Finish writing
Signed-off-by: Riccardo Finotello <riccardo.finotello@gmail.com>
This commit is contained in:
634
thesis.tex
634
thesis.tex
@@ -1,4 +1,4 @@
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\documentclass[10pt, aspectratio=169]{beamer}
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\documentclass[10pt, aspectratio=169, compress]{beamer}
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\usepackage[utf8]{inputenc}
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\usepackage[T1]{fontenc}
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@@ -119,30 +119,30 @@
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\end{center}
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}
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% \setbeamertemplate{footline}{%
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% \usebeamerfont{footnote}
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% \usebeamercolor{footnote}
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% \hfill
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% \insertframenumber{}~/~\inserttotalframenumber{}
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% \hspace{1em}
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% \vspace{1em}
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% \par
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% }
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\setbeamertemplate{footline}{%
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\usebeamerfont{footnote}
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\usebeamercolor{footnote}
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\hfill
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\insertframenumber{}~/~\inserttotalframenumber{}
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\hspace{1em}
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\vspace{1em}
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\par
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}
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% \AtBeginSection[]
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% {%
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% {%
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% \setbeamertemplate{footline}{}
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% \usebackgroundtemplate{%
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% \transparent{0.1}
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% \includegraphics[width=\paperwidth]{img/torino.png}
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% }
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% \addtobeamertemplate{background canvas}{\transfade[duration=0.25]}{}
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% \begin{frame}[noframenumbering]{\contentsname}
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% \tableofcontents[currentsection]
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% \end{frame}
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% }
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% }
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\AtBeginSection[]
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{%
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{%
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\setbeamertemplate{footline}{}
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\usebackgroundtemplate{%
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\transparent{0.1}
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\includegraphics[width=\paperwidth]{img/torino.png}
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}
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\addtobeamertemplate{background canvas}{\transfade[duration=0.25]}{}
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\begin{frame}[noframenumbering]{\contentsname}
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\tableofcontents[currentsection]
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\end{frame}
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}
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}
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\begin{document}
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@@ -601,7 +601,7 @@
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\end{frame}
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\begin{frame}{Doubling Trick and Spinor Representation}
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\begin{block}{Doubling Trick}
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\begin{equationblock}{Doubling Trick}
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\begin{equation*}
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\partial_z \mathcal{X}( z )
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=
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@@ -628,12 +628,12 @@
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}
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\end{equation*}
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where $\mathscr{H}_{\gtrless}^{(t)} = \qty{z \in \mathds{C} \mid \Im z \gtrless 0~\text{or}~z \in D_{(t)} }$ and $\updelta_{\pm} = \upeta \pm i 0^+$.
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\end{block}
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\end{equationblock}
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\pause
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\begin{tikzpicture}[remember picture, overlay]
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\draw[line width=4pt, red] (31em,6em) ellipse (0.8cm and 1.2cm);
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\draw[line width=4pt, red] (31em,6em) ellipse (0.8cm and 1cm);
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\end{tikzpicture}
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\pause
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@@ -700,8 +700,7 @@
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\frac{1}{\Upgamma( c_n )}\,
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\tensor[_2]{F}{_1}( a_n,\, b_n;\, c_n;\, \upomega_z )
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\\
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\qty( -\upomega_z )^{1 - c_n}\,
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\frac{1}{\Upgamma( 2 - c_n )}\,
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\frac{\qty( -\upomega_z )^{1 - c_n}}{\Upgamma( 2 - c_n )}\,
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\tensor[_2]{F}{_1}( a_n + 1 - c_n,\, b_n + 1 - c_n;\, 2 - c_n;\, \upomega_z )
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)
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\end{equation*}
