average several measure- ments st = = More recent measurements are more important so we would like to take a weighted average Suppose we are tracking the position of an aeroplane using a laser sensor at discrete time intervals x0 x1 3/68 Mitesh M. Khapra CS7015 (Deep Learning) : Lecture 11 1 X xt−aw−a (x∗w)t a=0 input filter convolution Now suppose our sensor is noisy To obtain a less noisy estimate we would like to average several measure- ments st = = More recent measurements are more important so we would like to take a weighted average Suppose we are tracking the position of an aeroplane using a laser sensor at discrete time intervals x0 x1 x2 3/68 Mitesh M. Khapra CS7015 (Deep Learning) : Lecture 11 1 X xt−aw−a (x∗w)t a=0 input filter convolution To obtain a less noisy estimate we would like to average several measure- ments st = = More recent measurements are more important so we would like to take a weighted average Suppose we are tracking the position of an aeroplane using a laser sensor at discrete time intervals Now suppose our sensor is noisy x0 x1 x2 3/68 Mitesh M. Khapra CS7015 (Deep Learning) : Lecture 11 1 X xt−aw−a (x∗w)t a=0 input filter convolution st = = More recent measurements are more important so we would like to take a weighted average Suppose we are tracking the position of an aeroplane using a laser sensor at discrete time intervals Now suppose our sensor is noisy x0 x1 x2 To obtain a less noisy estimate we would like to average several measure- ments 3/68 Mitesh M. Khapra CS7015 (Deep Learning) : Lecture 11 1 X xt−aw−a (x∗w)t a=0 input filter convolution st = = Suppose we are tracking the position of an aeroplane using a laser sensor at discrete time intervals Now suppose our sensor is noisy x0 x1 x2 To obtain a less noisy estimate we would like to average several measure- ments More recent measurements are more important so we would like to take a weighted average 3/68 Mitesh M. Khapra CS7015 (Deep Learning) : Lecture 11 (x∗w)t input filter convolution Suppose we are tracking the position of an aeroplane using a laser sensor at discrete time intervals Now suppose our sensor is noisy x0 x1 x2 To obtain a less noisy estimate we would like to average several measure- 1 X ments st = xt−aw−a = a=0 More recent measurements are more important so we would like to take a weighted average 3/68 Mitesh M. Khapra CS7015 (Deep Learning) : Lecture 11 input filter convolution Suppose we are tracking the position of an aeroplane using a laser sensor at discrete time intervals Now suppose our sensor is noisy x0 x1 x2 To obtain a less noisy estimate we would like to average several measure- 1 X ments st = xt−aw−a = (x∗w)t a=0 More recent measurements are more important so we would like to take a weighted average 3/68 Mitesh M. Khapra CS7015 (Deep Learning) : Lecture 11 Suppose we are tracking the position of an aeroplane using a laser sensor at discrete time intervals Now suppose our sensor is noisy x0 x1 x2 To obtain a less noisy estimate we would like to average several measure- 1 X ments st = xt−aw−a = (x∗w)t a=0 More recent measurements are more important so we would like to take a input filter weighted average convolution 3/68 Mitesh M. Khapra CS7015 (Deep Learning) : Lecture 11 The weight array (w) is known as the filter We just slide the filter over the input and compute the value of st based on a win- dow around xt s = x w + x w + x w + x w + x w + x w + x w 6 6 0 5 −1 4 −2 3 −3 2 −4 1 −5 Here0 −6 the input (and the kernel) is one dimensional Can we use a convolutional operation on a 2D input also? In practice, we would only sum over a 6 X small window st = xt−aw−a a=0 4/68 Mitesh M. Khapra CS7015 (Deep Learning) : Lecture 11 We just slide the filter over the input and compute the value of st based on a win- dow around xt s = x w + x w + x w + x w + x w + x w + x w 6 6 0 5 −1 4 −2 3 −3 2 −4 1 −5 Here0 −6 the input (and the kernel) is one dimensional Can we use a convolutional operation on a 2D input also? In practice, we would only sum over a 6 X small window st = xt−aw−a The weight array (w) is known as the a=0 filter 4/68 Mitesh M. Khapra CS7015 (Deep Learning) : Lecture 11 Here the input (and the kernel) is one dimensional Can we use a convolutional operation on a 2D input also? In practice, we would only sum over a 6 X small window st = xt−aw−a The weight array (w) is known as the a=0 filter We just slide the filter over the input and compute the value of st based on a win- dow around xt w−6 w−5 w−4 w−3 w−2 w−1 w0 W 0.01 0.01 0.02 0.02 0.04 0.4 0.5 X 1.00 1.10 1.20 1.40 1.70 1.80 1.90 2.10 2.20 2.40 2.50 2.70 S 0.00 1.80 0.00 0.00 0.00 0.00 0.00 s6 = x6w0 + x5w−1 + x4w−2 + x3w−3 + x2w−4 + x1w−5 + x0w−6 4/68 Mitesh M. Khapra CS7015 (Deep Learning) : Lecture 11 Here the input (and the kernel) is one dimensional Can we use a convolutional operation on a 2D input also? In practice, we would only sum over a 6 X small window st = xt−aw−a The weight array (w) is known as the a=0 filter We just slide the filter over the input and compute the value of st based on a win- dow around xt w−6 w−5 w−4 w−3 w−2 w−1 w0 W 0.01 0.01 0.02 0.02 0.04 0.4 0.5 X 1.00 1.10 1.20 1.40 1.70 1.80 1.90 2.10 2.20 2.40 2.50 2.70 S 0.00 1.80 1.96 0.00 0.00 0.00 0.00 s6 = x6w0 + x5w−1 + x4w−2 + x3w−3 + x2w−4 + x1w−5 + x0w−6 4/68 Mitesh M. Khapra CS7015 (Deep Learning) : Lecture 11 Here the input (and the kernel) is one dimensional Can we use a convolutional operation on a 2D input also? In practice, we would only sum over a 6 X small window st = xt−aw−a The weight array (w) is known as the a=0 filter We just slide the filter over the input and compute the value of st based on a win- dow around xt w−6 w−5 w−4 w−3 w−2 w−1 w0 W 0.01 0.01 0.02 0.02 0.04 0.4 0.5 X 1.00 1.10 1.20 1.40 1.70 1.80 1.90 2.10 2.20 2.40 2.50 2.70 S 0.00 1.80 1.96 2.11 0.00 0.00 0.00 s6 = x6w0 + x5w−1 + x4w−2 + x3w−3 + x2w−4 + x1w−5 + x0w−6 4/68 Mitesh M. Khapra CS7015 (Deep Learning) : Lecture 11 Here the input (and the kernel) is one dimensional Can we use a convolutional operation on a 2D input also? In practice, we would only sum over a 6 X small window st = xt−aw−a The weight array (w) is known as the a=0 filter We just slide the filter over the input and compute the value of st based on a win- dow around xt w−6 w−5 w−4 w−3 w−2 w−1 w0 W 0.01 0.01 0.02 0.02 0.04 0.4 0.5 X 1.00 1.10 1.20 1.40 1.70 1.80 1.90 2.10 2.20 2.40 2.50 2.70 S 0.00 1.80 1.96 2.11 2.16 0.00 0.00 s6 = x6w0 + x5w−1 + x4w−2 + x3w−3 + x2w−4 + x1w−5 + x0w−6 4/68 Mitesh M.