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44
.gitea/workflows/xelatex.yaml
Normal file
44
.gitea/workflows/xelatex.yaml
Normal file
@@ -0,0 +1,44 @@
|
||||
name: Compile PDF
|
||||
run-name: ${{ gitea.actor }} is compiling a PDF 🚀
|
||||
on: [push]
|
||||
|
||||
jobs:
|
||||
Compile-PDF:
|
||||
runs-on: ubuntu-latest
|
||||
steps:
|
||||
- run: echo "🎉 The job was automatically triggered by a ${{ gitea.event_name }} event."
|
||||
- run: echo "🐧 This job is now running on a ${{ runner.os }} server hosted by Gitea!"
|
||||
- run: echo "🔎 The name of your branch is ${{ gitea.ref }} and your repository is ${{ gitea.repository }}."
|
||||
- name: Check out repository code
|
||||
uses: actions/checkout@v4
|
||||
- run: echo "💡 The ${{ gitea.repository }} repository has been cloned to the runner."
|
||||
- run: echo "🖥️ The workflow is now ready to test your code on the runner."
|
||||
- name: List files in the repository
|
||||
run: |
|
||||
ls ${{ gitea.workspace }}
|
||||
- name: Compile LaTeX document
|
||||
uses: xu-cheng/latex-action@v2
|
||||
with:
|
||||
root_file: cv.tex
|
||||
latexmk_use_xelatex: true
|
||||
- name: List files in the repository
|
||||
run: |
|
||||
ls ${{ gitea.workspace }}
|
||||
- name: Archive artifacs
|
||||
uses: christopherhx/gitea-upload-artifact@v4
|
||||
with:
|
||||
name: thesis
|
||||
path: thesis.pdf
|
||||
- name: Upload to S3
|
||||
uses: bxb100/action-upload@main
|
||||
with:
|
||||
provider: s3
|
||||
provider_options: |
|
||||
root=/
|
||||
region=${{ secrets.S3REGION }}
|
||||
bucket=${{ secrets.S3BUCKET }}
|
||||
endpoint=${{ secrets.S3ENDPOINT }}
|
||||
access_key_id=${{ secrets.S3ACCESSKEY }}
|
||||
secret_access_key=${{ secrets.S3ACCESSSECRET }}
|
||||
include: '*.pdf'
|
||||
- run: echo "🍏 This job's status is ${{ job.status }}."
|
||||
309
.gitignore
vendored
309
.gitignore
vendored
@@ -1,13 +1,308 @@
|
||||
## Core latex/pdflatex auxiliary files:
|
||||
*.pdf
|
||||
*.aux
|
||||
*.fdb_latexmk
|
||||
*.fls
|
||||
*.lof
|
||||
*.log
|
||||
*.synctex.gz
|
||||
*.lot
|
||||
*.fls
|
||||
*.out
|
||||
*.toc
|
||||
*.fmt
|
||||
*.fot
|
||||
*.cb
|
||||
*.cb2
|
||||
.*.lb
|
||||
|
||||
## Intermediate documents:
|
||||
*.dvi
|
||||
*.xdv
|
||||
*-converted-to.*
|
||||
# these rules might exclude image files for figures etc.
|
||||
# *.ps
|
||||
# *.eps
|
||||
# *.pdf
|
||||
|
||||
## Generated if empty string is given at "Please type another file name for output:"
|
||||
.pdf
|
||||
|
||||
## Bibliography auxiliary files (bibtex/biblatex/biber):
|
||||
*.bbl
|
||||
*.bbl-SAVE-ERROR
|
||||
*.bcf
|
||||
*.blg
|
||||
*.thm
|
||||
*-blx.aux
|
||||
*-blx.bib
|
||||
*.run.xml
|
||||
*.toc
|
||||
*.xdv
|
||||
thesis.pdf
|
||||
|
||||
## Build tool auxiliary files:
|
||||
*.fdb_latexmk
|
||||
*.synctex
|
||||
*.synctex(busy)
|
||||
*.synctex.gz
|
||||
*.synctex.gz(busy)
|
||||
*.pdfsync
|
||||
*.rubbercache
|
||||
rubber.cache
|
||||
|
||||
## Build tool directories for auxiliary files
|
||||
# latexrun
|
||||
latex.out/
|
||||
|
||||
## Auxiliary and intermediate files from other packages:
|
||||
# algorithms
|
||||
*.alg
|
||||
*.loa
|
||||
|
||||
# achemso
|
||||
acs-*.bib
|
||||
|
||||
# amsthm
|
||||
*.thm
|
||||
|
||||
# beamer
|
||||
*.nav
|
||||
*.pre
|
||||
*.snm
|
||||
*.vrb
|
||||
|
||||
# changes
|
||||
*.soc
|
||||
|
||||
# comment
|
||||
*.cut
|
||||
|
||||
# cprotect
|
||||
*.cpt
|
||||
|
||||
# elsarticle (documentclass of Elsevier journals)
|
||||
*.spl
|
||||
|
||||
# endnotes
|
||||
*.ent
|
||||
|
||||
# fixme
|
||||
*.lox
|
||||
|
||||
# feynmf/feynmp
|
||||
*.mf
|
||||
*.mp
|
||||
*.t[1-9]
|
||||
*.t[1-9][0-9]
|
||||
*.tfm
|
||||
|
||||
#(r)(e)ledmac/(r)(e)ledpar
|
||||
*.end
|
||||
*.?end
|
||||
*.[1-9]
|
||||
*.[1-9][0-9]
|
||||
*.[1-9][0-9][0-9]
|
||||
*.[1-9]R
|
||||
*.[1-9][0-9]R
|
||||
*.[1-9][0-9][0-9]R
|
||||
*.eledsec[1-9]
|
||||
*.eledsec[1-9]R
|
||||
*.eledsec[1-9][0-9]
|
||||
*.eledsec[1-9][0-9]R
|
||||
*.eledsec[1-9][0-9][0-9]
|
||||
*.eledsec[1-9][0-9][0-9]R
|
||||
|
||||
# glossaries
|
||||
*.acn
|
||||
*.acr
|
||||
*.glg
|
||||
*.glo
|
||||
*.gls
|
||||
*.glsdefs
|
||||
*.lzo
|
||||
*.lzs
|
||||
*.slg
|
||||
*.slo
|
||||
*.sls
|
||||
|
||||
# uncomment this for glossaries-extra (will ignore makeindex's style files!)
|
||||
# *.ist
|
||||
|
||||
# gnuplot
|
||||
*.gnuplot
|
||||
*.table
|
||||
|
||||
# gnuplottex
|
||||
*-gnuplottex-*
|
||||
|
||||
# gregoriotex
|
||||
*.gaux
|
||||
*.glog
|
||||
*.gtex
|
||||
|
||||
# htlatex
|
||||
*.4ct
|
||||
*.4tc
|
||||
*.idv
|
||||
*.lg
|
||||
*.trc
|
||||
*.xref
|
||||
|
||||
# hypdoc
|
||||
*.hd
|
||||
|
||||
# hyperref
|
||||
*.brf
|
||||
|
||||
# knitr
|
||||
*-concordance.tex
|
||||
# TODO Uncomment the next line if you use knitr and want to ignore its generated tikz files
|
||||
# *.tikz
|
||||
*-tikzDictionary
|
||||
|
||||
# listings
|
||||
*.lol
|
||||
|
||||
# luatexja-ruby
|
||||
*.ltjruby
|
||||
|
||||
# makeidx
|
||||
*.idx
|
||||
*.ilg
|
||||
*.ind
|
||||
|
||||
# minitoc
|
||||
*.maf
|
||||
*.mlf
|
||||
*.mlt
|
||||
*.mtc[0-9]*
|
||||
*.slf[0-9]*
|
||||
*.slt[0-9]*
|
||||
*.stc[0-9]*
|
||||
|
||||
# minted
|
||||
_minted*
|
||||
*.pyg
|
||||
|
||||
# morewrites
|
||||
*.mw
|
||||
|
||||
# newpax
|
||||
*.newpax
|
||||
|
||||
# nomencl
|
||||
*.nlg
|
||||
*.nlo
|
||||
*.nls
|
||||
|
||||
# pax
|
||||
*.pax
|
||||
|
||||
# pdfpcnotes
|
||||
*.pdfpc
|
||||
|
||||
# sagetex
|
||||
*.sagetex.sage
|
||||
*.sagetex.py
|
||||
*.sagetex.scmd
|
||||
|
||||
# scrwfile
|
||||
*.wrt
|
||||
|
||||
# svg
|
||||
svg-inkscape/
|
||||
|
||||
# sympy
|
||||
*.sout
|
||||
*.sympy
|
||||
sympy-plots-for-*.tex/
|
||||
|
||||
# pdfcomment
|
||||
*.upa
|
||||
*.upb
|
||||
|
||||
# pythontex
|
||||
*.pytxcode
|
||||
pythontex-files-*/
|
||||
|
||||
# tcolorbox
|
||||
*.listing
|
||||
|
||||
# thmtools
|
||||
*.loe
|
||||
|
||||
# TikZ & PGF
|
||||
*.dpth
|
||||
*.md5
|
||||
*.auxlock
|
||||
|
||||
# titletoc
|
||||
*.ptc
|
||||
|
||||
# todonotes
|
||||
*.tdo
|
||||
|
||||
# vhistory
|
||||
*.hst
|
||||
*.ver
|
||||
|
||||
# easy-todo
|
||||
*.lod
|
||||
|
||||
# xcolor
|
||||
*.xcp
|
||||
|
||||
# xmpincl
|
||||
*.xmpi
|
||||
|
||||
# xindy
|
||||
*.xdy
|
||||
|
||||
# xypic precompiled matrices and outlines
|
||||
*.xyc
|
||||
*.xyd
|
||||
|
||||
# endfloat
|
||||
*.ttt
|
||||
*.fff
|
||||
|
||||
# Latexian
|
||||
TSWLatexianTemp*
|
||||
|
||||
## Editors:
|
||||
# WinEdt
|
||||
*.bak
|
||||
*.sav
|
||||
|
||||
# Texpad
|
||||
.texpadtmp
|
||||
|
||||
# LyX
|
||||
*.lyx~
|
||||
|
||||
# Kile
|
||||
*.backup
|
||||
|
||||
# gummi
|
||||
.*.swp
|
||||
|
||||
# KBibTeX
|
||||
*~[0-9]*
|
||||
|
||||
# TeXnicCenter
|
||||
*.tps
|
||||
|
||||
# auto folder when using emacs and auctex
|
||||
./auto/*
|
||||
*.el
|
||||
|
||||
# expex forward references with \gathertags
|
||||
*-tags.tex
|
||||
|
||||
# standalone packages
|
||||
*.sta
|
||||
|
||||
# Makeindex log files
|
||||
*.lpz
|
||||
|
||||
# xwatermark package
|
||||
*.xwm
|
||||
|
||||
# REVTeX puts footnotes in the bibliography by default, unless the nofootinbib
|
||||
# option is specified. Footnotes are the stored in a file with suffix Notes.bib.
|
||||
# Uncomment the next line to have this generated file ignored.
|
||||
#*Notes.bib
|
||||
|
||||
@@ -8,7 +8,7 @@ I cannot help expressing the deepest gratitude to Harold: even though he was not
|
||||
He is surely a brilliant scientist and a great collaborator, but if he is not first of all a friend then I do not know who can be.
|
||||
I also wish to thank Marco and Carlo for all the support they gave me whenever they could and the advice they provided at all times.
|
||||
|
||||
Life as a Ph.D.\ student would have been incredibly tough were it not for the great people who were with me all the time.
|
||||
Life as a graduate student would have been incredibly tough were it not for the great people who were with me all the time.
|
||||
I was not yet officially inside my Ph.D.\ programme when Alberto welcomed me to the office and showed me how to survive as a student and get the most from the experience as a person.
|
||||
Even though he will not admit it, Riccardo helped me to discover dedication in the darkest moments, while contextually Giovanni taught me how to bring light and humanity in those, in the face of adversities.
|
||||
In all this, with his silence \emph{à la Piemontese}, Francesco represented the needed balance.
