2733 lines
52 KiB
Plaintext
2733 lines
52 KiB
Plaintext
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\end_header
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\begin_body
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\begin_layout Title
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\size giant
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Convolutional Neural Networks with DIGITS
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\end_layout
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\begin_layout Author
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Andy Pack
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\end_layout
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EEEM063
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\begin_inset Newline newline
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May 2021
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\size large
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Department of Electrical and Electronic Engineering
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Faculty of Engineering and Physical Sciences
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University of Surrey
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\end_layout
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\begin_layout Abstract
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Investigations are made into 3 broad influences on a convolutional neural
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network's performance including the subject dataset, hyper-parameters and
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architecture.
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These investigations were conducted using the Stanford Cars dataset and
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the seminal AlexNet architecture.
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The proportions of dataset dedicated to training, validation and testing
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were varied with higher accuracy obtained by heavily biasing towards testing.
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Offline data augmentation was investigated by expanding the training dataset
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using rotations and horizontal flips.
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This significantly increased performance.
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A peak in accuracy was identified when varying the number of epochs with
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overfitting occuring beyond this critical epoch value.
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Various learning rate schedules were investigated with dynamic learning
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rates throughout the training period far out-performing a fixed learning
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rate.
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Finally, the architecture of the network was investigated by varying the
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dimensions of the final dense layers, the kernel size of the convoluional
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layers and by including new layers.
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All of these investigations were able to report higher accuracy than the
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standard AlexNet.
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\begin_layout Right Footer
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Andy Pack / 6420013
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\end_layout
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\begin_layout Left Footer
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May 2021
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\end_layout
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EEEM063 Coursework
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\begin_layout Section
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Introduction
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\end_layout
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\begin_layout Standard
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Although much of the theory for convolutional neural networks (CNNs) was
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developed throughout the 20th century, their importance to the field of
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computer vision was not widely appreciated until the early 2010s
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\begin_inset CommandInset citation
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LatexCommand cite
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key "alexnet"
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literal "false"
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\end_inset
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.
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\end_layout
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\begin_layout Standard
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Although CNNs can appear opaque when attempting to understand how decisions
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are made, they are not black boxes and there are many ways to affect a
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model's performance.
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This work presents investigations into how a CNN's performance is affected
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by the subject dataset, the architecture of the network and the parameters
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used when training.
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Section
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "sec:Investigations-Scope"
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plural "false"
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caps "false"
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noprefix "false"
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\end_inset
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outlines the scope of the investigations made herein, describing the motivation
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for the variations and expectations as to how this would affect performance.
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The results for these investigations are presented in section
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "sec:Results"
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plural "false"
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caps "false"
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noprefix "false"
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\end_inset
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with interpretations made in the following section.
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Section
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LatexCommand ref
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reference "sec:Conclusions"
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plural "false"
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caps "false"
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noprefix "false"
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\end_inset
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summarises and concludes the work.
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\end_layout
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\begin_layout Section
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Investigations Scope
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\begin_inset CommandInset label
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LatexCommand label
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name "sec:Investigations-Scope"
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\end_inset
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\end_layout
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\begin_layout Standard
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The investigations presented in this work use the Stanford Cars dataset
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\begin_inset CommandInset citation
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LatexCommand cite
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key "cars"
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literal "false"
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\end_inset
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, a selection of 16,185 images of 196 different classes of car.
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In terms of network architecture, the seminal AlexNet
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\begin_inset CommandInset citation
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LatexCommand cite
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key "alexnet"
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literal "false"
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\end_inset
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was used as the template for the investigations presented.
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\end_layout
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\begin_layout Subsection
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Dataset Processing
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\end_layout
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\begin_layout Standard
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Prior to more in-depth investigations, how the dataset is divided into training,
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validation and test data was investigated in order to identify a suitable
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proportion for later work.
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As a fixed size dataset, a balance must be struck between how much is reserved
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for training the network and how much should be used to evaluate the network
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\begin_inset CommandInset citation
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LatexCommand cite
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key "glassbox-train-props"
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literal "false"
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\end_inset
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.
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Throughout this paper, the term
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\emph on
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split
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\emph default
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will be used to denote a single division of the dataset into the three
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required subsets.