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@@ -1177,13 +1176,586 @@
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\subsection[NBO]{Null Boost Orbifold}
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\begin{frame}{Null Boost Orbifold}
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Start from $\qty( x^+,\, x^-,\, x^2,\, \vec{x} ) \in \mathscr{M}^{1,\, D-1}$:
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\begin{equation*}
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\begin{cases}
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u & = x^-
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\\
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z & = \frac{x^2}{\Updelta\, x^-}
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\\
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v & = x^+ - \frac{1}{2} \frac{\qty( x^2 )^2}{x^-}
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\end{cases}
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\qquad
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\Rightarrow
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\qquad
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\dd{s}^2 = -2 \dd{u} \dd{v} + \qty( \Updelta\, u )^2\, \dd{z}^2 + \updelta_{ij} \dd{x}^i \dd{x}^j
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\end{equation*}
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\pause
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\begin{equationblock}{Killing Vector and Null Boost Oribfold}
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\begin{equation*}
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\upkappa = -i \qty( 2 \uppi \Updelta ) J_{+2} = 2 \uppi \partial_z
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\Rightarrow
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z \sim z + 2 \uppi n
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\end{equation*}
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\end{equationblock}
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\pause
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Consider \highlight{scalar QED:}
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\begin{equation*}
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\upphi_{\qty{ k_+,\, l,\, \vec{k},\, r}}\qty( u,\, v,\, z,\, \vec{x} )
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=
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e^{i \qty( k_+ v + l z + \vec{k} \cdot \vec{x} )}\,
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\widetilde{\upphi}_{\qty{ k_+,\, l,\, \vec{k},\, r}}\qty( u )
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=
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\frac{e^{i \qty( k_+ v + l z + \vec{k} \cdot \vec{x} )}}{\sqrt{\qty( 2 \uppi )^D\, \abs{2 \Updelta k_+ u}}}\,
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e^{-i \frac{l^2}{2 \Updelta^2 k_+} \frac{1}{u} + i \frac{\norm{\vec{k}}^2 + r}{2 k_+} u}
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\end{equation*}
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\end{frame}
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\begin{frame}{Scalar QED Interactions}
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Scalar--photon interactions:
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\begin{equation*}
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S_{\text{sQED}}^{\text{(int)}}
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=
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\int\limits_{\Upomega} \dd[D]{x} \sqrt{- g }\,
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\qty(%
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-i\, e\, g^{\upalpha\upbeta} a_{\upalpha} \qty( \upphi^*\, \partial_{\upbeta} \upphi - \partial_{\upbeta} \upphi^*\, \upphi )
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+ e^2\, g^{\upalpha\upbeta} a_{\upalpha} a_{\upbeta} \abs{\upphi}^2
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- \frac{g_4}{4}\, \abs{\upphi}^4
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)
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\end{equation*}
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\pause
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Terms involved:
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\begin{equation*}
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\begin{split}
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\mathcal{I}^{\qty[\upnu]}_{\qty{N}}
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& =
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\int\limits_{-\infty}^{+\infty} \dd{u}
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\abs{\Updelta\, u} u^{\upnu}
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\prod\limits_{i = 1}^N
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\widetilde{\upphi}_{\qty{ k_{+\, (i)},\, l_{(i)},\, \vec{k}_{(i)},\, r_{(i)}}}\qty( u )
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\\
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\mathcal{J}^{\qty[\upnu]}_{\qty{N}}
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& =
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\int\limits_{-\infty}^{+\infty} \dd{u}
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\abs{\Updelta} \abs{u}^{1 + \upnu}
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\prod\limits_{i = 1}^N
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\widetilde{\upphi}_{\qty{ k_{+\, (i)},\, l_{(i)},\, \vec{k}_{(i)},\, r_{(i)}}}\qty( u )
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\end{split}
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\end{equation*}
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\pause
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\begin{center}
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\it
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most terms \textbf{do not converge} and cannot be recovered even with a \textbf{distributional interpretions} due to the term $\propto u^{-1}$ in the exponentatial
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\end{center}
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\end{frame}
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\begin{frame}{String and Field Theory}
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So far:
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\begin{itemize}
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\item field theory presents \textbf{divergences}
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\pause
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\item issues are \textbf{still present} in sQED (eikonal?)