|
||||
|
||||
@@ -66,7 +66,7 @@ For larger values of the hyperparameter $\alpha$, $w$ (and $b$) assume smaller v
|
||||
\subsection{Support Vector Machines for Regression}
|
||||
\label{sec:app:svr}
|
||||
|
||||
This family of supervised \ml algorithms were created with classification tasks in mind~\cite{Cortes:1995:SupportvectorNetworks} but have proven to be effective also for regression problems~\cite{Drucker:1997:SupportVectorRegression}.
|
||||
This family of supervised \ml algorithms was created with classification tasks in mind~\cite{Cortes:1995:SupportvectorNetworks} but have proven to be effective also for regression problems~\cite{Drucker:1997:SupportVectorRegression}.
|
||||
Differently from the linear regression, instead of minimising the squared distance of each sample, the algorithm assigns a penalty to predictions of samples $x^{(i)} \in \R^F$ (for $i = 1, 2, \dots, N$) which are further away than a certain hyperparameter $\varepsilon$ from their true value $y$, allowing however a \textit{soft margin} of tolerance represented by the penalties $\zeta$ above and $\xi$ below.
|
||||
This is achieved by minimising $w,\, b,\, \zeta$ and $\xi$ in the function:\footnotemark{}
|
||||
\footnotetext{%
|
||||
|
||||
@@ -125,7 +125,7 @@ that is we just need to consider the left coset where $R_{(t)}$ is a representat
|
||||
=
|
||||
\qty{ R_{(t)} \sim \cO_{(t)} R_{(t)} },
|
||||
\end{equation}
|
||||
where $\cO_{(t)} = \rS\qty( \OO{2} \times \OO{2} )$ is defined as
|
||||
where $\cO_{(t)} \in \rS\qty( \OO{2} \times \OO{2} )$ is defined as
|
||||
\begin{equation}
|
||||
\cO_{(t)}
|
||||
=
|
||||
@@ -349,16 +349,16 @@ One way to deal with them is to introduce the \emph{doubling trick} by gluing th
|
||||
Let then $\cU_{(t,\, t+1)} = U_{(t+1)}\, U_{(t)}$ and $\tcU_{(t,\, t+1)} = U_{(\bart)}\, U_{(t)}\, U_{(t+1)}\, U_{(\bart)}$.
|
||||
The boundary conditions in terms of the doubling field are:
|
||||
\begin{eqnarray}
|
||||
\ipd{z} \cX( x_t + e^{2 \pi i}( \eta + i\, 0^+ ) )
|
||||
\ipd{z} \cX( x_{(t)} + e^{2 \pi i}( \eta + i\, 0^+ ) )
|
||||
& = &
|
||||
\cU_{(t,\, t+1)}
|
||||
\ipd{z} \cX( x_t + \eta + i\, 0^+ ),
|
||||
\cU_{(t,\, t+1)}\,
|
||||
\ipd{z} \cX( x_{(t)} + \eta + i\, 0^+ ),
|
||||
\label{eq:top_monodromy}
|
||||
\\
|
||||
\partial \cX( x_t + e^{2 \pi i}( \eta - i\, 0^+ ) )
|
||||
\ipd{z} \cX( x_{(t)} + e^{2 \pi i}( \eta - i\, 0^+ ) )
|
||||
& = &
|
||||
\tcU_{(t,\, t+1)}
|
||||
\ipd{z} \cX( x_t + \eta - i\, 0^+ ),
|
||||
\tcU_{(t,\, t+1)}\,
|
||||
\ipd{z} \cX( x_{(t)} + \eta - i\, 0^+ ),
|
||||
\label{eq:bottom_monodromy}
|
||||
\end{eqnarray}
|
||||
for $0 < \eta < \min\qty( \abs{x_{(t-1)} - x_{(t)}}, \abs{x_{(t)} - x_{(t+1)}} )$ in order to consider only the two adjacent D-branes $D_{(t)}$ and $D_{(t+1)}$.
|
||||
|
||||
@@ -2039,7 +2039,7 @@ Using the algebra~\eqref{eq:ns-algebra} we compute the \ope of fermion fields as
|
||||
\qquad
|
||||
\abs{w} < \abs{z},
|
||||
\end{equation}
|
||||
where the operation $\no{\cdot}$ is the normal ordering with respect to the \SL{2}{R} vacuum defined in~\eqref{eq:NS_SL2_vacuum}.
|
||||
where the operation $\no{\cdot}$ is the normal ordering with respect to the \SL{2}{\R} vacuum defined in~\eqref{eq:NS_SL2_vacuum}.
|
||||
We then get the expression of the stress-energy tensor:
|
||||
\begin{equation}
|
||||
\begin{split}
|
||||
@@ -2189,7 +2189,7 @@ From the usual definition of the stress-energy tensor in terms of the Virasoro g
|
||||
\end{split}
|
||||
\end{equation}
|
||||
|
||||
We already hinted to the fact that the vacua state involved are not in general \SL{2}{R} invariant.
|
||||
We already hinted to the fact that the vacua state involved are not in general \SL{2}{\R} invariant.
|
||||
In particular we can see that that the excited vacua \eexcvacket is a primary field
|
||||
\begin{equation}
|
||||
\begin{split}
|
||||
@@ -2394,7 +2394,7 @@ The last expression shows that the energy momentum tensor $\cT( z )$ is radial t
|
||||
First of all we notice that the vacuum $\Gexcvacket$ is actually $\GGexcvacket$, i.e.\ it depends only on $x_{(t)}$ and $\rE_{(t)}$.
|
||||
We can try to interpret the previous result in the light of the usual \cft approach.
|
||||
In particular we can refine the idea we discussed after~\eqref{eq:asymp_beha_Psi_on_exc_vac} that the singularity in the modes~\eqref{eq:generic-case-basis} and~\eqref{eq:generic-case-basis-conjugate} at the point $x_{(t)}$ is associated with a primary conformal operator which creates \eexcvacket with $\rE = \rE_{(t)}$.
|
||||
By comparison with the stress energy tensor of an excited vacuum~\eqref{eq:T_excited_vacuum}, from the second order singularity we learn that at the points $x_{(t)}$ there is an operator which creates the excited vacuum \GGexcvacket from the \SL{2}{R} vacuum \regvacuum.
|
||||
By comparison with the stress energy tensor of an excited vacuum~\eqref{eq:T_excited_vacuum}, from the second order singularity we learn that at the points $x_{(t)}$ there is an operator which creates the excited vacuum \GGexcvacket from the \SL{2}{\R} vacuum \regvacuum.
|
||||
Given the discussion in the previous section this is an excited spin field $\rS_{\rE_{(t)}}\qty( x_{(t)}) = e^{i \rE_{(t)} \phi( x_{(t)} )}$.
|
||||
The first order singularities in $x_{(u)} - x_{(t)}$ are then the result of the interaction between two of the previous excited spin fields.
|
||||
Using the \cft operator approach we postulate that the following identification holds
|
||||
@@ -2818,7 +2818,7 @@ Therefore we have
|
||||
\end{equation}
|
||||
which can be solved by
|
||||
\begin{equation}
|
||||
\ln \left\langle
|
||||
\left\langle
|
||||
\rR\qty[%
|
||||
\rS_{\rE_{(t)}}\qty(x_{(t)})
|
||||
\prod\limits_{\substack{u = 1 \\ u \neq t}}^N
|
||||
@@ -2828,7 +2828,7 @@ which can be solved by
|
||||
=
|
||||
\cN_0
|
||||
\qty( \qty{\rE_{(t)}} )
|
||||
\prod\limits_{\substack{t = 1}{t > u}}^N
|
||||
\prod\limits_{\substack{t = 1 \\ t > u}}^N
|
||||
\qty( x_{(u)} - x_{(t)} )^{\rE_{(u)} \rE_{(t)}}.
|
||||
\end{equation}
|
||||
The constant $\cN_0\qty( \qty{\rE_{(t)}} )$ which depends on the $\rE_{(t)}$ only can be fixed by using the \ope
|
||||
|
||||
@@ -42,7 +42,7 @@ While Nambu and Goto's formulation is fairly direct in its definition, it is usu
|
||||
\eta_{\mu\nu}.
|
||||
\label{eq:conf:polyakov}
|
||||
\end{equation}
|
||||
The \eom for the string $X^{\mu}\qty(\tau, \sigma)$ is therefore:
|
||||
The \eom for the string $X^{\mu}\qty(\tau, \sigma)$ are therefore:
|
||||
\begin{equation}
|
||||
\frac{1}{\sqrt{- \det \gamma}}\,
|
||||
\ipd{\alpha}
|
||||
@@ -572,19 +572,21 @@ which show that $c_{\text{ghost}} = - 26$.
|
||||
The central charge is therefore cancelled in the full theory (bosonic string and reparametrisation ghosts) when the spacetime dimensions are $D = 26$.
|
||||
In fact let $\cT_{\text{full}} = \cT + \cT_{\text{ghost}}$ and $\overline{\cT}_{\text{full}} = \overline{\cT} + \overline{\cT}_{\text{ghost}}$, then:
|
||||
\begin{equation}
|
||||
\eval{\cT_{\text{full}}( z )}_{\order{(z - w)^{-4}}}
|
||||
=
|
||||
\eval{\overline{\cT}_{\text{full}}( \barz )}_{\order{(\barz - \barw)^{-4}}}
|
||||
=
|
||||
c + c_{\text{ghost}}
|
||||
=
|
||||
\frac{D}{2} - 13
|
||||
=
|
||||
0
|
||||
\quad
|
||||
\Leftrightarrow
|
||||
\quad
|
||||
D = 26.
|
||||
\begin{split}
|
||||
\eval{\cT_{\text{full}}( z ) \cT_{\text{full}}( z )}_{\order{(z - w)^{-4}}}
|
||||
=
|
||||
\eval{\overline{\cT}_{\text{full}}( \barz ) \overline{\cT}_{\text{full}}( \barz )}_{\order{(\barz - \barw)^{-4}}}
|
||||
& =
|
||||
\frac{c + c_{\text{ghost}}}{2}
|
||||
\\
|
||||
& =
|
||||
\frac{D}{2} - 13
|
||||
=
|
||||
0
|
||||
\\
|
||||
& \Leftrightarrow
|
||||
D = 26.
|
||||
\end{split}
|
||||
\end{equation}
|
||||
$\cT_{\text{full}}$ and $\overline{\cT}_{\text{full}}$ are then primary fields with conformal weight $-2$.
|
||||
|
||||
@@ -695,19 +697,21 @@ These are conformal fields with conformal weights $\qty( \frac{3}{2},\, 0 )$ and
|
||||
Their central charge becomes $c_{\text{ghost}} = c_{bc} + c_{\beta\gamma} = -26 + 11 = -15$ (see \cref{note:conf:ghosts} for the general computation).
|
||||
When considering the full theory $\cT_{\text{full}} = \cT + \cT_{\text{ghost}}$ and $\overline{\cT}_{\text{full}} = \overline{\cT} + \overline{\cT}_{\text{ghost}}$ the central charge vanishes only in 10-dimensional spacetime:
|
||||
\begin{equation}
|
||||
\eval{\cT_{\text{full}}( z )}_{\order{(z - w)^{-4}}}
|
||||
=
|
||||
\eval{\overline{\cT}_{\text{full}}( \barz )}_{\order{(\barz - \barw)^{-4}}}
|
||||
=
|
||||
c + c_{\text{ghost}}
|
||||
=
|
||||
\frac{3}{2}\, D - 15
|
||||
=
|
||||
0
|
||||
\quad
|
||||
\Leftrightarrow
|
||||
\quad
|
||||
D = 10.
|
||||
\begin{split}
|
||||
\eval{\cT_{\text{full}}( z ) \cT_{\text{full}}( z )}_{\order{(z - w)^{-4}}}
|
||||
=
|
||||
\eval{\overline{\cT}_{\text{full}}( \barz ) \overline{\cT}_{\text{full}}( \barz )}_{\order{(\barz - \barw)^{-4}}}
|
||||
& =
|
||||
\frac{c + c_{\text{ghost}}}{2}
|
||||
\\
|
||||
& =
|
||||
\frac{3}{4}\, D - \frac{15}{2}
|
||||
=
|
||||
0
|
||||
\\
|
||||
& \Leftrightarrow
|
||||
D = 10.
