Convolutional Operation

Vertical Edge Detection

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How it works verticaledgedetected

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edge detected

HorizontalEdge Detection

horizontal filterKennel

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other filteroptions

I O 1 Sobelfilter puts emphasis on the central row pixel2 O 2I O l

3 O 3 Scharerfilter puts emphasis on the central row pixel10 O 103 O 3

flip toget horizontal edgedetection

W WzWs Learn these as parameters such that this

Wy w w gives us a goodedge detector

W W W Learning isevenmore robusthelps learn these features its trying to detectcan learn edges at angles too

Paddingconvolutional

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problems

shrinking output

throwing away info fromedges

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pad with zeros

p padding amount 1 inAn example

Valid Same convolutions

Valid no padding applied

nan f if d ftl x n ftl

same pad so the output is same as the inputsize

nt2p f 1 x fht2p ft fx f t2P ftl x fht2p ftl

f is usually odd

Strided Convolutions

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dimensions

Mxn f xf nt2p f nt2p f1 I tlpaddingp strides s S

Convolutions Over Volume

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wildly channelsto 1 ooo oooI 0 1 ooo oooI 0 1 Ooo ooo

Multiple Filters

verticalfilter

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2differentfilters applied

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dimensionN x n x he f if he n f 11 n th XMc

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of 1 biasparameter perfiter Rf

Rew t b

horizontalfilter

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Notation

If layer 1 is a convolution layer

f filtersize

p padding

s stride

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output n n nMn nd t 2p f

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filter f f not

activations a my xnw n

weights f xf xn xndetothfromlastlayer I t of fitersinlayerd

bias n I l l n

Examplef 3 f 5 f Ss I s z s 2p o p p p olofilters wfilters yofilters

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vectorizing a

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Types of layers in a convolutional network

convolution cow

pooling pool

fully connected Fc

Pooling Layers

Max Poolingf hyper

parameters

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getting thema6 3

from eachcolor

Some of features or activations from previous layerthen max pooling detects a particular feature and

preserves it dueto thehighnumber

no parameters only hyperparameters fixed computation

example

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Average Pooling

f 2S 2

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helps make the sizeof the matrix smaller by taking theaverages

Example of a fullConvolutional Network

convI conv2pool1 pool2 FC3 FLY

7 i i imaxpoolMaxpool Softmax

layer3 layer4layer1 layer 2

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As we take a picture suppose RGB, and we apply a filter/kernel to it, we are able to make that picture go through a filter like edge detections and leave out other features of the image. The image we get is particular to that filter. As we apply more filters/kernels to the image, we can stack these output images and we get images that have certain filters applied to them and these images tend to be smaller in width and height as compared to the actual images.We can view this as a neural network if we try to stack all the pixels of the original picture and connect it to the weights which are the values of the pixels in the filter. The concept of convolutional neural networks is that we connect a lot of these pixels values / input units to the weights / hidden units but not all of them to each one of the hidden units. The missing connections or the less connections help us to end up with an easier network with less parameters than a traditional neural network where all input units are connected to every one of the hidden units.As use this filter to get another image that we feed again to another convolutional network, this helps us separate or individually feed these features to further layers which eventually help us identify what the image is. We train the parameters, i.e the pixel values of the filter, to make new filters that help us detect features important in identifying the image. As we apply the filter we get a part or a feature of the image important for our classification. What pooling does is it helps us to kind of average out and make the size of the height and width smaller to prevent having a large number of parameters. It is like a control check on the network and helps us keep the number of parameters in control.

Why Convolutions

CONV nets have comparatively way lessparameters

Parameter Sharing A feature detector like vertical horizontaledgedetectors are

useful in all partsofthe image

Sparsityof connections ineach layer eachoutputvalue dependsonly ona

small number of inputs

weights

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Pixelmatrix

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Originalimage 02 Weightvalues

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