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\pause
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\item divergences are \textbf{not (only) gravitational}
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\end{itemize}
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\pause
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\begin{equationblock}{Massive String States}
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\begin{equation*}
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V_M\qty( x;\, k,\, S,\, \upxi )
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=
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\colon
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\qty(%
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\frac{i}{\sqrt{2 \upalpha'}}\,
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\upxi \cdot \partial^2_x X( x,\, x )
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+
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\qty( \frac{i}{\sqrt{2 \upalpha'}} )^2\,
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S_{\upalpha\upbeta}
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\partial_x X^{\upalpha}( x,\, x )
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\partial_x X^{\upbeta}( x,\, x )
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)
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e^{i k \cdot X( x,\, x )}
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\colon
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\end{equation*}
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\end{equationblock}
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\pause
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\begin{center}
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\it
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string theory cannot do \textbf{better than field theory} (EFT) if the latter \textbf{does not exist} (even a Wilson line around $z$ does not prevent such behaviour)
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\end{center}
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\end{frame}
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\begin{frame}{Resolution and Motivation}
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Introduce the \highlight{generalised NBO:}
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\begin{equation*}
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\begin{cases}
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u & = x^-
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\\
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z & = \frac{1}{2 x^-} \qty( \frac{x^2}{\Updelta_2} + \frac{x^3}{\Updelta_3} )
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\\
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w & = \frac{1}{2 x^-} \qty( \frac{x^2}{\Updelta_2} - \frac{x^3}{\Updelta_3} )
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\\
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v & = x^+ - \frac{1}{2 x^-} \qty( \qty( x^2 )^2 + \qty( x^3 )^2 )
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\end{cases}
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\qquad
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\Rightarrow
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\qquad
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\upkappa
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=
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-2 \uppi i \qty( \Updelta_2 J_{+2} + \Updelta_3 J_{+3} )
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=
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2 \uppi \partial_z
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\end{equation*}
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\pause
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\begin{equationblock}{Distributional Interpretation}
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\begin{equation*}
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\widetilde{\upphi}_{\qty{ k_+,\, p,\, l,\, \vec{k},\, r}}\qty( u )
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=
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\frac{1}{2 \sqrt{\qty(2 \uppi)^D \abs{\Updelta_2 \Updelta_3 k_+}}}
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\frac{1}{\abs{u}}
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e^{-i\, \qty( \frac{1}{8 k_+ u} \qty[ \frac{(l + p)^2}{\Updelta_2^2} + \frac{(l - p)^2}{\Updelta_3^2} ] - \frac{\norm{\vec{k}}^2 + r}{2 k_+} u )}
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\end{equation*}
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\end{equationblock}
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\end{frame}
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\begin{frame}{On the Divergences and Their Nature}
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\begin{itemize}
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\item divergences are present in sQED and \textbf{open string} sector
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\pause
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\item singularities $\Rightarrow$ \textbf{massive states} are no longer spectators
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\pause
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\item vanishing volume (\textbf{compact orbifold directions}) $\Rightarrow$ particles ``cannot escape''
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\pause
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\item \textbf{non compact} orbifold directions $\Rightarrow$ interpretation of \textbf{amplitudes as distributions}
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\pause
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\item issue not restricted to NBO/GNBO but also BO, null brane, etc. (it is a \textbf{general issues} connected to the geometry of the underlying space)