|
||||
\end{split}
|
||||
\label{eq:super:dimensions}
|
||||
\end{equation}
|
||||
|
||||
@@ -1280,7 +1284,7 @@ The field $\cA^a$ forms a vector representation of the group \SO{D-1-p} and from
|
||||
\end{figure}
|
||||
|
||||
It is also possible to add non dynamical degrees of freedom (\dof) to the open string endpoints.
|
||||
They are known as \emph{Chan-Paton factors}~\cite{Paton:1969:GeneralizedVenezianoModel}.
|
||||
They are known as \emph{Chan-Paton factors}~\cite{Chan:1969:GeneralizedVenezianoModel}.
|
||||
They have no dynamics and do not spoil Poincaré or conformal invariance in the action of the string.
|
||||
Each state can then be labelled by $i$ and $j$ running from $1$ to $N$.
|
||||
Matrices $\tensor{\lambda}{^a_{ij}}$ thus form a basis for expanding wave functions and states:
|
||||
|
||||
@@ -12,7 +12,7 @@ In fact in~\cite{Liu:2002:StringsTimeDependentOrbifold} the four tachyons amplit
|
||||
\begin{equation}
|
||||
A_4 \sim \int\limits_{q \sim \infty} \frac{\dd{q}}{\abs{q}} \ccA( q )
|
||||
\end{equation}
|
||||
where $\ccA_{\text{closed}}( q ) \sim q^{4 - \ap \norm{\vec{p}_{\perp}}^2}$ and $\ccA_{\text{closed}}( q ) \sim q^{1 - \ap \norm{\vec{p}_{\perp}}^2} \tr\qty( \liebraket{T_1}{T_2}_+ \liebraket{T_3}{T_4}_+ )$ ($T_i$ for $i = 1,\, 2,\, 3,\, 4$ are Chan-Paton matrices).
|
||||
where $\ccA_{\text{closed}}( q ) \sim q^{4 - \ap \norm{\vec{p}_{\perp}}^2}$ and $\ccA_{\text{open}}( q ) \sim q^{1 - \ap \norm{\vec{p}_{\perp}}^2} \tr\qty( \liebraket{T_1}{T_2}_+ \liebraket{T_3}{T_4}_+ )$ ($T_i$ for $i = 1,\, 2,\, 3,\, 4$ are Chan-Paton matrices).
|
||||
Moreover divergences in string amplitudes are not limited to four points: interestingly we show that the open string three point amplitude with two tachyons and the first massive state may be divergent when some \emph{physical} polarisations are chosen.
|
||||
The true problem is therefore not related to a gravitational issue but to the non existence of the effective field theory.
|
||||
In fact when we express the theory using the eigenmodes of the kinetic terms some coefficients do not exist, not even as a distribution.
|
||||
@@ -21,7 +21,7 @@ The issue can be roughly traced back to the vanishing volume of a subspace and t
|
||||
|
||||
As an introduction to the problem we first deal with singularities of the open string sector.
|
||||
We try to build a consistent scalar \qed and show that the vertex with four scalar fields is ill defined.
|
||||
Divergences in scalar QED are due to the behaviour of the eigenfunctions of the scalar d'Alembertian near the singularity but in a somehow unexpected way.
|
||||
Divergences in scalar \qed are due to the behaviour of the eigenfunctions of the scalar d'Alembertian near the singularity but in a somehow unexpected way.
|
||||
Near the singularity $u = 0$ in lightcone coordinates almost all eigenfunctions behave as $\frac{1}{\sqrt{\abs{u}}} e^{i \frac{\cA}{u}}$ with $\cA \neq 0$.
|
||||
The product of $N$ eigenfunctions gives a singularity $\abs{u}^{-N/2}$ which is technically not integrable.
|
||||
However the exponential term $e^{i \frac{\cA}{u}}$ allows for an interpretation as distribution when $\cA = 0$ is not an isolated point.
|
||||
@@ -3547,7 +3547,7 @@ Differently from the \nbo, in this case the orbifold generator~\eqref{eq:nbo_kil
|
||||
\kappa & = - 2 \pi i \Delta\, J_{+2} - 2 \pi i R P_3
|
||||
\\
|
||||
& =
|
||||
2 \pi\, (\Delta\, \ipd{z} + R,\ \ipd{3}).
|
||||
2 \pi\, (\Delta\, \ipd{z} + R\, \ipd{3}).
|
||||
\end{split}
|
||||
\end{equation}
|
||||
with metric
|
||||
|
||||
150
thesis.bib
150
thesis.bib
@@ -4,8 +4,7 @@
|
||||
author = {Abadi, Martín and Agarwal, Ashish and Barham, Paul and Brevdo, Eugene and Chen, Zhifeng and Citro, Craig and Corrado, Greg S. and Davis, Andy and Dean, Jeffrey and Devin, Matthieu and Ghemawat, Sanjay and Goodfellow, Ian and Harp, Andrew and Irving, Geoffrey and Isard, Michael and Jia, Yangqing and Jozefowicz, Rafal and Kaiser, Lukasz and Kudlur, Manjunath and Levenberg, Josh and Mané, Dandelion and Monga, Rajat and Moore, Sherry and Murray, Derek and Olah, Chris and Schuster, Mike and Shlens, Jonathon and Steiner, Benoit and Sutskever, Ilya and Talwar, Kunal and Tucker, Paul and Vanhoucke, Vincent and Vasudevan, Vijay and Viégas, Fernanda and Vinyals, Oriol and Warden, Pete and Wattenberg, Martin and Wicke, Martin and Yu, Yuan and Zheng, Xiaoqiang},
|
||||
date = {2015},
|
||||
url = {https://www.tensorflow.org/},
|
||||
file = {/home/riccardo/.local/share/zotero/files/abadi_et_al_2015_tensorflow.pdf},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/abadi_et_al_2015_tensorflow.pdf}
|
||||
}
|
||||
|
||||
@article{Abel:2003:FlavourChangingNeutral,
|
||||
@@ -59,7 +58,6 @@
|
||||
eprint = {hep-th/0612110},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/abel_goodsell_2007_realistic_yukawa_couplings_through_instantons_in_intersecting_brane_worlds8.pdf},
|
||||
keywords = {⚠️ Invalid DOI},
|
||||
number = {10}
|
||||
}
|
||||
|
||||
@@ -293,8 +291,7 @@
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {1808.04730},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/ardizzone_et_al_2019_analyzing_inverse_problems_with_invertible_neural_networks.pdf;/home/riccardo/.local/share/zotero/storage/NQJPI658/1808.html},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/ardizzone_et_al_2019_analyzing_inverse_problems_with_invertible_neural_networks.pdf;/home/riccardo/.local/share/zotero/storage/NQJPI658/1808.html}
|
||||
}
|
||||
|
||||
@article{Arduino:2020:OriginDivergencesTimeDependent,
|
||||
@@ -400,8 +397,7 @@
|
||||
volume = {13},
|
||||
pages = {281--305},
|
||||
file = {/home/riccardo/.local/share/zotero/files/bergstra_bengio_2012_random_search_for_hyper-parameter_optimization.pdf},
|
||||
issue = {Feb},
|
||||
keywords = {⛔ No DOI found}
|
||||
issue = {Feb}
|
||||
}
|
||||
|
||||
@article{Berkooz:1996:BranesIntersectingAngles,
|
||||
@@ -673,9 +669,8 @@
|
||||
@online{Caffo::DataScienceSpecialization,
|
||||
title = {Data {{Science Specialization}}},
|
||||
author = {Caffo, Brian and Leek, Jeff and Peng, Roger D.},
|
||||
journaltitle = {Coursera},
|
||||
url = {https://www.coursera.org/specializations/jhu-data-science},
|
||||
keywords = {⛔ No DOI found}
|
||||
organization = {{Coursera}}
|
||||
}
|
||||
|
||||
@inproceedings{Calabi:1957:KahlerManifoldsVanishing,
|
||||
@@ -729,8 +724,7 @@
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {1909.08699},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/caramello_jr_2019_introduction_to_orbifolds.pdf;/home/riccardo/.local/share/zotero/storage/N6FSCMLT/1909.html},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/caramello_jr_2019_introduction_to_orbifolds.pdf;/home/riccardo/.local/share/zotero/storage/N6FSCMLT/1909.html}
|
||||
}
|
||||
|
||||
@article{Carifio:2017:MachineLearningString,
|
||||
@@ -769,8 +763,7 @@
|
||||
author = {Caruana, Rich and Niculescu-Mizil, Alexandru},
|
||||
date = {2006},
|
||||
pages = {161--168},
|
||||
file = {/home/riccardo/.local/share/zotero/files/caruana_niculescu-mizil_2006_an_empirical_comparison_of_supervised_learning_algorithms.pdf},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/caruana_niculescu-mizil_2006_an_empirical_comparison_of_supervised_learning_algorithms.pdf}
|
||||
}
|
||||
|
||||
@article{Chamoun:2004:FermionMassesMixing,
|
||||
@@ -792,6 +785,22 @@
|
||||
number = {9}
|
||||
}
|
||||
|
||||
@article{Chan:1969:GeneralizedVenezianoModel,
|
||||
title = {Generalized {{Veneziano}} Model with Isospin},
|
||||
author = {Chan, Hong-Mo and Paton, Jack E.},
|
||||
date = {1969},
|
||||
journaltitle = {Nuclear Physics B},
|
||||
shortjournal = {Nuclear Physics B},
|
||||
volume = {10},
|
||||
pages = {516--520},
|
||||
issn = {05503213},
|
||||
doi = {10/chp79v},
|
||||
file = {/home/riccardo/.local/share/zotero/files/paton_chan_hong-mo_1969_generalized_veneziano_model_with_isospin.pdf},
|
||||
keywords = {archived},
|
||||
langid = {english},
|
||||
number = {3}
|
||||
}
|
||||
|
||||
@article{Chen:2008:RealisticWorldIntersecting,
|
||||
title = {A {{Realistic World}} from {{Intersecting D6}}-{{Branes}}},
|
||||
author = {Chen, Ching-Ming and Li, Tianjun and Mayes, van Eric and Nanopoulos, Dimitri V.},
|
||||
@@ -850,8 +859,7 @@
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {hep-ph/0703027},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/cleaver_2007_in_search_of_the_(minimal_supersymmetric)_standard_model_string.pdf},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/cleaver_2007_in_search_of_the_(minimal_supersymmetric)_standard_model_string.pdf}
|
||||
}
|
||||
|
||||
@article{Cole:2019:SearchingLandscapeFlux,
|
||||
@@ -933,7 +941,6 @@
|
||||
volume = {20},
|
||||
pages = {273--297},
|
||||
file = {/home/riccardo/.local/share/zotero/files/cortes_vapnik_1995_support-vector_networks.pdf},
|
||||
keywords = {❓ Multiple DOI},
|
||||
number = {3}
|
||||
}
|
||||
|
||||
@@ -1042,7 +1049,6 @@
|
||||
eprint = {hep-th/0007235},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/david_2000_tachyon_condensation_in_the_d0-d4_system.pdf},
|
||||
keywords = {⚠️ Invalid DOI},
|
||||
number = {10}
|
||||
}
|
||||
|
||||
@@ -1174,8 +1180,7 @@
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {hep-th/9912275},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/di_vecchia_liccardo_1999_d-branes_in_string_theory.pdf},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/di_vecchia_liccardo_1999_d-branes_in_string_theory.pdf}