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\end_layout
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\begin_layout Standard
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Although the dataset is of a fixed size, there are methods to artificially
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expand the set of training data by performing image manipulations such
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as rotations and zooms
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\begin_inset CommandInset citation
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LatexCommand cite
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key "tds-alexnet,learnopencv-alexnet"
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literal "false"
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\end_inset
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.
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This aims to teach the network invariance to such transforms during classificat
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ion.
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A Python script was written to take a training dataset and perform a range
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of manipulations in order to create a synthetically larger training set.
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The expansion factor,
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\begin_inset Formula $E$
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\end_inset
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, is used to described the scale factor for the new dataset's size.
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The ideal rotation angle was investigated by rotating all images by a given
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value.
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\end_layout
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\begin_layout Subsection
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Meta-Parameters
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\end_layout
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\begin_layout Standard
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The number of epochs that a network is trained for is important for balancing
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the fit to the training set.
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Too few and the CNN will be underfitted whereas too many and the network
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will be too specific to the training set.
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\end_layout
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\begin_layout Standard
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The learning rate of a CNN is critical for attaining high-performance results
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\begin_inset CommandInset citation
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LatexCommand cite
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key "tds-lr-schedules"
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literal "false"
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\end_inset
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.
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The value and how it changes over the range of training epochs or the
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\emph on
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learning schedule
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\emph default
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are investigated.
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A fixed learning rate will first be evaluated before varying the parameter
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as a function of epochs in the form of a sigmoid function, exponential
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decay and a step-down schedule with a step,
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\begin_inset Formula $S=33\%$
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\end_inset
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for two steps at 1/3 and 2/3 of the total epochs.
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These learning schedules were evaluated over 50 and 100 epochs to investigate
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how this affects test accuracy.
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\end_layout
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\begin_layout Subsection
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Network Architectures
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\end_layout
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\begin_layout Subsubsection
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Convolutional Layers
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\end_layout
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\begin_layout Standard
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The convolutional layers of AlexNet are responsible for applying subsequent
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image manipulations by convolving the sample with a kernel of learned parameter
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s
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\begin_inset CommandInset citation
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LatexCommand cite
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key "cmabridge-cnns"
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literal "false"
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\end_inset
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.
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The kernel size of each layer was varied in order visualise performance.
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\end_layout
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\begin_layout Subsubsection
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Fully-Connected Layers
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\end_layout
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\begin_layout Standard
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Following the convolutional stages there are three dense or fully-connected
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layers which provide two key features in image classification.
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The first is flattening the 2D cross-section of the preceding convolutional
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layers into a 1D representation for propagation to a final one-hot vector
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output.
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The second is as a traditional multi-layer perceptron classifier, taking
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the high-level visual insights of the later convolutional layers and reasoning
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these into a final classification
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\begin_inset CommandInset citation
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LatexCommand cite
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key "learnopencv-alexnet"
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literal "false"
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\end_inset
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.
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\end_layout
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\begin_layout Standard
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When treated as an MLP, these can instead be considered as 2 hidden layers
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and a single output layer for AlexNet.
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As the last layer is of a fixed number of nodes equal to the number of
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classes and is required to form the one-hot vector output, it is treated
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separately to the others.
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Within this paper, when reporting the number of fully-connected layers
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it is the number of hidden layers without the output layer.
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\end_layout
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\begin_layout Subsection
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New Layers
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\end_layout
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\begin_layout Standard
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It has been shown that the early layers (~1-3 in AlexNet) of CNNs are responsibl
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e for identifying low-level features such as edges while the latter layers
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(~3-5) perform higher level reasoning including texture
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\begin_inset CommandInset citation
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LatexCommand cite
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key "cmabridge-cnns"
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literal "false"
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\end_inset
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.
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The addition of a new layer in both of these regions of the network was
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investigated.
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Reasonable values for kernel sizes and number of layers were selected consideri
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ng the values from the neighbouring layers.
