Дълбоко обучение с Tensorflow

Лекция 5. Конволюционни невронни мрежи

Lecture 5

Convolutional Neural Nets

Agenda

• What CNNs Can Do
• Why CNNs
• Convolutional Neural Network Basics
• Convolutional Filters and Weight-Sharing
• Basic CNN Architecture
• Data Augmentation

What Can CNNs Do?

• Image Classification
• Object Detection
• Neural Style Transfer
• Face Recognition
• Image Synthesis

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Image Classification

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Object Detection

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`Neural Style Transfer

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`Neural Style Transfer

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Face Recognition

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Why CNNs?

Different lighting, contrast, viewpoints

Number of Parameters

• 1000x1000 pixel image with three channels then we would have 3 million input features.
• If the first layer has 1000 neurons the neural net with just one layer would have approximately 3 billion parameters.

Traditional Approaches

Traditional Approaches

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CNN Basics

CNN Principles

• Translation invariance - Our network should respond similarly to the same patch, regardless of where it appears in the image.
• Locality principle - Our network should focus on local regions, without regard for the contents of the image in distant regions.

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WbWhat Is a CNN?

• The convolutional neural network (CNN) is a specialized feedforward neural network designed to process multi-dimensional data, e.g., images
• A CNN is a special case of neural networks which uses convolution instead of full matrix multiplication in the hidden layers
• A CNN architecture is typically comprised of convolutional layers, pooling (subsampling) layers, and fully-connected layers (LeNet-5)

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What is a Convolution?

• In each convolutional layer of a CNN, a convolutional operation is performed along with the input of predefined width and strides. Each of these convolutional operations is called a "kernel" or a "filter" and is somewhat equivalent to a "neuron" in an MLP
• An activation function is applied after each convolution to produce the output

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Convolution Operation

• A single unit of a convolutional layer is only connected to a small receptive field of its input, where the weights of its connections define a filter
• The convolution operation is used to slide the filter across the input, producing activations at each receptive field

Convolution Operation

• The shaded portions are the first output element and the input and kernel array elements used in its computation:

0×0+1×1+3×2+4×3=19

Parameters Defining Convolution

Convolutions are defined by two key parameters:

• Size of the filters extracted from the inputs. These are typically 3×3 (most frequently used), or 5×5
• Depth of the output feature map - The number of filters computed by the convolution

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Main Concepts Behind Convolutional Neural Networks

• Sparse-connectivity: A single element in the feature map is connected to only a small patch of pixels. (This is very different from connecting to the whole input image, in the case of multilayer perceptrons.)
• Parameter-sharing: The same weights are used for different patches of the input image.
• Many layers: Combining extracted local patterns to global patterns

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Weight Sharing

• A "feature detector" (filter, kernel) slides over the inputs to generate a feature map
• Rationale: A feature detector that works well in one region may also work well in another region
• A big reduction in parameters to fit
• Multiple "feature detectors" (kernels) are used to create multiple feature maps

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Edge Detection Example

How Do We Choose the Weights of the Filters?

We use Gradient Descent and Backpropagation to find the optimal weights of the different filters.

Padding

• Padding can increase the height and width of the output.
• Padding works by adding an appropriate number of rows and columns on each side of the input feature map
• This is often used to give the output the same height and width as the input to avoid undesirable shrinkage of the output
• Padding ensures that all pixels are used equally frequently.
• Typically we pick symmetric padding on both sides of the input height and width.

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Padding

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Padding

Some padding terminologies:

• “valid” padding: no padding
• “same” padding: padding so that the output dimension is the same as the input

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Stride

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• The distance between two successive windows is a parameter of the convolution, called its stride, which defaults to 1
• It is possible to have strided convolutions: convolutions with a stride higher than 1.

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Stride of 2 Example

Pooling

• Pooling is an exceedingly simple operation. It does exactly what its name indicates, aggregate results over a window of values
• A big difference from convolution is that max-pooling is usually done with 2×2 windows and stride 2, to downsample the feature maps by a factor of 2
• Pooling does not have any learnable parameters

Pooling

Size Before and After Convolutions

Convolutions with Color Channels

Convolutions with Color Channels

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Convolving 6X6X3 with 3X3X3 gives you a 4X4 2D output

Convolutions with Color Channels

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Convolution Operation with Multiple Filters

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• Multiple filters can be used in a convolution layer to detect multiple features.
• The output of the layer then will have the same number of channels as the number of filters in the layer.

Convolution Operation with Multiple Filters

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One Convolution Layer

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Finally to make up a convolution layer, a bias is added and an activation function such as ReLU or tanh is applied.

One Convolution Layer Number of Parameters

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• If you have 10 filters 3x3x3 how many parameters do you have in this layer?
• Does the number of parameters depend on the input size?

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One Convolution Layer Number of Parameters

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If you have 10 filters 3x3x3 how many parameters do you have in this layer?

Weights = 3*3*3 = 27

Bias = 1

Total parameters per filter = 28

Total Params for 10 Filters = 10 * 28 = 280 params

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Basic CNN Architecture

Le Net CNN Architecture

Handwritten digit recognition, developed by Yann Lecun in the 90s.

At a high level, LeNet (LeNet-5) consists of two parts: (i) a convolutional encoder consisting of two convolutional layers; and (ii) a dense block consisting of three fully connected layers;

The basic units in each convolutional block are a convolutional layer, a sigmoid activation function, and a subsequent average pooling operation.

Note that while ReLUs and max-pooling work better, these discoveries had not yet been made at the time.

Each convolutional layer uses a 5×5 kernel.

Hidden Layers

Le Net

Le Net

Illustrated Example

Data Augmentation

Data Augmentation

• Image augmentation generates random images based on existing training data to improve the generalization ability of models.
• In order to obtain definitive results during prediction, we usually only apply image augmentation to training examples, and do not use image augmentation with random operations during prediction.
• Deep learning frameworks provide many different image augmentation methods, which can be applied simultaneously.

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Data Augmentation

Questions?

References

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• Convolutional Neural Networks (Course 4 of the Deep Learning Specialization)
• CS231n: Deep Learning for Computer Vision - Stanford University
• Introduction to Deep Learning by Sebastian Raschka
• Dive into Deep Learning - Zhang, Lipton, Li

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