|
||||
}
|
||||
|
||||
@article{DiVecchia:2000:BranesStringTheory,
|
||||
@@ -1203,8 +1208,7 @@
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {hep-th/0601067},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/di_vecchia_et_al_2006_boundary_state_for_magnetized_d9_branes_and_one-loop_calculation.pdf},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/di_vecchia_et_al_2006_boundary_state_for_magnetized_d9_branes_and_one-loop_calculation.pdf}
|
||||
}
|
||||
|
||||
@article{DiVecchia:2007:WrappedMagnetizedBranes,
|
||||
@@ -1313,8 +1317,7 @@
|
||||
author = {Drucker, Harris and Burges, Christopher JC and Kaufman, Linda and Smola, Alex J and Vapnik, Vladimir},
|
||||
date = {1997},
|
||||
pages = {155--161},
|
||||
file = {/home/riccardo/.local/share/zotero/files/drucker_et_al_1996_support_vector_regression_machines.pdf},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/drucker_et_al_1996_support_vector_regression_machines.pdf}
|
||||
}
|
||||
|
||||
@article{Duo:2007:NewTwistField,
|
||||
@@ -1343,8 +1346,7 @@
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {2007.13379},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/erbin_finotello_2020_inception_neural_network_for_complete_intersection_calabi-yau_3-folds.pdf},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/erbin_finotello_2020_inception_neural_network_for_complete_intersection_calabi-yau_3-folds.pdf}
|
||||
}
|
||||
|
||||
@online{Erbin:2020:MachineLearningComplete,
|
||||
@@ -1356,8 +1358,7 @@
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {2007.15706},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/erbin_finotello_2020_machine_learning_for_complete_intersection_calabi-yau_manifolds.pdf},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/erbin_finotello_2020_machine_learning_for_complete_intersection_calabi-yau_manifolds.pdf}
|
||||
}
|
||||
|
||||
@article{Faraggi:2020:MachineLearningClassification,
|
||||
@@ -1397,7 +1398,6 @@
|
||||
url = {http://jmlr.org/papers/v15/delgado14a.html},
|
||||
abstract = {We evaluate 179 classifiers arising from 17 families (discriminant analysis, Bayesian, neural networks, support vector machines, decision trees, rule-based classifiers, boosting, bagging, stacking, random forests and other ensembles, generalized linear models, nearest-neighbors, partial least squares and principal component regression, logistic and multinomial regression, multiple adaptive regression splines and other methods), implemented in Weka, R (with and without the caret package), C and Matlab, including all the relevant classifiers available today. We use 121 data sets, which represent the whole UCI data base (excluding the large- scale problems) and other own real problems, in order to achieve significant conclusions about the classifier behavior, not dependent on the data set collection. The classifiers most likely to be the bests are the random forest (RF) versions, the best of which (implemented in R and accessed via caret) achieves 94.1\% of the maximum accuracy overcoming 90\% in the 84.3\% of the data sets. However, the difference is not statistically significant with the second best, the SVM with Gaussian kernel implemented in C using LibSVM, which achieves 92.3\% of the maximum accuracy. A few models are clearly better than the remaining ones: random forest, SVM with Gaussian and polynomial kernels, extreme learning machine with Gaussian kernel, C5.0 and avNNet (a committee of multi-layer perceptrons implemented in R with the caret package). The random forest is clearly the best family of classifiers (3 out of 5 bests classifiers are RF), followed by SVM (4 classifiers in the top-10), neural networks and boosting ensembles (5 and 3 members in the top-20, respectively).},
|
||||
file = {/home/riccardo/.local/share/zotero/files/fernández-delgado_et_al_2014_do_we_need_hundreds_of_classifiers_to_solve_real_world_classification_problems.pdf},
|
||||
keywords = {⛔ No DOI found},
|
||||
number = {90}
|
||||
}
|
||||
|
||||
@@ -1427,8 +1427,7 @@
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {1912.07617},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/finotello_pesando_2019_2d_fermion_on_the_strip_with_boundary_defects_as_a_cft_with_excited_spin_fields.pdf},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/finotello_pesando_2019_2d_fermion_on_the_strip_with_boundary_defects_as_a_cft_with_excited_spin_fields.pdf}
|
||||
}
|
||||
|
||||
@article{Finotello:2019:ClassicalSolutionBosonic,
|
||||
@@ -1561,8 +1560,7 @@
|
||||
author = {Glorot, Xavier and Bordes, Antoine and Bengio, Yoshua},
|
||||
date = {2011},
|
||||
pages = {315--323},
|
||||
file = {/home/riccardo/.local/share/zotero/files/glorot_et_al_2011_deep_sparse_rectifier_neural_networks.pdf},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/glorot_et_al_2011_deep_sparse_rectifier_neural_networks.pdf}
|
||||
}
|
||||
|
||||
@article{Goddard:1973:QuantumDynamicsMassless,
|
||||
@@ -1755,8 +1753,7 @@
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {hep-th/9702155},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/greene_1997_string_theory_on_calabi-yau_manifolds.pdf},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/greene_1997_string_theory_on_calabi-yau_manifolds.pdf}
|
||||
}
|
||||
|
||||
@article{Halverson:2019:BranesBrainsExploring,
|
||||
@@ -2011,8 +2008,7 @@
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {1502.03167},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/ioffe_szegedy_2015_batch_normalization.pdf;/home/riccardo/.local/share/zotero/storage/L94NDAT8/1502.html},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/ioffe_szegedy_2015_batch_normalization.pdf;/home/riccardo/.local/share/zotero/storage/L94NDAT8/1502.html}
|
||||
}
|
||||
|
||||
@article{Jackiw:1992:ElectromagneticFieldsMassless,
|
||||
@@ -2050,8 +2046,7 @@
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {math/0108088},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/joyce_2002_lectures_on_calabi-yau_and_special_lagrangian_geometry2.pdf},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/joyce_2002_lectures_on_calabi-yau_and_special_lagrangian_geometry2.pdf}
|
||||
}
|
||||
|
||||
@article{Kachru:2003:SitterVacuaString,
|
||||
@@ -2080,8 +2075,7 @@
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {1312.6114},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/kingma_welling_2014_auto-encoding_variational_bayes2.pdf;/home/riccardo/.local/share/zotero/storage/KYP8BISG/1312.html},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/kingma_welling_2014_auto-encoding_variational_bayes2.pdf;/home/riccardo/.local/share/zotero/storage/KYP8BISG/1312.html}
|
||||
}
|
||||
|
||||
@online{Kingma:2017:AdamMethodStochastic,
|
||||
@@ -2093,8 +2087,7 @@
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {1412.6980},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/kingma_ba_2017_adam3.pdf;/home/riccardo/.local/share/zotero/storage/9JQ8YQL7/1412.html},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/kingma_ba_2017_adam3.pdf;/home/riccardo/.local/share/zotero/storage/9JQ8YQL7/1412.html}
|
||||
}
|
||||
|
||||
@online{Kingma:2017:AdamMethodStochastica,
|
||||
@@ -2106,8 +2099,7 @@
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {1412.6980},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/kingma_ba_2017_adam.pdf;/home/riccardo/.local/share/zotero/files/kingma_ba_2017_adam2.pdf;/home/riccardo/.local/share/zotero/storage/EYEANITG/1412.html},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/kingma_ba_2017_adam.pdf;/home/riccardo/.local/share/zotero/files/kingma_ba_2017_adam2.pdf;/home/riccardo/.local/share/zotero/storage/EYEANITG/1412.html}
|
||||
}
|
||||
|
||||
@article{Kiritsis:1994:StringPropagationGravitational,
|
||||
@@ -2188,8 +2180,7 @@
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {2003.13679},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/krippendorf_syvaeri_2020_detecting_symmetries_with_neural_networks2.pdf;/home/riccardo/.local/share/zotero/storage/F9KQKQ3Q/2003.html},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/krippendorf_syvaeri_2020_detecting_symmetries_with_neural_networks2.pdf;/home/riccardo/.local/share/zotero/storage/F9KQKQ3Q/2003.html}
|
||||
}
|
||||
|
||||
@article{Liu:2002:StringsTimeDependentOrbifold,
|
||||
@@ -2226,7 +2217,6 @@
|
||||
eprint = {hep-th/0206182},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/liu_et_al_2002_strings_in_time_dependent_orbifolds.pdf},
|
||||
keywords = {⚠️ Invalid DOI},
|
||||
langid = {english},
|
||||
number = {10}
|
||||
}
|
||||
@@ -2293,7 +2283,6 @@
|
||||
journaltitle = {The Journal of Machine Learning Research},
|
||||
volume = {17},
|
||||
pages = {2853--2884},
|
||||
keywords = {⛔ No DOI found},
|
||||
number = {1}
|
||||
}
|
||||
|
||||
@@ -2318,8 +2307,7 @@
|
||||
booktitle = {Proceedings of the {{IEEE}} Conference on Computer Vision and Pattern Recognition},
|
||||
author = {Monti, Federico and Boscaini, Davide and Masci, Jonathan and Rodola, Emanuele and Svoboda, Jan and Bronstein, Michael M.},
|
||||
date = {2017},
|
||||
pages = {5115--5124},
|
||||
keywords = {⛔ No DOI found}
|
||||
pages = {5115--5124}
|
||||
}
|
||||
|
||||