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\end_layout
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\begin_layout Section
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Results
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\begin_inset CommandInset label
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LatexCommand label
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name "sec:Results"
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\end_inset
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\end_layout
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\begin_layout Subsection
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Dataset
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\end_layout
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\begin_layout Subsubsection
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Train/Validation/Test Proportions
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Top-1 and Top-5 test accuracy for different train/validation/test proportions
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\begin_inset CommandInset label
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name "fig:split-barh"
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Different splits of the cars dataset were made, the test accuracies can
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be seen in figure
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LatexCommand ref
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reference "fig:split-barh"
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plural "false"
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caps "false"
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noprefix "false"
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\end_inset
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and the number of images in each subset can be seen in appendix
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\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "sec:Dataset-Image-Counts"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
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|
|
\end_inset
|
|
|
|
.
|
|
A fixed learning rate of 0.001 was used over 100 epochs.
|
|
Increasing the proportion of data reserved for training the model can be
|
|
seen to increase the classification accuracy while varying the proportion
|
|
between the test and validation split had little effect.
|
|
The 80/10/10 split was deemed an appropriate balance of proportions and,
|
|
unless otherwise stated, the 80/10/10 split is used for later experiments.
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Data Augmentation
|
|
\end_layout
|
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\begin_layout Standard
|
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\begin_inset Float figure
|
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wide false
|
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sideways false
|
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status open
|
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\begin_layout Plain Layout
|
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\noindent
|
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\align center
|
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\begin_inset Float figure
|
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wide false
|
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sideways false
|
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status open
|
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|
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\begin_layout Plain Layout
|
|
\noindent
|
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\align center
|
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\begin_inset Graphics
|
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filename ../cars/data-aug-investigations/rot-accuracy.png
|
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lyxscale 30
|
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width 50col%
|
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|
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\end_inset
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\end_layout
|
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\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
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|
|
\begin_layout Plain Layout
|
|
Batch size = 128, AlexNet's default
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:rot-128b"
|
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\end_inset
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\end_layout
|
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\end_inset
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\end_layout
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\end_inset
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\begin_inset Float figure
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
|
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\noindent
|
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\align center
|
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\begin_inset Graphics
|
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filename ../cars/data-aug-investigations/rot-accuracy-256batch.png
|
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lyxscale 30
|
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width 50col%
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\end_inset
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\end_layout
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\begin_layout Plain Layout
|
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\begin_inset Caption Standard
|
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\begin_layout Plain Layout
|
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Batch size = 256
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:rot-256b"
|
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
|
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\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
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|
|
\begin_layout Plain Layout
|
|
Test accuracies for different rotation degrees when augmenting the training
|
|
set with fixed or dynamic batch size
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:rot-accuracy"
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|
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\end_inset
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\end_layout
|
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\end_inset
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\end_layout
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\end_inset
|
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|
|
\end_layout
|
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|
|
\begin_layout Standard
|
|
Test results for varied degrees of rotation when augmenting the training
|
|
data can be seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:rot-accuracy"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
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|
|
.
|
|
In
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:rot-128b"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
, the batch size was set to 128, the default value and one used for the
|
|
unaugmented experiment for comparison later.
|
|
Figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:rot-256b"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
doubles the batch size to match the doubled training dataset.
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:data-aug-best-barh"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
presents the test accuracies for different training pre-processing methods
|
|
including flipping the image horizontally and the best reported results
|
|
from the rotation experiment.
|
|
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:data-aug-best-barh-128E"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
reports results with the previously described scaling of batch size with
|
|
training set size to maintain a constant number of network changes throughout
|
|
\begin_inset Foot
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
A batch size of
|
|
\begin_inset Formula $6\times128=768$
|
|
\end_inset
|
|
|
|
for
|
|
\emph on
|
|
full
|
|
\emph default
|
|
processing could not fit into the memory of the test equipment and as such
|
|
a batch accumulation of 6 was used to simulate the larger batch size.