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\end{itemize}
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\pause
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\vspace{2em}
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\begin{center}
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\it
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spacetime singularities are \textbf{hidden into contact terms} and interactions with \textbf{massive states} (the gravitational eikonal deals with massless interactions)
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\end{center}
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\begin{tikzpicture}[remember picture, overlay]
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\draw[line width=4pt, red] (0em, 4.5em) rectangle (40em, 1em);
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\end{tikzpicture}
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\end{frame}
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\section[Deep Learning]{Deep Learning the Geometry of String Theory}
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\begin{frame}{CCC}
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c
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\subsection[Introduction]{Machine Learning and Deep Learning}
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\begin{frame}{The Simplest Calabi--Yau}
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Focus on Calabi--Yau \highlight{3-folds:}
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\begin{equation*}
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h^{r,\, s} = \dim\limits_{\mathds{C}} H_{\overline{\partial}}^{r,\, s}\qty( M,\, \mathds{C} )
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\qquad
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\Rightarrow
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\qquad
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\begin{cases}
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h^{0,\, 0} & = h^{3,\, 0} = 1
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\\
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h^{r,\, 0} & = 0 \quad \text{if} \quad r \neq 3
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\\
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h^{r,\, s} & = h^{3 - r,\, 3 - s}
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\\
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h^{1,\, 1},\, h^{2,\, 1} \in \mathds{N}
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\end{cases}
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\end{equation*}
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\pause
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\begin{block}{Complete Intersection Calabi--Yau Manifolds}
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Intersection of hypersurfaces in
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\begin{equation*}
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\mathcal{A} = \mathds{P}^{n_1} \times \dots \times \mathds{P}^{n_m}
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\end{equation*}
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where
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\begin{equation*}
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\mathds{P}^n\colon
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\qquad
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\begin{cases}
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p_a\qty( Z^0,\, \dots,\, Z^n ) & = P_{I_1 \dots I_a} Z^{I_1} \dots Z^{I_a} = 0
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\\
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p_a\qty( \uplambda Z^0,\, \dots,\, \uplambda Z^n ) & = \uplambda^a p_a\qty( Z^0,\, \dots,\, Z^n )
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\end{cases}
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\end{equation*}
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\end{block}
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\end{frame}
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\begin{frame}{Representation of the Output}
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CICY can be generalised to \highlight{$m$ projective spaces and $k$ equations.}
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The problem is thus mapped to:
|
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\begin{equation*}
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||||
\begin{tabular}{@{}lccc@{}}
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$\mathscr{R}\colon$
|
||||
&
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$\mathds{Z}^{m \times k}$
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&
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$\longrightarrow$
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&
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$\mathds{N}$
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||||
\\[1em]
|
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&
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$\qty[%
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||||
\begin{tabular}{@{}c|ccc@{}}
|
||||
$\mathds{P}^{n_1}$ & $a_1^1$ & $\dots$ & $a_k^1$
|
||||
\\
|
||||
$\vdots$ & $\vdots$ & $\ddots$ & $\vdots$
|
||||
\\
|
||||
$\mathds{P}^{n_m}$ & $a_1^m$ & $\dots$ & $a_k^m$
|
||||
\end{tabular}
|
||||
]$
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&
|
||||
$\longrightarrow$
|
||||
&
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||||
$h^{1,\, 1} \quad \text{or} \quad h^{2,\, 1}$
|
||||
\end{tabular}
|
||||
\end{equation*}
|
||||
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\pause
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\begin{block}{Machine Learning Approach}
|
||||
What is $\mathscr{R}$?