@article{Mutter:2019:DeepLearningHeterotic,
|
||||
@@ -2348,8 +2336,7 @@
|
||||
pages = {15862--15871},
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {1910.13593},
|
||||
eprinttype = {arxiv},
|
||||
keywords = {⛔ No DOI found}
|
||||
eprinttype = {arxiv}
|
||||
}
|
||||
|
||||
@article{Nilsson:1990:GeneralNSRString,
|
||||
@@ -2429,22 +2416,6 @@
|
||||
number = {5}
|
||||
}
|
||||
|
||||
@article{Paton:1969:GeneralizedVenezianoModel,
|
||||
title = {Generalized {{Veneziano}} Model with Isospin},
|
||||
author = {Paton, Jack E. and {Chan Hong-Mo}},
|
||||
date = {1969},
|
||||
journaltitle = {Nuclear Physics B},
|
||||
shortjournal = {Nuclear Physics B},
|
||||
volume = {10},
|
||||
pages = {516--520},
|
||||
issn = {05503213},
|
||||
doi = {10/chp79v},
|
||||
file = {/home/riccardo/.local/share/zotero/files/paton_chan_hong-mo_1969_generalized_veneziano_model_with_isospin.pdf},
|
||||
keywords = {archived},
|
||||
langid = {english},
|
||||
number = {3}
|
||||
}
|
||||
|
||||
@article{Pedregosa:2011:ScikitlearnMachineLearning,
|
||||
title = {Scikit-Learn: {{Machine}} Learning in Python},
|
||||
author = {Pedregosa, Fabian and Varoquaux, Gaël and Gramfort, Alexandre and Michel, Vincent and Thirion, Bertrand and Grisel, Olivier and Blondel, Mathieu and Prettenhofer, Peter and Weiss, Ron and Dubourg, Vincent and Vanderplas, Jake and Passos, Alexandre and Cournapeau, David and Brucher, Matthieu and Perrot, Matthieu and Duchesnay, Édouard},
|
||||
@@ -2454,7 +2425,6 @@
|
||||
pages = {2825--2830},
|
||||
url = {http://jmlr.org/papers/v12/pedregosa11a.html},
|
||||
file = {/home/riccardo/.local/share/zotero/files/pedregosa_et_al_2011_scikit-learn2.pdf},
|
||||
keywords = {⛔ No DOI found},
|
||||
number = {85}
|
||||
}
|
||||
|
||||
@@ -2464,8 +2434,7 @@
|
||||
author = {Peng, Chao and Zhang, Xiangyu and Yu, Gang and Luo, Guiming and Sun, Jian},
|
||||
date = {2017},
|
||||
pages = {4353--4361},
|
||||
file = {/home/riccardo/.local/share/zotero/files/peng_et_al_2017_large_kernel_matters–improve_semantic_segmentation_by_global_convolutional.pdf},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/peng_et_al_2017_large_kernel_matters–improve_semantic_segmentation_by_global_convolutional.pdf}
|
||||
}
|
||||
|
||||
@article{Pesando:2008:MultibranesBoundaryStates,
|
||||
@@ -2511,8 +2480,7 @@
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {1107.5525},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/pesando_2011_the_generating_function_of_amplitudes_with_n_twisted_and_m_untwisted_states.pdf},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/pesando_2011_the_generating_function_of_amplitudes_with_n_twisted_and_m_untwisted_states.pdf}
|
||||
}
|
||||
|
||||
@article{Pesando:2011:StringsArbitraryConstant,
|
||||
@@ -2659,8 +2627,7 @@
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {hep-th/9611050},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/polchinski_1996_tasi_lectures_on_d-branes.pdf},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/polchinski_1996_tasi_lectures_on_d-branes.pdf}
|
||||
}
|
||||
|
||||
@book{Polchinski:1998:StringTheoryIntroduction,
|
||||
@@ -2727,8 +2694,7 @@
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {1401.4082},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/rezende_et_al_2014_stochastic_backpropagation_and_approximate_inference_in_deep_generative_models2.pdf;/home/riccardo/.local/share/zotero/storage/HKC6H5VK/1401.html},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/rezende_et_al_2014_stochastic_backpropagation_and_approximate_inference_in_deep_generative_models2.pdf;/home/riccardo/.local/share/zotero/storage/HKC6H5VK/1401.html}
|
||||
}
|
||||
|
||||
@article{Rudolph:1994:ConvergenceAnalysisCanonical,
|
||||
@@ -2858,8 +2824,7 @@
|
||||
booktitle = {Advances in Neural Information Processing Systems},
|
||||
author = {Snoek, Jasper and Larochelle, Hugo and Adams, Ryan P.},
|
||||
date = {2012},
|
||||
pages = {2951--2959},
|
||||
keywords = {⛔ No DOI found}
|
||||
pages = {2951--2959}
|
||||
}
|
||||
|
||||
@article{Soldate:1987:PartialwaveUnitarityClosedstring,
|
||||
@@ -2886,8 +2851,7 @@
|
||||
volume = {15},
|
||||
pages = {1929--1958},
|
||||
url = {http://jmlr.org/papers/v15/srivastava14a.html},
|
||||
file = {/home/riccardo/.local/share/zotero/files/srivastava_et_al_2014_dropout.pdf;/home/riccardo/.local/share/zotero/files/srivastava_et_al_2014_dropout2.pdf},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/srivastava_et_al_2014_dropout.pdf;/home/riccardo/.local/share/zotero/files/srivastava_et_al_2014_dropout2.pdf}
|
||||
}
|
||||
|
||||
@article{Stieberger:1992:YukawaCouplingsBosonic,
|
||||
@@ -2917,8 +2881,7 @@
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {hep-th/0302219},
|
||||
eprinttype = {arxiv},
|
||||
file = {/home/riccardo/.local/share/zotero/files/susskind_2003_the_anthropic_landscape_of_string_theory.pdf},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/susskind_2003_the_anthropic_landscape_of_string_theory.pdf}
|
||||
}
|
||||
|
||||
@inproceedings{Szegedy:2015:GoingDeeperConvolutions,
|
||||
@@ -2930,8 +2893,7 @@
|
||||
abstract = {We propose a deep convolutional neural network architecture codenamed "Inception", which was responsible for setting the new state of the art for classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC 2014). The main hallmark of this architecture is the improved utilization of the computing resources inside the network. This was achieved by a carefully crafted design that allows for increasing the depth and width of the network while keeping the computational budget constant. To optimize quality, the architectural decisions were based on the Hebbian principle and the intuition of multi-scale processing. One particular incarnation used in our submission for ILSVRC 2014 is called GoogLeNet, a 22 layers deep network, the quality of which is assessed in the context of classification and detection.},
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {1409.4842},
|
||||
eprinttype = {arxiv},
|
||||
keywords = {⛔ No DOI found}
|
||||
eprinttype = {arxiv}
|
||||
}
|
||||
|
||||
@online{Szegedy:2016:Inceptionv4InceptionresnetImpact,
|
||||
@@ -2940,8 +2902,7 @@
|
||||
date = {2016},
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {1602.07261},
|
||||
eprinttype = {arxiv},
|
||||
keywords = {⛔ No DOI found}
|
||||
eprinttype = {arxiv}
|
||||
}
|
||||
|
||||
@inproceedings{Szegedy:2016:RethinkingInceptionArchitecture,
|
||||
@@ -2952,8 +2913,7 @@
|
||||
pages = {2818--2826},
|
||||
archivePrefix = {arXiv},
|
||||
eprint = {1512.00567},
|
||||
eprinttype = {arxiv},
|
||||
keywords = {⛔ No DOI found}
|
||||
eprinttype = {arxiv}
|
||||
}
|
||||
|
||||
@article{Taylor:2015:FtheoryGeometryMost,
|
||||
@@ -3025,8 +2985,7 @@
|
||||
booktitle = {Advances in Neural Information Processing Systems},
|
||||
author = {Thrun, Sebastian},
|
||||
date = {1996},
|
||||
pages = {640--646},
|
||||
keywords = {⛔ No DOI found}
|
||||
pages = {640--646}
|
||||
}
|
||||
|
||||
@inproceedings{Tompson:2015:EfficientObjectLocalization,
|
||||
@@ -3064,8 +3023,7 @@
|
||||
date = {2005},
|
||||
url = {http://cds.cern.ch/record/933469/files/cer-002601054.pdf},
|
||||
abstract = {We review the construction of chiral four-dimensional compactifications of string theory with different systems of D-branes, including type IIA intersecting D6-branes and type IIB magnetised D-branes. Such models lead to four-dimensional theories with non-abelian gauge interactions and charged chiral fermions. We discuss the application of these techniques to building of models with spectrum as close as possible to the Standard Model, and review their main phenomenological properties. We finally describe how to implement the tecniques to construct these models in flux compactifications, leading to models with realistic gauge sectors, moduli stabilization and supersymmetry breaking soft terms.},
|
||||
file = {/home/riccardo/.local/share/zotero/files/uranga_2005_tasi_lectures_on_string_compactification,_model_building,_and_fluxes.pdf},
|
||||
keywords = {⛔ No DOI found}
|
||||
file = {/home/riccardo/.local/share/zotero/files/uranga_2005_tasi_lectures_on_string_compactification,_model_building,_and_fluxes.pdf}
|
||||
}
|
||||
|
||||
@article{vanderWalt:2011:NumPyArrayStructure,
|
||||
@@ -3112,8 +3070,7 @@
|
||||
volume = {33},
|
||||
pages = {128--128},
|
||||
issn = {0026-1335},
|
||||
url = {http://eudml.org/doc/176041},
|
||||
keywords = {⛔ No DOI found}
|
||||
url = {http://eudml.org/doc/176041}
|
||||
}
|
||||
|
||||
@article{Yau:1977:CalabiConjectureNew,
|
||||
@@ -3146,8 +3103,7 @@
|
||||
booktitle = {Proceedings of the {{IEEE}} International Conference on Computer Vision},
|
||||
author = {Zhu, Jun-Yan and Park, Taesung and Isola, Phillip and Efros, Alexei A},
|
||||
date = {2017},
|
||||
pages = {2223--2232},
|
||||
keywords = {⛔ No DOI found}
|
||||
pages = {2223--2232}
|
||||
}
|
||||
|
||||
@book{Zwiebach:2009:FirstCourseString,
|
||||
|
||||
@@ -44,7 +44,7 @@
|
||||
version={4.0}]{doclicense} %---- licence
|
||||
\RequirePackage[nottoc]{tocbibind} %------------ put bibliography in TOC
|
||||
\RequirePackage[backend=biber,
|
||||
citestyle=numeric-comp,
|
||||
citestyle=numeric-icomp,
|
||||
sorting=none,
|
||||
sortcites=true,
|
||||
style=ieee,
|
||||
|
||||
BIN
thesis.pdf