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
.
|
|
|
|
\emph on
|
|
Full
|
|
\emph default
|
|
pre-processing significantly expanded the training dataset by rotating
|
|
the image both clockwise and counter-clockwise by the given degrees and
|
|
then flipping both the rotated and original images for an expansion factor
|
|
of 6.
|
|
With the fixed batch size (
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:data-aug-best-barh-fixed"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
), augmenting the dataset more than doubled the accuracy.
|
|
Rotation performed better than flipping the images while the described
|
|
|
|
\emph on
|
|
full
|
|
\emph default
|
|
combination performing best.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
With a constant number of network updates (figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:data-aug-best-barh-128E"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
), data augmentation still performed better than the unaugmented dataset
|
|
however the performance was not as high as with a constant batch size.
|
|
Full processing performed worse than either flipping or rotating in this
|
|
case but still performed better than the unaugmented control.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../cars/data-aug-investigations/best-barh.png
|
|
lyxscale 30
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Batch size = 128
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:data-aug-best-barh-fixed"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
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|
|
\end_layout
|
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|
|
\end_inset
|
|
|
|
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../cars/data-aug-investigations/best-barh-256batch.png
|
|
lyxscale 30
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Batch size =
|
|
\begin_inset Formula $128E$
|
|
\end_inset
|
|
|
|
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:data-aug-best-barh-128E"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Best top-1 and top-5 test accuracies for different data augmentation methods
|
|
with fixed or dynamic batch size
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:data-aug-best-barh"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Meta-Parameters
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Epochs
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../cars/epochs-accuracy.png
|
|
lyxscale 30
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Test accuracies
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:epochs-accuracy"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../cars/epochs-loss.png
|
|
lyxscale 30
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Final validation loss
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:epochs-loss"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Test results for varied training epochs with a sigmoid learning rate decay
|
|
of
|
|
\begin_inset Formula $\gamma=0.1$
|
|
\end_inset
|
|
|
|
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:epochs-results"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The effect of varying the number of training epochs can be seen visualised
|
|
in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:epochs-results"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
More epochs can be seen to dramatically increase performance until ~70
|
|
epochs, after this the accuracy gradually declines.
|
|
The opposite trend can be seen in the loss of figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:epochs-loss"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Fixed Learning Rate
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../cars/lr-investigations/fixed-accuracy-50e.png
|
|
lyxscale 30
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
50 Epochs
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:fixed-accuracy-50e"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../cars/lr-investigations/fixed-accuracy.png
|
|
lyxscale 30
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
100 Epochs
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:fixed-accuracy-100e"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Test accuracies for fixed learning schedules results
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:fixed-results"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
In order to evaluate different learning rates and learning schedules, initial
|
|
investigations were made across six decades of a fixed learning rate over
|
|
50 and 100 epochs.
|
|
The accuracies and final validation loss can be seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:fixed-results"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
For a fixed learning rate, values between 0.01 and 0.001 gave the best accuracy
|
|
with values both larger or smaller giving a top-1 accuracy less than 10%.
|
|
The highest value between 50 and 100 epochs were comparable at around 33%
|
|
and 35% respectively.
|
|
\begin_inset Note Comment
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
The final validation loss can be seen to generally follow the inverse trend,
|
|
the lowest values lie between 0.01 and 0.001.
|
|
Interestingly, a learning rate of
|
|
\begin_inset Formula $1\times10^{-4}$
|
|
\end_inset
|
|
|
|
had a validation loss that somewhat interpolated the surrounding values
|
|
for
|
|
\begin_inset Formula $1\times10^{-5}$
|
|
\end_inset
|
|
|
|
and
|
|
\begin_inset Formula $1\times10^{-3}$
|
|
\end_inset
|
|
|
|
however the accuracy does not reflect this, instead being much lower at
|
|
2%.
|
|
\begin_inset Flex TODO Note (Margin)
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
reword?
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Step-Down
|
|
\end_layout
|
|
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\begin_layout Standard
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\begin_inset Float figure
|
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wide false
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sideways false
|
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status open
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\begin_layout Plain Layout
|
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\noindent
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\align center
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\begin_inset Float figure
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wide false
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sideways false
|
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status open
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\begin_layout Plain Layout
|
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\noindent
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\align center
|
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\begin_inset Graphics
|
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filename ../cars/lr-investigations/step-down-accuracy-50e.png
|
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lyxscale 30
|
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width 50col%
|
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\end_inset
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\end_layout
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\begin_layout Plain Layout
|
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\begin_inset Caption Standard
|
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\begin_layout Plain Layout
|
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50 Epochs
|
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\end_layout
|
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\end_inset
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\end_layout
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\end_inset
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\begin_inset Float figure
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wide false
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sideways false
|
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status open
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\begin_layout Plain Layout
|
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\noindent
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\align center
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\begin_inset Graphics
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filename ../cars/lr-investigations/step-down-accuracy.png
|
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lyxscale 30
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width 50col%
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\begin_inset Caption Standard
|
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\begin_layout Plain Layout
|
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100 Epochs
|
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Plain Layout
|
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\begin_inset Caption Standard
|
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\begin_layout Plain Layout
|
|
Test accuracies for different step-down learning schedules.