|
||||
\begin{equation*}
|
||||
\mathscr{R}( M ) \longrightarrow \mathscr{R}_n( M;\, w )
|
||||
\qquad
|
||||
\text{s.t.}
|
||||
\qquad
|
||||
\lim\limits_{n \to \infty} f( M;\, w ) = \lim\limits_{n \to \infty} \abs{\mathscr{R}( M ) - \mathscr{R}_n( M;\, w )} = 0
|
||||
\end{equation*}
|
||||
\end{block}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Machine Learning}
|
||||
\begin{itemize}
|
||||
\item exchange \textbf{analytical solution} with \textbf{optimisation problem}
|
||||
|
||||
\pause
|
||||
|
||||
\item use \textbf{various algorithms} and exploit \textbf{large datasets}
|
||||
|
||||
\pause
|
||||
|
||||
\item learn a \textbf{representation} rather than a \textbf{solution}
|
||||
|
||||
\pause
|
||||
|
||||
\item effectively use knowledge from \textbf{computer science, mathematics and physics} to solve problems
|
||||
\end{itemize}
|
||||
|
||||
\pause
|
||||
|
||||
\begin{center}
|
||||
\includegraphics[width=0.7\linewidth]{img/label-distribution_orig}
|
||||
\end{center}
|
||||
\end{frame}
|
||||
|
||||
|
||||
\subsection[Machine Learning]{Machine Learning for String Theory}
|
||||
|
||||
|
||||
\begin{frame}{Exploratory Data Analysis}
|
||||
Machine Learning \highlight{pipeline:}
|
||||
\begin{center}
|
||||
\textbf{exploratory} data analysis
|
||||
$\rightarrow$
|
||||
feature \textbf{selection}
|
||||
$\rightarrow$
|
||||
Hodge numbers
|
||||
\end{center}
|
||||
|
||||
\pause
|
||||
|
||||
\begin{columns}
|
||||
\begin{column}{0.5\linewidth}
|
||||
\centering
|
||||
\includegraphics[width=0.9\columnwidth]{img/corr-matrix_orig}
|
||||
\end{column}
|
||||
\hfill
|
||||
\begin{column}{0.5\linewidth}
|
||||
\centering
|
||||
\includegraphics[width=0.9\columnwidth, trim={0 0 6in 0}, clip]{img/scalar-features_orig}
|
||||
\end{column}
|
||||
\end{columns}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Dataset}
|
||||
\begin{itemize}
|
||||
\item $7890$ CICY manifolds (full dataset)
|
||||
|
||||
\pause
|
||||
|
||||
\item \textbf{dataset pruning}: no product spaces, no ``very far'' outliers (reduction of $0.49\%$)
|
||||
|
||||
\pause
|
||||
|
||||
\item $h^{1,\, 1} \in \qty[ 1,\, 16 ]$ and $h^{2,\, 1} \in \qty[ 15,\, 86 ]$
|
||||
|
||||
\pause
|
||||
|
||||
\item $80\%$ training, $10\%$ validation, $10\%$ test
|
||||
|
||||
\pause
|
||||
|
||||
\item choose \textbf{regression}, but evaluate using \textbf{accuracy} (round the result)
|
||||
\end{itemize}
|
||||
|
||||
\pause
|
||||
|
||||
\begin{center}
|
||||
\includegraphics[width=0.7\linewidth]{img/label-distribution-compare_orig}
|
||||
\end{center}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Machine Learning}
|
||||
\centering
|
||||
\includegraphics[width=0.85\linewidth]{img/ml_map}
|
||||
|
||||
\pause
|
||||
|
||||
\begin{tikzpicture}[remember picture, overlay]
|
||||
\draw[line width=10pt, red, -latex] (-18em,1em) -- (-14.5em, 6em);
|
||||
\draw[line width=10pt, red, -latex] (19em, 7em) -- (14em, 4em);
|
||||
\end{tikzpicture}
|
||||
|
||||
\pause
|
||||
|
||||
\begin{tikzpicture}[remember picture, overlay]
|
||||
\draw[line width=4pt, red] (12em,12em) ellipse (2cm and 1.5cm);
|
||||
\end{tikzpicture}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{A Word on PCA}
|
||||
\begin{columns}
|
||||
\begin{column}{0.4\linewidth}
|
||||
What is PCA for a $X \in \mathds{R}^{n \times p}$?