BIN
thesis.pdf
Binary file not shown.
16
thesis.tex
16
thesis.tex
@@ -1,3 +1,5 @@
|
||||
% !TeX root = thesis.tex
|
||||
% !TeX program = xelatex
|
||||
\documentclass[a4paper,11pt,twoside]{thesis}
|
||||
|
||||
\usepackage[british]{babel}
|
||||
@@ -54,11 +56,11 @@
|
||||
\newcommand{\cint}[1]{\ensuremath{\oint\limits_{\ccC_{#1}}}}
|
||||
|
||||
%---- states
|
||||
\newcommand{\regvacuum}{\ensuremath{\ket{0}_{\SL{2}{R}}}\xspace}
|
||||
\newcommand{\regvacuumin}{\ensuremath{\ket{0_{(\text{in})}}_{\SL{2}{R}}}\xspace}
|
||||
\newcommand{\regvacuumout}{\ensuremath{\ket{0_{(\text{out})}}_{\SL{2}{R}}}\xspace}
|
||||
\newcommand{\regvacuuminconj}{\ensuremath{\tensor[_{\SL{2}{R}}]{\bra{0_{(\text{in})}}}{}}\xspace}
|
||||
\newcommand{\regvacuumoutconj}{\ensuremath{\tensor[_{\SL{2}{R}}]{\bra{0_{(\text{out})}}}{}}\xspace}
|
||||
\newcommand{\regvacuum}{\ensuremath{\ket{0}_{\SL{2}{\R}}}\xspace}
|
||||
\newcommand{\regvacuumin}{\ensuremath{\ket{0_{(\text{in})}}_{\SL{2}{\R}}}\xspace}
|
||||
\newcommand{\regvacuumout}{\ensuremath{\ket{0_{(\text{out})}}_{\SL{2}{\R}}}\xspace}
|
||||
\newcommand{\regvacuuminconj}{\ensuremath{\tensor[_{\SL{2}{\R}}]{\bra{0_{(\text{in})}}}{}}\xspace}
|
||||
\newcommand{\regvacuumoutconj}{\ensuremath{\tensor[_{\SL{2}{\R}}]{\bra{0_{(\text{out})}}}{}}\xspace}
|
||||
\newcommand{\twsvacket}{\ensuremath{\ket{\mathrm{T}}}\xspace}
|
||||
\newcommand{\twsvacbra}{\ensuremath{\bra{\mathrm{T}}}\xspace}
|
||||
\newcommand{\excvacket}{\ensuremath{\ket{T_{\rE,\, \brE}}}\xspace}
|
||||
@@ -110,13 +112,13 @@
|
||||
|
||||
%---- ABSTRACT
|
||||
\begin{abstractpage}
|
||||
\input{sec/abstract.tex}
|
||||
\input{sec/abstract.tex}
|
||||
\end{abstractpage}
|
||||
\cleardoubleplainpage{}
|
||||
|
||||
%---- ACKNOWLEDGENTS
|
||||
\begin{acknowledgmentspage}
|
||||
\input{sec/acknowledgments.tex}
|
||||
\input{sec/acknowledgments.tex}
|
||||
\end{acknowledgmentspage}
|
||||
\cleardoubleplainpage{}
|
||||
|
||||
|
||||
@@ -2,13 +2,13 @@
|
||||
\newlength{\layerheight}
|
||||
\newlength{\perspective}
|
||||
\newlength{\filters}
|
||||
%\newlength{\unit}
|
||||
%\newlength{\myunit}
|
||||
|
||||
\setlength{\layer}{3cm}
|
||||
\setlength{\layerheight}{3cm}
|
||||
\setlength{\perspective}{1cm}
|
||||
\setlength{\filters}{0.01cm}
|
||||
\setlength{\unit}{0.225cm}
|
||||
\setlength{\myunit}{0.225cm}
|
||||
|
||||
\begin{tikzpicture}
|
||||
|
||||
@@ -50,13 +50,13 @@
|
||||
|
||||
% flatten layer
|
||||
\foreach \x in {2,...,7} {
|
||||
\filldraw[fill=cyan!10, draw=black] (4 * \layer + 3cm, 0.5cm * \x) circle (\unit);
|
||||
\draw (4 * \layer + 3cm + \unit, 0.5cm * \x) -- (5 * \layer + 2cm - \unit, 2.5cm);
|
||||
\filldraw[fill=cyan!10, draw=black] (4 * \layer + 3cm, 0.5cm * \x) circle (\myunit);
|
||||
\draw (4 * \layer + 3cm + \myunit, 0.5cm * \x) -- (5 * \layer + 2cm - \myunit, 2.5cm);
|
||||
};
|
||||
\node[anchor=north, scale=0.5, below=15pt, align=center] at (4 * \layer + 3cm, 1cm) {flatten};
|
||||
|
||||
% output layer
|
||||
\filldraw[fill=cyan!10, draw=black] (5 * \layer + 2cm, 2.5cm - \unit) -- (5 * \layer + 2cm, 2.5cm) circle (\unit) -- (5 * \layer + 2cm, 2.5cm + \unit);
|
||||
\filldraw[fill=cyan!10, draw=black] (5 * \layer + 2cm, 2.5cm - \myunit) -- (5 * \layer + 2cm, 2.5cm) circle (\myunit) -- (5 * \layer + 2cm, 2.5cm + \myunit);
|
||||
\draw (5 * \layer + 2cm + 0.05cm, 2.5cm) node[anchor=north, below=10pt, text width=2cm, scale=0.35, align=center] {output layer [1 unit]} -- (5 * \layer + 2cm + 0.10cm, 2.5cm) -- (5 * \layer + 2cm + 0.15cm, 2.5cm + 0.05cm);
|
||||
|
||||
% draw first convolution
|
||||
@@ -81,15 +81,15 @@
|
||||
\filldraw[fill=red!50, draw=black, fill opacity=0.5] (3 * \layer + 40 * \filters + 0.4 * \perspective, 0.6 * \layerheight + 0.4 * \perspective) -- (4 * \layer, 0.3 * \layerheight) -- (3 * \layer + 40 * \filters, 0.6 * \layerheight) -- cycle;
|
||||
|
||||
% draw the "flatenisation"
|
||||
\draw[dashed] (4 * \layer + 20 * \filters, \layerheight) -- (4 * \layer + 3 cm, 3.5cm + \unit) -- (4 * \layer + 20 * \filters + \perspective, \layerheight + \perspective) -- cycle;
|
||||
\draw[dashed] (4 * \layer + 20 * \filters, 0cm) -- (4 * \layer + 3 cm, 1cm - \unit) -- (4 * \layer + 20 * \filters + \perspective, \perspective) -- cycle;
|
||||
\draw[dashed] (4 * \layer + 20 * \filters, \layerheight) -- (4 * \layer + 3 cm, 3.5cm + \myunit) -- (4 * \layer + 20 * \filters + \perspective, \layerheight + \perspective) -- cycle;
|
||||
\draw[dashed] (4 * \layer + 20 * \filters, 0cm) -- (4 * \layer + 3 cm, 1cm - \myunit) -- (4 * \layer + 20 * \filters + \perspective, \perspective) -- cycle;
|
||||
|
||||
% hidden layer labels
|
||||
\node[anchor=base, align=center, text width=3.9cm, scale=0.75] (c) at (11cm, 5.5cm) {convolutional layers ($5 \times 5$ kernel, ReLU activation)};
|
||||
\draw[->] (c) -- (\layer + 180 * \filters + \perspective, \layerheight + \perspective + \unit);
|
||||
\draw[->] (c) -- (2 * \layer + 100 * \filters + \perspective, \layerheight + \perspective + \unit);
|
||||
\draw[->] (c) -- (3 * \layer + 40 * \filters + \perspective, \layerheight + \perspective + \unit);
|
||||
\draw[->] (c) -- (4 * \layer + 0.5 * \perspective, \layerheight + \perspective + \unit);
|
||||
\draw[->] (c) -- (\layer + 180 * \filters + \perspective, \layerheight + \perspective + \myunit);
|
||||
\draw[->] (c) -- (2 * \layer + 100 * \filters + \perspective, \layerheight + \perspective + \myunit);
|
||||
\draw[->] (c) -- (3 * \layer + 40 * \filters + \perspective, \layerheight + \perspective + \myunit);
|
||||
\draw[->] (c) -- (4 * \layer + 0.5 * \perspective, \layerheight + \perspective + \myunit);
|
||||
|
||||
\end{tikzpicture}
|
||||
|
||||
|
||||
98
tikz/fc.pgf
98
tikz/fc.pgf
@@ -1,159 +1,159 @@
|
||||
\newlength{\unit}
|
||||
\newlength{\myunit}
|
||||
\newlength{\layer}
|
||||
|
||||
\setlength{\unit}{0.225cm}
|
||||
\setlength{\myunit}{0.225cm}
|
||||
\setlength{\layer}{1cm}
|
||||
|
||||
\begin{tikzpicture}
|
||||
|
||||
% draw the first layer
|
||||
\filldraw[fill=cyan!10, draw=black] (\layer, -0.75cm - \unit) -- (\layer, -0.75cm) circle (\unit) -- (\layer, -0.75cm + \unit);
|
||||
\filldraw[fill=cyan!10, draw=black] (\layer, -0.75cm - \myunit) -- (\layer, -0.75cm) circle (\myunit) -- (\layer, -0.75cm + \myunit);
|
||||
\draw (\layer + 0.05cm, -0.75cm) node[anchor=north, below=10pt, text width=2cm, scale=0.35, align=center] {FC layer [876 units]} -- (\layer + 0.10cm, -0.75cm) -- (\layer + 0.15cm, -0.75cm + 0.05cm);
|
||||
\node[anchor=base, scale=0.35] at (\layer, -0.75cm + 1.25 * \unit) {$\vdots$};
|
||||
\node[anchor=base, scale=0.35] at (\layer, -0.75cm + 1.25 * \myunit) {$\vdots$};
|
||||
|
||||
\foreach \x in {0,...,5} {
|
||||
\filldraw[fill=cyan!10, draw=black] (\layer, 0.5cm * \x - \unit) -- (\layer, 0.5cm * \x) circle (\unit) -- (\layer, 0.5cm * \x + \unit);
|
||||
\filldraw[fill=cyan!10, draw=black] (\layer, 0.5cm * \x - \myunit) -- (\layer, 0.5cm * \x) circle (\myunit) -- (\layer, 0.5cm * \x + \myunit);
|
||||
\draw (\layer + 0.05cm, 0.5cm * \x) -- (\layer + 0.10cm, 0.5cm * \x) -- (\layer + 0.15cm, 0.5cm * \x + 0.05cm);
|
||||
};
|
||||
|
||||
\filldraw[fill=cyan!10, draw=black] (\layer, 3.25cm - \unit) -- (\layer, 3.25cm) circle (\unit) -- (\layer, 3.25cm + \unit);
|
||||
\filldraw[fill=cyan!10, draw=black] (\layer, 3.25cm - \myunit) -- (\layer, 3.25cm) circle (\myunit) -- (\layer, 3.25cm + \myunit);
|
||||
\draw (\layer + 0.05cm, 3.25cm) -- (\layer + 0.10cm, 3.25cm) -- (\layer + 0.15cm, 3.25cm + 0.05cm);
|
||||
\node[anchor=base, scale=0.35] at (\layer, 3.25cm - 2\unit) {$\vdots$};
|
||||
\node[anchor=base, scale=0.35] at (\layer, 3.25cm - 2\myunit) {$\vdots$};
|
||||
|
||||
% draw the second layer
|
||||
\filldraw[fill=cyan!10, draw=black] (2 * \layer, -\unit) -- (2 * \layer, 0cm) circle (\unit) -- (2 * \layer, \unit);
|
||||
\filldraw[fill=cyan!10, draw=black] (2 * \layer, -\myunit) -- (2 * \layer, 0cm) circle (\myunit) -- (2 * \layer, \myunit);
|
||||
\draw (2 * \layer + 0.05cm, 0cm) node[anchor=north, below=10pt, text width=2cm, scale=0.35, align=center] {FC layer [461 units]} -- (2 * \layer + 0.10cm, 0cm) -- (2 * \layer + 0.15cm, 0.05cm);
|
||||
\node[anchor=base, scale=0.35] at (2 * \layer, 1.25 * \unit) {$\vdots$};
|
||||
\node[anchor=base, scale=0.35] at (2 * \layer, 1.25 * \myunit) {$\vdots$};
|
||||
|
||||
\foreach \x in {1.5,...,3.5} {
|
||||
\filldraw[fill=cyan!10, draw=black] (2 * \layer, 0.5cm * \x - \unit) -- (2 * \layer, 0.5cm * \x) circle (\unit) -- (2 * \layer, 0.5cm * \x + \unit);
|
||||
\filldraw[fill=cyan!10, draw=black] (2 * \layer, 0.5cm * \x - \myunit) -- (2 * \layer, 0.5cm * \x) circle (\myunit) -- (2 * \layer, 0.5cm * \x + \myunit);
|
||||
\draw (2 * \layer + 0.05cm, 0.5cm * \x) -- (2 * \layer + 0.10cm, 0.5cm * \x) -- (2 * \layer + 0.15cm, 0.5cm * \x + 0.05cm);
|
||||
};
|
||||
|
||||
\filldraw[fill=cyan!10, draw=black] (2 * \layer, 2.5cm - \unit) -- (2 * \layer, 2.5cm) circle (\unit) -- (2 * \layer, 2.5cm + \unit);
|
||||
\filldraw[fill=cyan!10, draw=black] (2 * \layer, 2.5cm - \myunit) -- (2 * \layer, 2.5cm) circle (\myunit) -- (2 * \layer, 2.5cm + \myunit);
|
||||
\draw (2 * \layer + 0.05cm, 2.5cm) -- (2 * \layer + 0.10cm, 2.5cm) -- (2 * \layer + 0.15cm, 2.5cm + 0.05cm);
|
||||
\node[anchor=base, scale=0.35] at (2 * \layer, 2.5cm - 2\unit) {$\vdots$};
|
||||
\node[anchor=base, scale=0.35] at (2 * \layer, 2.5cm - 2\myunit) {$\vdots$};