|
|
Step of 1/3 for 2 learning rate drops
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:step-down-accuracy"
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
|
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\begin_layout Standard
|
|
Test accuracies for different step-down learning schedule can be seen in
|
|
figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:step-down-accuracy"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
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|
|
\end_inset
|
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.
|
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Over both 50 and 100 epochs, the step-down scale factor can be seen to
|
|
have little effect on test accuracy.
|
|
\end_layout
|
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|
|
\begin_layout Subsubsection
|
|
Exponential
|
|
\end_layout
|
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|
|
\begin_layout Standard
|
|
Different exponential learning decay rates were investigated, the results
|
|
can be seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:exp-results"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
From these results, a slow decay rate can be seen to give the best results,
|
|
values between 0.95 and 0.99 gave the highest accuracies over both training
|
|
periods.
|
|
Over 50 epochs, the performance drops faster than over 100 epochs as
|
|
\begin_inset Formula $\lambda$
|
|
\end_inset
|
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|
|
decreases.
|
|
\end_layout
|
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\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
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sideways false
|
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status open
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\begin_layout Plain Layout
|
|
\noindent
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\align center
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\begin_inset Float figure
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wide false
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sideways false
|
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status open
|
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\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../cars/lr-investigations/exp-accuracy-50e.png
|
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lyxscale 30
|
|
width 50col%
|
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\end_inset
|
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\end_layout
|
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\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
50 Epochs
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:exp-50e"
|
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\begin_inset Float figure
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wide false
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sideways false
|
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status open
|
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\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../cars/lr-investigations/exp-accuracy.png
|
|
lyxscale 30
|
|
width 50col%
|
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\end_inset
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\end_layout
|
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\begin_layout Plain Layout
|
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\begin_inset Caption Standard
|
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\begin_layout Plain Layout
|
|
100 Epochs
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:exp-100e"
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
|
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|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Test accuracies for different exponentially decaying learning schedules
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:exp-results"
|
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
|
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|
|
\begin_layout Subsubsection
|
|
Sigmoid
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Reasonable values of gamma for the sigmoid function were selected
|
|
\family roman
|
|
\series medium
|
|
\shape up
|
|
\size normal
|
|
\emph off
|
|
\bar no
|
|
\strikeout off
|
|
\xout off
|
|
\uuline off
|
|
\uwave off
|
|
\noun off
|
|
\color none
|
|
up to 0.4, as
|
|
\begin_inset Formula $\gamma$
|
|
\end_inset
|
|
|
|
increases beyond 0.5 the profile tends towards a step action.
|
|
Accuracies over 50 and 100 epochs were evaluated and can be seen in figure
|
|
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:sig-accuracy"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
|
|
\begin_inset Formula $\gamma$
|
|
\end_inset
|
|
|
|
had little effect on performance for 50 epochs with an average top-1 accuracy
|
|
of 40%.
|
|
Over 100 epochs, the performance increased from this value to 47% when
|
|
|
|
\begin_inset Formula $\gamma=0.05$
|
|
\end_inset
|
|
|
|
.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../cars/lr-investigations/sig-accuracy-50e.png
|
|
lyxscale 30
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
50 Epochs
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../cars/lr-investigations/sig-accuracy.png
|
|
lyxscale 30
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
100 Epochs
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Test accuracies for different sigmoid learning schedules
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:sig-accuracy"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
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|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Summary
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
A comparison of the best reported accuracies for the investigated learning
|
|
rate schedules can be seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:lr-best-barh"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
Over both 50 and 100 epochs, a fixed learning rate performed the worst
|
|
while using a learning schedule achieved a ~10% accuracy gain.
