finished chapter 2

This commit is contained in:
Clemens Dautermann 2020-01-25 16:42:10 +01:00
parent d02f0cdbbc
commit 8aec5e4d07
7 changed files with 205 additions and 196 deletions

View file

@ -41,83 +41,84 @@
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.3.2}Overfitting}{6}{subsubsection.1.3.2}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Overfitting\relax }}{6}{figure.caption.4}\protected@file@percent }
\newlabel{Overfitting}{{3}{6}{Overfitting\relax }{figure.caption.4}{}}
\abx@aux@cite{2}
\abx@aux@segm{0}{0}{2}
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {2}Verschiedene Techniken maschinellen Lernens}{7}{section.2}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}\IeC {\"U}berwachtes Lernen}{7}{subsection.2.1}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Un\IeC {\"u}berwachtes Lernen}{7}{subsection.2.2}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Best\IeC {\"a}rkendes Lernen}{7}{subsection.2.3}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {3}Neuronale Netze}{7}{section.3}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Maschinelles Lernen und menschliches Lernen}{7}{subsection.3.1}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Neuron \newline Quelle: simple.wikipedia.org/wiki/File:Neuron.svg\newline Copyright: CC Attribution-Share Alike von Nutzer Dhp1080,\newline bearbeitet}}{7}{figure.caption.5}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Der Aufbau eines neuronalen Netzes}{8}{subsection.3.2}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Berechnung des Ausgabevektors}{8}{subsection.3.3}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Ein einfaches neuronales Netz\relax }}{9}{figure.caption.6}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Der Plot der Sigmoid Funktion $\sigma (x)=\frac {e^x}{e^x+1}$\relax }}{10}{figure.caption.7}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Formel zur Berechnung eines Ausgabevektors aus einem Eingabevektor durch ein Layer Neuronen. \relax }}{11}{figure.caption.8}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Der Lernprozess}{11}{subsection.3.4}\protected@file@percent }
\abx@aux@cite{2}
\abx@aux@segm{0}{0}{2}
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {3}Neuronale Netze}{8}{section.3}\protected@file@percent }
\newlabel{sec:neuronale-netze}{{3}{8}{Neuronale Netze}{section.3}{}}
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Maschinelles Lernen und menschliches Lernen}{8}{subsection.3.1}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Neuron \newline Quelle: simple.wikipedia.org/wiki/File:Neuron.svg\newline Copyright: CC Attribution-Share Alike von Nutzer Dhp1080,\newline bearbeitet}}{8}{figure.caption.5}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Der Aufbau eines neuronalen Netzes}{9}{subsection.3.2}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Berechnung des Ausgabevektors}{9}{subsection.3.3}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Ein einfaches neuronales Netz\relax }}{10}{figure.caption.6}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Der Plot der Sigmoid Funktion $\sigma (x)=\frac {e^x}{e^x+1}$\relax }}{11}{figure.caption.7}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Formel zur Berechnung eines Ausgabevektors aus einem Eingabevektor durch ein Layer Neuronen. \relax }}{12}{figure.caption.8}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Der Lernprozess}{12}{subsection.3.4}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {3.5}Fehlerfunktionen}{12}{subsection.3.5}\protected@file@percent }
\abx@aux@cite{3}
\abx@aux@segm{0}{0}{3}
\abx@aux@segm{0}{0}{3}
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {3.5}Fehlerfunktionen}{12}{subsection.3.5}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.5.1}MSE -- Durchschnittlicher quadratischer Fehler}{12}{subsubsection.3.5.1}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Die Gleichung f\IeC {\"u}r den durchschnittlichen quadratischen Fehler\relax }}{12}{figure.caption.9}\protected@file@percent }
\newlabel{MSE_equation}{{8}{12}{Die Gleichung für den durchschnittlichen quadratischen Fehler\relax }{figure.caption.9}{}}
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.5.2}MAE -- Durchschnitztlicher absoluter Fehler}{12}{subsubsection.3.5.2}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Die Gleichung f\IeC {\"u}r den durchschnittlichen absoluten Fehler\relax }}{12}{figure.caption.10}\protected@file@percent }
\newlabel{MAE_equation}{{9}{12}{Die Gleichung für den durchschnittlichen absoluten Fehler\relax }{figure.caption.10}{}}
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.5.1}MSE -- Durchschnittlicher quadratischer Fehler}{13}{subsubsection.3.5.1}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Die Gleichung f\IeC {\"u}r den durchschnittlichen quadratischen Fehler\relax }}{13}{figure.caption.9}\protected@file@percent }
\newlabel{MSE_equation}{{8}{13}{Die Gleichung für den durchschnittlichen quadratischen Fehler\relax }{figure.caption.9}{}}