|
||||
\begin{itemize}
|
||||
\item find new coordinates to \textbf{``put the variance in order''}
|
||||
|
||||
\item \highlight{equivalently} compute the \textbf{eigenvectors} of $X X^T$ or the \textbf{singular values} of $X$
|
||||
|
||||
\item isolate \textbf{the signal} from the \textbf{background}
|
||||
|
||||
\item ease the machine learning job of finding a better representation of the input
|
||||
\end{itemize}
|
||||
\end{column}
|
||||
\hfill
|
||||
\begin{column}{0.6\linewidth}
|
||||
\centering
|
||||
\includegraphics[width=0.5\columnwidth]{img/marchenko-pastur}
|
||||
\includegraphics[width=\columnwidth]{img/svd_orig}
|
||||
\end{column}
|
||||
\end{columns}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Machine Learning Results}
|
||||
\begin{columns}
|
||||
\begin{column}{0.5\linewidth}
|
||||
\centering
|
||||
\textbf{Configuration Matrix Only}
|
||||
\includegraphics[width=0.8\columnwidth, trim={0 0 3.3in 0}, clip]{img/cicy_matrix_plots}
|
||||
\end{column}
|
||||
\hfill\pause
|
||||
\begin{column}{0.5\linewidth}
|
||||
\centering
|
||||
\textbf{Best Training Set}
|
||||
\includegraphics[width=0.8\columnwidth, trim={0 0 3.3in 0}, clip]{img/cicy_best_plots}
|
||||
\end{column}
|
||||
\end{columns}
|
||||
\end{frame}
|
||||
|
||||
\subsection[Deep Learning]{AI Implementations for Geometry and Strings}
|
||||
|
||||
\begin{frame}{Artificial Intelligence and Neural Networks}
|
||||
\begin{columns}
|
||||
\begin{column}{0.6\linewidth}
|
||||
\begin{itemize}
|
||||
\item use \textbf{gradient descent} to optimise \textbf{weights}
|
||||
|
||||
\item learn highly \textbf{non linear} representations of the input
|
||||
|
||||
\item can be \highlight{``large''} to have enough parameters
|
||||
|
||||
\item can be \highlight{``deep''} to to learn \textbf{complicated functions}
|
||||
\end{itemize}
|
||||
|
||||
\begin{block}{Neural Networks}
|
||||
\vspace{0.5em}
|
||||
\begin{tabular}{@{}lc@{}}
|
||||
fully connected:
|
||||
&
|
||||
$a^{\qty(i)\, \qty{l+1}} = \upphi\qty( a^{\qty(i)\, \qty{l}} \cdot W^{\qty{l}} + b^{\qty{l}} \mathds{1} )$
|
||||
\\
|
||||
convolutional:
|
||||
&
|
||||
$a^{\qty(i)\, \qty{l+1}} = \upphi\qty( a^{\qty(i)\, \qty{l}}\, *\, W^{\qty{l}} + b^{\qty{l}} \mathds{1} )$
|
||||
\end{tabular}
|
||||
\end{block}
|
||||
|
||||
Non linearity ensured by:
|
||||
\begin{equation*}
|
||||
\upphi( z ) = \mathrm{ReLU}\qty( z ) = \max\qty(0,\, z)
|
||||
\end{equation*}
|
||||
\end{column}
|
||||
\hfill
|
||||
\begin{column}{0.4\linewidth}
|
||||
\centering
|
||||
\resizebox{\columnwidth}{!}{\import{img}{fc.pgf}}
|
||||
\end{column}
|
||||
\end{columns}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Convolutional Neural Networks}
|
||||
Why convolutional?