|
|
Training for 100 epochs increased the accuracy by between 3% and 7% over
|
|
training for 50 epochs.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../cars/lr-investigations/best-barh-50e.png
|
|
lyxscale 30
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
50 Epochs
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../cars/lr-investigations/best-barh.png
|
|
lyxscale 30
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
100 Epochs
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Best top-1 and Top-5 test accuracies for investigated learning schedules
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:lr-best-barh"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Network Architectures
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Convolutional Kernel Size
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../cars/architecture-investigations/kernel-accuracy.png
|
|
lyxscale 30
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Top-1 test accuracy for different convolutional kernel sizes over 100 epochs
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:kernel-accuracy"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Test accuracies for varied convolutional kernel sizes can be seen in figure
|
|
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:kernel-accuracy"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
with the standard kernel sizes for AlexNet also marked.
|
|
Only one kernel size was changed at a time, the network is a standard AlexNet
|
|
apart from the subject layer.
|
|
In general, varying the kernel size of the earlier layers (1 and 2) had
|
|
little benefit on the accuracy, a kernel size of 3 for layer 1 performed
|
|
particularly bad with a ~7% lower accuracy.
|
|
Higher gains were made in the later layers, where a size of 5 or 7 tended
|
|
to perform better than the standard 3.
|
|
Layer 3 showed both the highest gain with a +6% from the original 3x3 to
|
|
5x5 and the highest loss with -10% from 3x3 to 11x11.
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Fully-Connected Layers
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../cars/architecture-investigations/fc-accuracy.png
|
|
lyxscale 30
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Top-1 test accuracy for different fully-connected layer shapes over 100
|
|
epochs
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:fc-accuracy"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The shape and number of fully-connected layers were varied, test results
|
|
can be seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:fc-accuracy"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
, AlexNet's standard 2 hidden layers each of 4,096 nodes can be seen marked
|
|
for reference.
|
|
Each number of layers shows a peak with a steep ascent and a more gradual
|
|
descent, as the number of layers increases the nodes associated with the
|
|
peak also increases.
|
|
The highest performance was for the standard 2 layers with 512 nodes.
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Additional Layers
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../cars/architecture-investigations/new-layer-kernel-accuracy.png
|
|
lyxscale 30
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Top-1 test accuracy for varied kernel size of additional convolutional layers
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:new-layer"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Test accuracies for varied kernel sizes in additional convolutional layers
|
|
can be seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:new-layer"
|
|
plural "false"
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caps "false"
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noprefix "false"
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\end_inset
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.
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A fixed number of filters was selected to interpolate the values of neighouring
|
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layers.
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A new layer between conv 1 and conv 2, layer 1.5, performed best with a
|
|
3x3 kernel (54%), increasing the size resulted in decreased accuracy.
|
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For layer 3.5, a 5x5 kernel performed best for a top-1 accuracy of 52%.
|
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\end_layout
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\begin_layout Subsubsection
|
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Summary
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\end_layout
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\begin_layout Standard
|
|
A comparison of the best reported accuracies for the investigated architecture
|
|
alterations can be seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:architecture-best-barh"
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plural "false"
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caps "false"
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noprefix "false"
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\end_inset
|
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|
|
.
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Each of the investigated architecture changes was able to outperform AlexNet.
|
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The largest increase was achieved by reducing the number of nodes in the
|
|
2 hidden dense layers from 4,096 to 512 for a ~10% increase to 57%.
|
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\end_layout
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\begin_layout Standard
|
|
\begin_inset Float figure
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
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|
\noindent
|
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\align center
|
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\begin_inset Graphics
|
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filename ../cars/architecture-investigations/best-barh.png
|
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lyxscale 30
|
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width 50col%
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\begin_inset Caption Standard
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\begin_layout Plain Layout
|
|
Best top-1 and Top-5 test accuracies for investigated architectures over
|
|
100 epochs with exponentially decaying learning rate,
|
|
\begin_inset Formula $\lambda=0.98$
|
|
\end_inset
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\begin_inset CommandInset label
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LatexCommand label
|
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name "fig:architecture-best-barh"
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Section
|
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Discussion
|
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\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "sec:Discussion"
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|
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\end_inset
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\end_layout
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|
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\begin_layout Subsection
|
|
Dataset
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
A high training proportion was found to increase the accuracy of the network.