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.5.2}MAE -- Durchschnitztlicher absoluter Fehler}{13}{subsubsection.3.5.2}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Die Gleichung f\IeC {\"u}r den durchschnittlichen absoluten Fehler\relax }}{13}{figure.caption.10}\protected@file@percent }
\newlabel{MAE_equation}{{9}{13}{Die Gleichung für den durchschnittlichen absoluten Fehler\relax }{figure.caption.10}{}}
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.5.3}Kreuzentropiefehler}{13}{subsubsection.3.5.3}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces Der Graph der Kreuzentropie Fehlerfunktion wenn das tats\IeC {\"a}chliche Label 1 ist\relax }}{13}{figure.caption.11}\protected@file@percent }
\newlabel{CEL_Graph}{{10}{13}{Der Graph der Kreuzentropie Fehlerfunktion wenn das tatsächliche Label 1 ist\relax }{figure.caption.11}{}}
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces Der Graph der Kreuzentropie Fehlerfunktion wenn das tats\IeC {\"a}chliche Label 1 ist\relax }}{14}{figure.caption.11}\protected@file@percent }
\newlabel{CEL_Graph}{{10}{14}{Der Graph der Kreuzentropie Fehlerfunktion wenn das tatsächliche Label 1 ist\relax }{figure.caption.11}{}}
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces Die Gleichung f\IeC {\"u}r den Kreuzentropiefehler\relax }}{14}{figure.caption.12}\protected@file@percent }
\newlabel{CEL_Function}{{11}{14}{Die Gleichung für den Kreuzentropiefehler\relax }{figure.caption.12}{}}
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Die Gleichung f\IeC {\"u}r den durchschnittlichen absoluten Fehler\relax }}{14}{figure.caption.13}\protected@file@percent }
\newlabel{CEL_Finction_cummulative}{{12}{14}{Die Gleichung für den durchschnittlichen absoluten Fehler\relax }{figure.caption.13}{}}
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {3.6}Gradientenverfahren und Backpropagation}{14}{subsection.3.6}\protected@file@percent }
\newlabel{Gradient_section}{{3.6}{14}{Gradientenverfahren und Backpropagation}{subsection.3.6}{}}
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces Die Gleichung f\IeC {\"u}r den Gradienten der Fehlerfunktion\relax }}{14}{figure.caption.14}\protected@file@percent }
\newlabel{Gradient_Function}{{13}{14}{Die Gleichung für den Gradienten der Fehlerfunktion\relax }{figure.caption.14}{}}
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Die Gleichung f\IeC {\"u}r den durchschnittlichen absoluten Fehler\relax }}{15}{figure.caption.13}\protected@file@percent }
\newlabel{CEL_Finction_cummulative}{{12}{15}{Die Gleichung für den durchschnittlichen absoluten Fehler\relax }{figure.caption.13}{}}
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {3.6}Gradientenverfahren und Backpropagation}{15}{subsection.3.6}\protected@file@percent }
\newlabel{Gradient_section}{{3.6}{15}{Gradientenverfahren und Backpropagation}{subsection.3.6}{}}
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces Die Gleichung f\IeC {\"u}r den Gradienten der Fehlerfunktion\relax }}{15}{figure.caption.14}\protected@file@percent }
\newlabel{Gradient_Function}{{13}{15}{Die Gleichung für den Gradienten der Fehlerfunktion\relax }{figure.caption.14}{}}
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.6.1}Lernrate}{15}{subsubsection.3.6.1}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces Die Gleichung f\IeC {\"u}r die Anpassung eines einzelnen Parameters\relax }}{15}{figure.caption.15}\protected@file@percent }
\newlabel{Learning_Rate_Function}{{14}{15}{Die Gleichung für die Anpassung eines einzelnen Parameters\relax }{figure.caption.15}{}}
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces $\eta $ ist hier zu gro\IeC {\ss } gew\IeC {\"a}hlt\relax }}{15}{figure.caption.16}\protected@file@percent }
\newlabel{Learning_Rate_Graphic}{{15}{15}{$\eta $ ist hier zu groß gewählt\relax }{figure.caption.16}{}}
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces $\eta $ ist hier zu gro\IeC {\ss } gew\IeC {\"a}hlt\relax }}{16}{figure.caption.16}\protected@file@percent }
\newlabel{Learning_Rate_Graphic}{{15}{16}{$\eta $ ist hier zu groß gewählt\relax }{figure.caption.16}{}}
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {3.7}Verschiedene Layerarten}{16}{subsection.3.7}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.7.1}Convolutional Layers}{16}{subsubsection.3.7.1}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces Eine Verbildlichung der Vorg\IeC {\"a}nge in einem convolutional Layer\newline Aus einer Animation von\newline https://github.com/vdumoulin/conv\_arithmetic/blob/master/README.md Vincent Dumoulin, Francesco Visin - A guide to convolution arithmetic for deep learning (BibTeX)}}{16}{figure.caption.17}\protected@file@percent }
\newlabel{Convolution_illustration}{{16}{16}{Eine Verbildlichung der Vorgänge in einem convolutional Layer\newline Aus einer Animation von\newline https://github.com/vdumoulin/conv\_arithmetic/blob/master/README.md\\ Vincent Dumoulin, Francesco Visin - A guide to convolution arithmetic for deep learning (BibTeX)}{figure.caption.17}{}}