|
||||
|
||||
% draw the third layer
|
||||
\filldraw[fill=cyan!10, draw=black] (3 * \layer, -\unit) -- (3 * \layer, 0cm) circle (\unit) -- (3 * \layer, \unit);
|
||||
\filldraw[fill=cyan!10, draw=black] (3 * \layer, -\myunit) -- (3 * \layer, 0cm) circle (\myunit) -- (3 * \layer, \myunit);
|
||||
\draw (3 * \layer + 0.05cm, 0cm) node[anchor=north, below=10pt, text width=2cm, scale=0.35, align=center] {FC layer [437 units]} -- (3 * \layer + 0.10cm, 0cm) -- (3 * \layer + 0.15cm, 0.05cm);
|
||||
\node[anchor=base, scale=0.35] at (3 * \layer, 1.25 * \unit) {$\vdots$};
|
||||
\node[anchor=base, scale=0.35] at (3 * \layer, 1.25 * \myunit) {$\vdots$};
|
||||
|
||||
\foreach \x in {1.5,...,3.5} {
|
||||
\filldraw[fill=cyan!10, draw=black] (3 * \layer, 0.5cm * \x - \unit) -- (3 * \layer, 0.5cm * \x) circle (\unit) -- (3 * \layer, 0.5cm * \x + \unit);
|
||||
\filldraw[fill=cyan!10, draw=black] (3 * \layer, 0.5cm * \x - \myunit) -- (3 * \layer, 0.5cm * \x) circle (\myunit) -- (3 * \layer, 0.5cm * \x + \myunit);
|
||||
\draw (3 * \layer + 0.05cm, 0.5cm * \x) -- (3 * \layer + 0.10cm, 0.5cm * \x) -- (3 * \layer + 0.15cm, 0.5cm * \x + 0.05cm);
|
||||
};
|
||||
|
||||
\filldraw[fill=cyan!10, draw=black] (3 * \layer, 2.5cm - \unit) -- (3 * \layer, 2.5cm) circle (\unit) -- (3 * \layer, 2.5cm + \unit);
|
||||
\filldraw[fill=cyan!10, draw=black] (3 * \layer, 2.5cm - \myunit) -- (3 * \layer, 2.5cm) circle (\myunit) -- (3 * \layer, 2.5cm + \myunit);
|
||||
\draw (3 * \layer + 0.05cm, 2.5cm) -- (3 * \layer + 0.10cm, 2.5cm) -- (3 * \layer + 0.15cm, 2.5cm + 0.05cm);
|
||||
\node[anchor=base, scale=0.35] at (3 * \layer, 2.5cm - 2\unit) {$\vdots$};
|
||||
\node[anchor=base, scale=0.35] at (3 * \layer, 2.5cm - 2\myunit) {$\vdots$};
|
||||
|
||||
% draw the fourth layer
|
||||
\filldraw[fill=cyan!10, draw=black] (4 * \layer, -0.75cm - \unit) -- (4 * \layer, -0.75cm) circle (\unit) -- (4 * \layer, -0.75cm + \unit);
|
||||
\filldraw[fill=cyan!10, draw=black] (4 * \layer, -0.75cm - \myunit) -- (4 * \layer, -0.75cm) circle (\myunit) -- (4 * \layer, -0.75cm + \myunit);
|
||||
\draw (4 * \layer + 0.05cm, -0.75cm) node[anchor=north, below=10pt, text width=2cm, scale=0.35, align=center] {FC layer [929 units]} -- (4 * \layer + 0.10cm, -0.75cm) -- (4 * \layer + 0.15cm, -0.75cm + 0.05cm);
|
||||
\node[anchor=base, scale=0.35] at (4 * \layer, -0.75cm + 1.25 * \unit) {$\vdots$};
|
||||
\node[anchor=base, scale=0.35] at (4 * \layer, -0.75cm + 1.25 * \myunit) {$\vdots$};
|
||||
|
||||
\foreach \x in {0,...,5} {
|
||||
\filldraw[fill=cyan!10, draw=black] (4 * \layer, 0.5cm * \x - \unit) -- (4 * \layer, 0.5cm * \x) circle (\unit) -- (4 * \layer, 0.5cm * \x + \unit);
|
||||
\filldraw[fill=cyan!10, draw=black] (4 * \layer, 0.5cm * \x - \myunit) -- (4 * \layer, 0.5cm * \x) circle (\myunit) -- (4 * \layer, 0.5cm * \x + \myunit);
|
||||
\draw (4 * \layer + 0.05cm, 0.5cm * \x) -- (4 * \layer + 0.10cm, 0.5cm * \x) -- (4 * \layer + 0.15cm, 0.5cm * \x + 0.05cm);
|
||||
};
|
||||
|
||||
\filldraw[fill=cyan!10, draw=black] (4 * \layer, 3.25cm - \unit) -- (4 * \layer, 3.25cm) circle (\unit) -- (4 * \layer, 3.25cm + \unit);
|
||||
\filldraw[fill=cyan!10, draw=black] (4 * \layer, 3.25cm - \myunit) -- (4 * \layer, 3.25cm) circle (\myunit) -- (4 * \layer, 3.25cm + \myunit);
|
||||
\draw (4 * \layer + 0.05cm, 3.25cm) -- (4 * \layer + 0.10cm, 3.25cm) -- (4 * \layer + 0.15cm, 3.25cm + 0.05cm);
|
||||
\node[anchor=base, scale=0.35] at (4 * \layer, 3.25cm - 2\unit) {$\vdots$};
|
||||
\node[anchor=base, scale=0.35] at (4 * \layer, 3.25cm - 2\myunit) {$\vdots$};
|
||||
|
||||
% draw the fifth layer
|
||||
\filldraw[fill=cyan!10, draw=black] (5 * \layer, -\unit) -- (5 * \layer, 0cm) circle (\unit) -- (5 * \layer, \unit);
|
||||
\filldraw[fill=cyan!10, draw=black] (5 * \layer, -\myunit) -- (5 * \layer, 0cm) circle (\myunit) -- (5 * \layer, \myunit);
|
||||
\draw (5 * \layer + 0.05cm, 0cm) node[anchor=north, below=10pt, text width=2cm, scale=0.35, align=center] {FC layer [404 units]} -- (5 * \layer + 0.10cm, 0cm) -- (5 * \layer + 0.15cm, 0.05cm);
|
||||
\node[anchor=base, scale=0.35] at (5 * \layer, 1.25 * \unit) {$\vdots$};
|
||||
\node[anchor=base, scale=0.35] at (5 * \layer, 1.25 * \myunit) {$\vdots$};
|
||||
|
||||
\foreach \x in {1.5,...,3.5} {
|
||||
\filldraw[fill=cyan!10, draw=black] (5 * \layer, 0.5cm * \x - \unit) -- (5 * \layer, 0.5cm * \x) circle (\unit) -- (5 * \layer, 0.5cm * \x + \unit);
|
||||
\filldraw[fill=cyan!10, draw=black] (5 * \layer, 0.5cm * \x - \myunit) -- (5 * \layer, 0.5cm * \x) circle (\myunit) -- (5 * \layer, 0.5cm * \x + \myunit);
|
||||
\draw (5 * \layer + 0.05cm, 0.5cm * \x) -- (5 * \layer + 0.10cm, 0.5cm * \x) -- (5 * \layer + 0.15cm, 0.5cm * \x + 0.05cm);
|
||||
};
|
||||
|
||||
\filldraw[fill=cyan!10, draw=black] (5 * \layer, 2.5cm - \unit) -- (5 * \layer, 2.5cm) circle (\unit) -- (5 * \layer, 2.5cm + \unit);
|
||||
\filldraw[fill=cyan!10, draw=black] (5 * \layer, 2.5cm - \myunit) -- (5 * \layer, 2.5cm) circle (\myunit) -- (5 * \layer, 2.5cm + \myunit);
|
||||
\draw (5 * \layer + 0.05cm, 2.5cm) -- (5 * \layer + 0.10cm, 2.5cm) -- (5 * \layer + 0.15cm, 2.5cm + 0.05cm);
|
||||
\node[anchor=base, scale=0.35] at (5 * \layer, 2.5cm - 2\unit) {$\vdots$};
|
||||
\node[anchor=base, scale=0.35] at (5 * \layer, 2.5cm - 2\myunit) {$\vdots$};
|
||||
|
||||
% draw the output layer
|
||||
\filldraw[fill=cyan!10, draw=black] (6 * \layer, 1.25cm - \unit) -- (6 * \layer, 1.25cm) circle (\unit) -- (6 * \layer, 1.25cm + \unit);
|
||||
\filldraw[fill=cyan!10, draw=black] (6 * \layer, 1.25cm - \myunit) -- (6 * \layer, 1.25cm) circle (\myunit) -- (6 * \layer, 1.25cm + \myunit);
|
||||
\draw (6 * \layer + 0.05cm, 1.25cm) node[anchor=north, below=10pt, text width=2cm, scale=0.35, align=center] {output layer [1 unit]} -- (6 * \layer + 0.10cm, 1.25cm) -- (6 * \layer + 0.15cm, 1.25cm + 0.05cm);
|
||||
|
||||
% draw weights 1 --> 2 and 4 --> 5
|
||||
\foreach \x in {\layer, 4 * \layer} {
|
||||
\foreach \y in {-0.75cm, 3.25cm} {
|
||||
\foreach \z in {0cm, 2.5cm} {
|
||||
\draw (\x + \unit, \y) -- (\x + \layer - \unit, \z);
|
||||
\draw (\x + \myunit, \y) -- (\x + \layer - \myunit, \z);
|
||||
};
|
||||
};
|
||||
\foreach \y in {0,...,5} {
|
||||
\foreach \z in {1.5,...,3.5} {
|
||||
\draw (\x + \unit, 0.5cm * \y) -- (\x + \layer - \unit, 0.5cm * \z);
|
||||
\draw (\x + \myunit, 0.5cm * \y) -- (\x + \layer - \myunit, 0.5cm * \z);
|
||||
};
|
||||
\foreach \z in {0cm, 2.5cm} {
|
||||
\draw (\x + \unit, 0.5 * \y) -- (\x + \layer - \unit, \z);
|
||||
\draw (\x + \myunit, 0.5 * \y) -- (\x + \layer - \myunit, \z);
|
||||
};
|
||||
};
|
||||
\foreach \y in {1.5,...,3.5} {
|
||||
\draw (\x + \unit, 3.25cm) -- (\x + \layer - \unit, 0.5cm * \y);
|
||||
\draw (\x + \unit, -0.75cm) -- (\x + \layer - \unit, 0.5cm * \y);
|
||||
\draw (\x + \myunit, 3.25cm) -- (\x + \layer - \myunit, 0.5cm * \y);
|
||||
\draw (\x + \myunit, -0.75cm) -- (\x + \layer - \myunit, 0.5cm * \y);
|
||||
};
|
||||
};
|
||||
|
||||
% draw weights 2 --> 3
|
||||
\foreach \y in {0cm, 2.5cm} {
|
||||
\foreach \z in {0cm, 2.5cm} {
|
||||
\draw (2 * \layer + \unit, \y) -- (2 * \layer + \layer - \unit, \z);
|
||||
\draw (2 * \layer + \myunit, \y) -- (2 * \layer + \layer - \myunit, \z);
|
||||
};
|
||||
};
|
||||
\foreach \y in {1.5,...,3.5} {
|
||||
\foreach \z in {1.5,...,3.5} {
|
||||
\draw (2 * \layer + \unit, 0.5cm * \y) -- (2 * \layer + \layer - \unit, 0.5cm * \z);
|
||||
\draw (2 * \layer + \myunit, 0.5cm * \y) -- (2 * \layer + \layer - \myunit, 0.5cm * \z);
|
||||
};
|
||||
\foreach \z in {0cm, 2.5cm} {
|
||||
\draw (2 * \layer + \unit, 0.5cm * \y) -- (2 * \layer + \layer - \unit, \z);
|
||||
\draw (2 * \layer + \myunit, 0.5cm * \y) -- (2 * \layer + \layer - \myunit, \z);
|
||||
};
|
||||
};
|
||||
\foreach \y in {1.5,...,3.5} {
|
||||
\draw (2 * \layer + \unit, 2.5cm) -- (2 * \layer + \layer - \unit, 0.5cm * \y);
|
||||
\draw (2 * \layer + \unit, 0cm) -- (2 * \layer + \layer - \unit, 0.5cm * \y);
|
||||
\draw (2 * \layer + \myunit, 2.5cm) -- (2 * \layer + \layer - \myunit, 0.5cm * \y);
|
||||
\draw (2 * \layer + \myunit, 0cm) -- (2 * \layer + \layer - \myunit, 0.5cm * \y);
|
||||
};
|
||||
|
||||
% draw weights 3 --> 4
|
||||
\foreach \y in {0cm, 2.5cm} {
|
||||
\foreach \z in {-0.75cm, 3.25cm} {
|
||||
\draw (3 * \layer + \unit, \y) -- (3 * \layer + \layer - \unit, \z);
|
||||
\draw (3 * \layer + \myunit, \y) -- (3 * \layer + \layer - \myunit, \z);
|
||||
};
|
||||
};
|
||||
\foreach \y in {1.5,...,3.5} {
|
||||
\foreach \z in {0,...,5} {
|
||||
\draw (3 * \layer + \unit, 0.5cm * \y) -- (3 * \layer + \layer - \unit, 0.5cm * \z);
|
||||
\draw (3 * \layer + \myunit, 0.5cm * \y) -- (3 * \layer + \layer - \myunit, 0.5cm * \z);
|
||||
};
|
||||
\foreach \z in {0cm, 2.5cm} {
|
||||
\draw (3 * \layer + \unit, 0.5cm * \y) -- (3 * \layer + \layer - \unit, \z);
|
||||
\draw (3 * \layer + \myunit, 0.5cm * \y) -- (3 * \layer + \layer - \myunit, \z);
|
||||
};
|
||||
};
|
||||
\foreach \y in {0,...,5} {
|
||||
\draw (3 * \layer + \unit, 2.5cm) -- (3 * \layer + \layer - \unit, 0.5cm * \y);
|
||||
\draw (3 * \layer + \unit, 0cm) -- (3 * \layer + \layer - \unit, 0.5cm * \y);
|
||||
\draw (3 * \layer + \myunit, 2.5cm) -- (3 * \layer + \layer - \myunit, 0.5cm * \y);
|
||||
\draw (3 * \layer + \myunit, 0cm) -- (3 * \layer + \layer - \myunit, 0.5cm * \y);
|
||||
};
|
||||
|