|
|
This is for two major reasons.
|
|
Increasing the number of images for training effectively increases the
|
|
length of training as more images are progagated each epoch.
|
|
Alongside this, increasing the training proportion also provides a more
|
|
complete view of the dataset.
|
|
Higher proportions will allow the network to see more of each class, with
|
|
a significantly lower proportion it would be possible that few if any of
|
|
a class is present in the training dataset.
|
|
The same can be argued for the test sets, however.
|
|
As the test set is reduced in complement to the training set's increase,
|
|
the breadth of qualities being evaluated is reduced as the number of examples
|
|
of each class is reduced.
|
|
This is the core of the balancing act in conducting both comprehensive
|
|
training and testing.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Offline augmentation of the training data proved to be an effective way
|
|
of increasing the accuracy of the evaluated networks.
|
|
When using rotation, small angles were the most effective, in practice
|
|
a random angle between 0 and 10 could be used.
|
|
Data augmentation increases performance as it presents the network with
|
|
different perspectives of the same images.
|
|
As such, the network can learn invariance to factors such as which way
|
|
the car is facing in the image.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The batch size scaling inline with the training set growth was conducted
|
|
in an effort to control for the amount of extra training being conducted.
|
|
When comparing data augmentation methods, difficulty comes in comparing
|
|
processing methods which expand the training set by different amounts.
|
|
Synthetically larger datasets not only present the network with new perspective
|
|
s of the images but also train the network for longer and as such it is
|
|
hard to define how much should be attributed to the
|
|
\emph on
|
|
quality
|
|
\emph default
|
|
of the synthetic data.
|
|
Scaling the batch size so as to maintain the number of network updates
|
|
reduced the accuracy as would be expected when attempting to control for
|
|
more training, however the full processing (
|
|
\begin_inset Formula $E=6$
|
|
\end_inset
|
|
|
|
) was reduced further than the
|
|
\begin_inset Formula $E=2$
|
|
\end_inset
|
|
|
|
processing methods.
|
|
This does not follow the hypothesis as it might be expected that more perspecti
|
|
ves of the training data would improve over a single rotation or flip.
|
|
This suggests that scaling the batch size as described was not a sufficient
|
|
method to control for the longer training periods.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
A method to better control for this in the future could be to define a constant
|
|
expansion factor across processing methods and then compose this extra
|
|
training data of different proportions of augmentations (rotations of varying
|
|
angles and flips) or to use online augmentation such that the images are
|
|
manipulated as they are presented to the network.
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Meta-Parameters
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
As presented, it can be seen that training a network beyond a threshold
|
|
number of epochs leads to diminishing performance as the network overfits
|
|
to the training set.
|
|
This reduces the network's ability to generalise as it effectively learns
|
|
|
|
\emph on
|
|
too much
|
|
\emph default
|
|
about the training data.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
From the comparisons of different learning rate schedules, it can be seen
|
|
from the similar performances that the employed specific function was not
|
|
as important as the need to decay the learning rate itself.
|
|
This is demonstrated in the 10% performance gain when using a dynamic learning
|
|
rate.
|
|
Considering the error surface with local minima that the weight set is
|
|
navigating, initially it is important to make large steps across the surface.
|
|
Towards the end of the training period, however, ideally the network will
|
|
be close to or within a minima.
|
|
At this point, large steps will reduce the performance of the network as
|
|
oscillating jumps over the minima are made instead of settling within.
|
|
By decaying the learning rate, both intentions can be actioned, initially
|
|
taking large steps to find the deepest possible minimum before reducing
|
|
the size of the movements in order to converge into it as opposed to circling
|
|
it.