|
||||
\begin{columns}
|
||||
\begin{column}{0.4\linewidth}
|
||||
\begin{itemize}[<+->]
|
||||
\item retain \textbf{spacial awareness}
|
||||
|
||||
\item smaller \textbf{no.\ of parameters} ($\approx 2 \times 10^5$ vs.\ $\approx 2 \times 10^6$)
|
||||
|
||||
\item weights are \textbf{shared}
|
||||
|
||||
\item CNN can isolate \textbf{``defining features''}
|
||||
|
||||
\item find patterns as in \textbf{computer vision}
|
||||
\end{itemize}
|
||||
\end{column}
|
||||
\hfill
|
||||
\begin{column}{0.6\linewidth}
|
||||
\centering
|
||||
\only<1>{\includegraphics[width=0.75\columnwidth, trim={12in 10in 0 0}, clip]{img/input_mat}}
|
||||
\only<2>{\includegraphics[width=0.75\columnwidth, trim={12in 5in 0 5in}, clip]{img/input_mat}}
|
||||
\only<3>{\includegraphics[width=0.75\columnwidth, trim={12in 0 0 10in}, clip]{img/input_mat}}
|
||||
\only<4->{\resizebox{\columnwidth}{!}{\import{img}{ccnn.pgf}}}
|
||||
\end{column}
|
||||
\end{columns}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Inception Neural Networks}
|
||||
Recent development by Google's deep learning teams led to:
|
||||
\begin{itemize}
|
||||
\item neural networks with \textbf{better generalisation properties}
|
||||
|
||||
\item smaller networks (both parameters and depth)
|
||||
|
||||
\item different \textbf{concurrent kernels} (e.g.\ one over \textbf{equations} one over \textbf{coordinates})
|
||||
\end{itemize}
|
||||
|
||||
\pause
|
||||
|
||||
\begin{center}
|
||||
\resizebox{0.75\linewidth}{!}{\import{img}{icnn.pgf}}
|
||||
\end{center}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Deep Learning Results and Generalisation Properties}
|
||||
\begin{columns}
|
||||
\begin{column}{0.5\linewidth}
|
||||
\centering
|
||||
\textbf{Best Training Set}
|
||||
\includegraphics[width=\columnwidth]{img/cicy_best_plots}
|
||||
\end{column}
|
||||
\hfill
|
||||
\begin{column}{0.5\linewidth}
|
||||
\centering
|
||||
\includegraphics[width=0.75\columnwidth]{img/inc_nn_learning_curve_h11}
|
||||
\includegraphics[width=0.75\columnwidth]{img/inc_nn_learning_curve}
|
||||
\end{column}
|
||||
\end{columns}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{A Few Comments and Future Directions}
|
||||
Why \highlight{deep learning in physics?}
|
||||
\begin{itemize}
|
||||
\item reliable \textbf{predictive method} \pause (provided good data analysis)
|
||||
|
||||
\pause
|
||||
|
||||
\item reliable \textbf{source of inspiration} \pause (provided good data analysis)
|
||||
|
||||
\pause
|
||||
|
||||
\item reliable \textbf{generalisation method} \pause (provided good data analysis)
|
||||
|
||||
\pause
|
||||
|
||||
\item \textbf{CNNs are powerful tools} (this is the \emph{first time in physics!})
|
||||
|
||||
\pause
|
||||
|
||||
\item interdisciplinary approach $=$ win-win situation!
|
||||
\end{itemize}
|
||||
|
||||
\pause
|
||||
|
||||
What now?
|
||||
|
||||
\begin{itemize}
|
||||
\item representation learning $\Rightarrow$ what is the best way to represent CICYs?
|
||||
|
||||
\pause
|
||||
|
||||
\item study invariances $\Rightarrow$ invariances should not influence the result (graph representations?)
|
||||
|
||||
\pause
|
||||
|
||||
\item higher dimensions $\Rightarrow$ what about CICY 4-folds?
|
||||
|
||||
\pause
|
||||
|
||||
\item geometric deep learning $\Rightarrow$ explain the geometry of the ``AI'' behind deep learning!
|
||||
|
||||
\pause
|
||||
|
||||
\item reinforcement learning $\Rightarrow$ give the rules, not the result!
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
|
||||
{%
|
||||
\setbeamertemplate{footline}{}
|
||||
\usebackgroundtemplate{%
|
||||
\transparent{0.1}
|
||||
\includegraphics[width=\paperwidth]{img/torino.png}
|
||||
}
|
||||
\addtobeamertemplate{background canvas}{\transfade[duration=0.25]}{}
|
||||
\begin{frame}[noframenumbering]{The End?}
|
||||
\begin{center}
|
||||
\Huge
|
||||
THANK YOU!
|
||||
\end{center}
|
||||
\end{frame}
|
||||
}
|
||||
|
||||
\end{document}
|
||||
|
||||
Reference in New Issue
Block a user