||||
% draw weights 5 --> output
|
||||
\foreach \y in {0cm, 2.5cm} {
|
||||
\draw (5 * \layer + \unit, \y) -- (5 * \layer + \layer - \unit, 1.25cm);
|
||||
\draw (5 * \layer + \myunit, \y) -- (5 * \layer + \layer - \myunit, 1.25cm);
|
||||
};
|
||||
\foreach \y in {1.5,...,3.5} {
|
||||
\draw (5 * \layer + \unit, 0.5cm * \y) -- (5 * \layer + \layer - \unit, 1.25cm);
|
||||
\draw (5 * \layer + \myunit, 0.5cm * \y) -- (5 * \layer + \layer - \myunit, 1.25cm);
|
||||
};
|
||||
|
||||
% draw hidden layers legend
|
||||
\node[anchor=base, align=center, text width=3.5cm, scale=0.5] (h) at (4cm, 4.5cm) {hidden layers (ReLU activation)};
|
||||
\draw[->] (h) -- (\layer + \unit, 3.6cm);
|
||||
\draw[->] (h) -- (2 * \layer + \unit, 2.85cm);
|
||||
\draw[->] (h) -- (3 * \layer + 0.5 * \unit, 2.85cm);
|
||||
\draw[->] (h) -- (\layer + \myunit, 3.6cm);
|
||||
\draw[->] (h) -- (2 * \layer + \myunit, 2.85cm);
|
||||
\draw[->] (h) -- (3 * \layer + 0.5 * \myunit, 2.85cm);
|
||||
\draw[->] (h) -- (4 * \layer, 3.6cm);
|
||||
\draw[->] (h) -- (5 * \layer - 0.5 * \unit, 2.85cm);
|
||||
\draw[->] (h) -- (5 * \layer - 0.5 * \myunit, 2.85cm);
|
||||
|
||||
\end{tikzpicture}
|
||||
|
||||
|
||||
@@ -2,7 +2,7 @@
|
||||
%\newlength{\layerheight}
|
||||
%\newlength{\perspective}
|
||||
%\newlength{\filters}
|
||||
%\newlength{\unit}
|
||||
%\newlength{\myunit}
|
||||
\newlength{\upperlevel}
|
||||
\newlength{\bottomlevel}
|
||||
\newlength{\concatheight}
|
||||
@@ -11,7 +11,7 @@
|
||||
\setlength{\layerheight}{3cm}
|
||||
\setlength{\perspective}{1cm}
|
||||
\setlength{\filters}{0.01cm}
|
||||
\setlength{\unit}{0.225cm}
|
||||
\setlength{\myunit}{0.225cm}
|
||||
\setlength{\upperlevel}{2.25cm}
|
||||
\setlength{\bottomlevel}{-2.25cm}
|
||||
\setlength{\concatheight}{0cm}
|
||||
@@ -52,8 +52,8 @@
|
||||
\node[anchor=south west, scale=0.65, rotate=45] at (2 * \layer, \concatheight + \layerheight) {$64 @ 12 \times 15$};
|
||||
|
||||
\draw (\layer + 32 * \filters + 1.2 * \perspective, \upperlevel + 0.5 * \layerheight) -- (\layer + 32 * \filters + 1.7 * \perspective, \upperlevel + 0.5 * \layerheight) -- (\layer + 32 * \filters + 1.7 * \perspective, \bottomlevel + 0.5 * \layerheight) -- (\layer + 32 * \filters + 1.2 * \perspective, \bottomlevel + 0.5 * \layerheight);
|
||||
\filldraw[fill=red!20, draw=black] (\layer + 32 * \filters + 1.7 * \perspective, \concatheight + 0.5 * \layerheight) node[anchor=center, scale=0.8] {$C$} circle (\unit);
|
||||
\draw[-latex] (\layer + 32 * \filters + 1.7 * \perspective + \unit, \concatheight + 0.5 * \layerheight) -- (\layer + 32 * \filters + 1.7 * \perspective + 3 * \unit, \concatheight + 0.5 * \layerheight);
|
||||
\filldraw[fill=red!20, draw=black] (\layer + 32 * \filters + 1.7 * \perspective, \concatheight + 0.5 * \layerheight) node[anchor=center, scale=0.8] {$C$} circle (\myunit);
|
||||
\draw[-latex] (\layer + 32 * \filters + 1.7 * \perspective + \myunit, \concatheight + 0.5 * \layerheight) -- (\layer + 32 * \filters + 1.7 * \perspective + 3 * \myunit, \concatheight + 0.5 * \layerheight);
|
||||
|
||||
% second layer
|
||||
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (3 * \layer, \upperlevel) -- (3 * \layer + 64 * \filters, \upperlevel) -- (3 * \layer + 64 * \filters + \perspective, \upperlevel + \perspective) -- (3 * \layer + \perspective, \upperlevel + \perspective) -- cycle;
|
||||
@@ -82,8 +82,8 @@
|
||||
\node[anchor=south west, scale=0.65, rotate=45] at (4 * \layer, \concatheight + \layerheight) {$128 @ 12 \times 15$};
|
||||
|
||||
\draw (3 * \layer + 64 * \filters + 1.1 * \perspective, \upperlevel + 0.5 * \layerheight) -- (3 * \layer + 64 * \filters + 1.6 * \perspective, \upperlevel + 0.5 * \layerheight) -- (3 * \layer + 64 * \filters + 1.6 * \perspective, \bottomlevel + 0.5 * \layerheight) -- (3 * \layer + 64 * \filters + 1.1 * \perspective, \bottomlevel + 0.5 * \layerheight);
|
||||
\filldraw[fill=red!20, draw=black] (3 * \layer + 64 * \filters + 1.6 * \perspective, \concatheight + 0.5 * \layerheight) node[anchor=center, scale=0.8] {$C$} circle (\unit);
|
||||
\draw[-latex] (3 * \layer + 64 * \filters + 1.6 * \perspective + \unit, \concatheight + 0.5 * \layerheight) -- (3 * \layer + 64 * \filters + 1.6 * \perspective + 3 * \unit, \concatheight + 0.5 * \layerheight);
|
||||
\filldraw[fill=red!20, draw=black] (3 * \layer + 64 * \filters + 1.6 * \perspective, \concatheight + 0.5 * \layerheight) node[anchor=center, scale=0.8] {$C$} circle (\myunit);
|
||||
\draw[-latex] (3 * \layer + 64 * \filters + 1.6 * \perspective + \myunit, \concatheight + 0.5 * \layerheight) -- (3 * \layer + 64 * \filters + 1.6 * \perspective + 3 * \myunit, \concatheight + 0.5 * \layerheight);
|
||||
|
||||
% third layer
|
||||
\filldraw[dashed, fill=orange!20, draw=black, fill opacity=0.5] (5 * \layer, \upperlevel) -- (5 * \layer + 32 * \filters, \upperlevel) -- (5 * \layer + 32 * \filters + \perspective, \upperlevel + \perspective) -- (5 * \layer + \perspective, \upperlevel + \perspective) -- cycle;
|
||||
@@ -112,23 +112,23 @@
|
||||
\node[anchor=south west, scale=0.65, rotate=45] at (6 * \layer, \concatheight + \layerheight) {$64 @ 12 \times 15$};
|
||||
|
||||
\draw (5 * \layer + 32 * \filters + 1.2 * \perspective, \upperlevel + 0.5 * \layerheight) -- (5 * \layer + 32 * \filters + 1.7 * \perspective, \upperlevel + 0.5 * \layerheight) -- (5 * \layer + 32 * \filters + 1.7 * \perspective, \bottomlevel + 0.5 * \layerheight) -- (5 * \layer + 32 * \filters + 1.2 * \perspective, \bottomlevel + 0.5 * \layerheight);
|
||||
\filldraw[fill=red!20, draw=black] (5 * \layer + 32 * \filters + 1.7 * \perspective, \concatheight + 0.5 * \layerheight) node[anchor=center, scale=0.8] {$C$} circle (\unit);
|
||||
\draw[-latex] (5 * \layer + 32 * \filters + 1.7 * \perspective + \unit, \concatheight + 0.5 * \layerheight) -- (5 * \layer + 32 * \filters + 1.7 * \perspective + 3 * \unit, \concatheight + 0.5 * \layerheight);
|
||||
\filldraw[fill=red!20, draw=black] (5 * \layer + 32 * \filters + 1.7 * \perspective, \concatheight + 0.5 * \layerheight) node[anchor=center, scale=0.8] {$C$} circle (\myunit);
|
||||
\draw[-latex] (5 * \layer + 32 * \filters + 1.7 * \perspective + \myunit, \concatheight + 0.5 * \layerheight) -- (5 * \layer + 32 * \filters + 1.7 * \perspective + 3 * \myunit, \concatheight + 0.5 * \layerheight);
|
||||
|
||||
% flatten layer
|
||||
\foreach \x in {0,...,4} {
|
||||
\filldraw[fill=cyan!10, draw=black] (6 * \layer + 3cm, \concatheight + \unit + 0.75 * \x cm) circle (\unit);
|
||||
\draw (6 * \layer + 3cm + \unit, \concatheight + \unit + 0.75 * \x cm) -- (7 * \layer + 2cm - \unit, \concatheight + \unit + 0.5 * \layerheight);
|
||||
\filldraw[fill=cyan!10, draw=black] (6 * \layer + 3cm, \concatheight + \myunit + 0.75 * \x cm) circle (\myunit);
|
||||
\draw (6 * \layer + 3cm + \myunit, \concatheight + \myunit + 0.75 * \x cm) -- (7 * \layer + 2cm - \myunit, \concatheight + \myunit + 0.5 * \layerheight);
|
||||
};
|
||||
\node[anchor=north, scale=0.5, below=15pt, align=center] at (6 * \layer + 3cm, \concatheight + \unit) {flatten};
|
||||
\node[anchor=north, scale=0.5, below=15pt, align=center] at (6 * \layer + 3cm, \concatheight + \myunit) {flatten};
|
||||
|
||||
% draw the "flatenisation"
|
||||
\draw[dashed] (6 * \layer + 64 * \filters, \layerheight) -- (6 * \layer + 3 cm, 3cm + 2 * \unit) -- (6 * \layer + 64 * \filters + \perspective, \layerheight + \perspective) -- cycle;
|
||||
\draw[dashed] (6 * \layer + 64 * \filters, \layerheight) -- (6 * \layer + 3 cm, 3cm + 2 * \myunit) -- (6 * \layer + 64 * \filters + \perspective, \layerheight + \perspective) -- cycle;
|
||||
\draw[dashed] (6 * \layer + 64 * \filters, 0cm) -- (6 * \layer + 3 cm, 0cm) -- (6 * \layer + 64 * \filters + \perspective, \perspective) -- cycle;
|
||||
|
||||
% output layer
|
||||
\filldraw[fill=cyan!10, draw=black] (7 * \layer + 2cm, \concatheight + \unit + 0.5 * \layerheight - \unit) -- (7 * \layer + 2cm, \concatheight + \unit + 0.5 * \layerheight) circle (\unit) -- (7 * \layer + 2cm, \concatheight + \unit + 0.5 * \layerheight + \unit);
|
||||
\draw (7 * \layer + 2cm + 0.05cm, \concatheight + \unit + 0.5 * \layerheight) node[anchor=north, below=10pt, text width=2cm, scale=0.35, align=center] {output layer [1 unit]} -- (7 * \layer + 2cm + 0.10cm, \concatheight + \unit + 0.5 * \layerheight) -- (7 * \layer + 2cm + 0.15cm, \concatheight + \unit + 0.5 * \layerheight + 0.05cm);
|
||||
\filldraw[fill=cyan!10, draw=black] (7 * \layer + 2cm, \concatheight + \myunit + 0.5 * \layerheight - \myunit) -- (7 * \layer + 2cm, \concatheight + \myunit + 0.5 * \layerheight) circle (\myunit) -- (7 * \layer + 2cm, \concatheight + \myunit + 0.5 * \layerheight + \myunit);
|
||||
\draw (7 * \layer + 2cm + 0.05cm, \concatheight + \myunit + 0.5 * \layerheight) node[anchor=north, below=10pt, text width=2cm, scale=0.35, align=center] {output layer [1 unit]} -- (7 * \layer + 2cm + 0.10cm, \concatheight + \myunit + 0.5 * \layerheight) -- (7 * \layer + 2cm + 0.15cm, \concatheight + \myunit + 0.5 * \layerheight + 0.05cm);
|
||||
|
||||
% draw the first convolution
|
||||
\filldraw[fill=red!50, draw=black, fill opacity=0.2] (1cm, 0.9 * \layerheight) -- (1cm + \perspective, 0.9 * \layerheight + \perspective) -- (1cm + \perspective, \layerheight + \perspective) -- (1cm, \layerheight) -- cycle;
|
||||
|
||||
Reference in New Issue
Block a user