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Network Architectures
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
From the reported results each investigation outperformed the standard AlexNet
|
|
architecture.
|
|
It is worth specifying the significance of this, however.
|
|
It would be inaccurate from these results to suggest that these derivative
|
|
architectures are better than AlexNet as the performance is a function
|
|
of the dataset, the specific dataset split used, the learning rate schedule
|
|
and number of training epochs.
|
|
Instead what is being stated is that, for the specific values of those,
|
|
a more optimal architecture than the standard AlexNet was found.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Looking to the dense layer shape investigations, each number of layers has
|
|
a similar profile in the described steep rise and gradual descent.
|
|
As the number of layers increases, the number of hidden nodes required
|
|
to achieve the same performance increases.
|
|
This implies a required relation between the dimensions of the dense layers
|
|
to attain acceptable performance as both a deep MLP section of few nodes
|
|
and a shallow MLP of many nodes will not be sufficient.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The higher increase in performance by adding layer 1.5 than 3.5 would suggest
|
|
that more low-level feature learning capacity was more effective for the
|
|
dataset than higher-level capacity.
|
|
Both were higher than the best reported accuracy from varying AlexNet's
|
|
kernel sizes which would suggest that the existing convolutional stages
|
|
were well suited to the dataset as standard.
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Conclusions
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "sec:Conclusions"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Investigations into the factors affecting convolutional neural network have
|
|
been presented.
|
|
The effect of balancing the proportion of data to be partitioned between
|
|
training and testing was investigated.
|
|
Increasing the amount of training data as much as possible was shown to
|
|
increase the accuracy.
|
|
Offline data augmentation using a selection of image rotations and flips
|
|
was shown to more than double the test accuracy.
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
A dynamic learning rate schedule was shown to be important in achieving
|
|
high-performance accuracy as opposed to a fixed value.
|
|
The choice of decay function did not significantly affect the best reported
|
|
accuracy.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Derivative architectures of AlexNet were shown to increase performance when
|
|
altering the dense layers shape, the convolutional kernel sizes and when
|
|
including additional convolutional layers.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Newpage newpage
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "sec:bibliography"
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset CommandInset bibtex
|
|
LatexCommand bibtex
|
|
btprint "btPrintCited"
|
|
bibfiles "references"
|
|
options "bibtotoc"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
\start_of_appendix
|
|
Dataset Image Counts
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "sec:Dataset-Image-Counts"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float table
|
|
placement H
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\noindent
|
|
\align center
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="7" columns="4">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="center" valignment="top">
|
|
<column alignment="center" valignment="top">
|
|
<column alignment="center" valignment="top">
|
|
<column alignment="center" valignment="top">
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
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|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Number of Images
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell multicolumn="2" alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
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\begin_layout Plain Layout
|
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|
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</cell>
|
|
<cell multicolumn="2" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
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\begin_layout Plain Layout
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|
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</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
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\begin_layout Plain Layout
|
|
Split
|
|
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|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Training
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Validation
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Test
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
90/5/5
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
14,566
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
809
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
810
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
80/10/10
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
12,948
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1,618
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1,619
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
70/15/15
|
|
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|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
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|
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\begin_layout Plain Layout
|
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11,329
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|
|
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</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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|
\begin_inset Text
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2,427
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\end_inset
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</cell>
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
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\begin_inset Text
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2,429
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</cell>
|
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</row>
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<row>
|
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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\begin_layout Plain Layout
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50/25/25
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</cell>
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
|
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8,092
|
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|
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\end_inset
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</cell>
|
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
|
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4,046
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</cell>
|
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
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4,047
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</cell>
|
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</row>
|
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<row>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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50/5/45
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</cell>
|
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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\begin_inset Text
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8,092
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</cell>
|
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
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\begin_inset Text
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\begin_layout Plain Layout
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809
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|
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\end_inset
|
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</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
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7,284
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</cell>
|
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</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
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|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
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\begin_layout Plain Layout
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Number of images in each subset for each evaluated split
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\begin_inset CommandInset label
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LatexCommand label
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name "tab:split-image-counts"
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Section
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Training Set Expander Script
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\end_layout
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\begin_layout Standard
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\begin_inset CommandInset include
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LatexCommand lstinputlisting
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filename "../data_aug.py"
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lstparams "caption={Python script for synthetically expanding a DIGITs training set},label={script:data_aug}"
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\end_inset
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\end_layout
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\end_body
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\end_document
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