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces Erkennt obere horizontale Kanten\relax }}{17}{figure.caption.18}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces Erkennt linke vertikale Kanten\relax }}{17}{figure.caption.18}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces Erkennt untere horizontale Kanten\relax }}{17}{figure.caption.18}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {20}{\ignorespaces Erkennt rechte vertikale Kanten\relax }}{17}{figure.caption.18}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {21}{\ignorespaces Das Beispielbild aus dem Mnist Datensatz\relax }}{17}{figure.caption.19}\protected@file@percent }
\newlabel{Filter_Example_raw}{{21}{17}{Das Beispielbild aus dem Mnist Datensatz\relax }{figure.caption.19}{}}
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {22}{\ignorespaces Die jeweils oben stehenden Filter wurden auf das Beispielbild angewandt.\relax }}{17}{figure.caption.20}\protected@file@percent }
\newlabel{Filter_output dargestellt}{{22}{17}{Die jeweils oben stehenden Filter wurden auf das Beispielbild angewandt.\relax }{figure.caption.20}{}}
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {23}{\ignorespaces Beispiele f\IeC {\"u}r low- mid- und high-level Features in Convolutional Neural Nets\newline Quelle: https://tvirdi.github.io/2017-10-29/cnn/}}{18}{figure.caption.21}\protected@file@percent }
\newlabel{HL_features_conv}{{23}{18}{Beispiele für low- mid- und high-level Features in Convolutional Neural Nets\newline Quelle: https://tvirdi.github.io/2017-10-29/cnn/}{figure.caption.21}{}}
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.7.2}Pooling Layers}{18}{subsubsection.3.7.2}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {24}{\ignorespaces Max Pooling mit $2\times 2$ gro\IeC {\ss }en Submatritzen\newline Quelle: https://computersciencewiki.org/index.php/Max-pooling\_/\_Pooling CC BY NC SA Lizenz}}{19}{figure.caption.22}\protected@file@percent }
\newlabel{Maxpool}{{24}{19}{Max Pooling mit $2\times 2$ großen Submatritzen\newline Quelle: https://computersciencewiki.org/index.php/Max-pooling\_/\_Pooling\\ CC BY NC SA Lizenz}{figure.caption.22}{}}
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {25}{\ignorespaces Average Pooling mit $2\times 2$ gro\IeC {\ss }en Submatritzen\newline Aus: Dominguez-Morales, Juan Pedro. (2018). Neuromorphic audio processing through real-time embedded spiking neural networks. Abbildung 33}}{19}{figure.caption.23}\protected@file@percent }
\newlabel{AvgPool}{{25}{19}{Average Pooling mit $2\times 2$ großen Submatritzen\newline Aus: Dominguez-Morales, Juan Pedro. (2018). Neuromorphic audio processing through real-time embedded spiking neural networks. Abbildung 33}{figure.caption.23}{}}
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {26}{\ignorespaces Gegen\IeC {\"u}berstellung von Max und Average Pooling\relax }}{20}{figure.caption.24}\protected@file@percent }
\newlabel{Pooling_Mnist}{{26}{20}{Gegenüberstellung von Max und Average Pooling\relax }{figure.caption.24}{}}
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {4}PyTorch}{21}{section.4}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Datenvorbereitung}{21}{subsection.4.1}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Definieren des Netzes}{21}{subsection.4.2}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {4.3}Trainieren des Netzes}{21}{subsection.4.3}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {5}Fallbeispiel I:\newline Ein Klassifizierungsnetzwerk f\IeC {\"u}r handgeschriebene Ziffern}{21}{section.5}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Aufgabe}{21}{subsection.5.1}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Der MNIST Datensatz}{21}{subsection.5.2}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Fragmentbasierte Erkennung}{21}{subsection.5.3}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {5.4}Ergebnis}{21}{subsection.5.4}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {6}Fallbeispiel II:\newline Eine selbsttrainierende KI f\IeC {\"u}r Tic-Tac-Toe}{21}{section.6}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {6.1}Das Prinzip}{21}{subsection.6.1}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {6.2}Chance-Tree Optimierung}{21}{subsection.6.2}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {6.3}L\IeC {\"o}sung mittels eines neuronalen Netzes}{21}{subsection.6.3}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {6.4}Vergleich}{21}{subsection.6.4}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {7}Schlusswort}{21}{section.7}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.7.1}Convolutional Layers}{17}{subsubsection.3.7.1}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces Eine Verbildlichung der Vorg\IeC {\"a}nge in einem convolutional Layer\newline Aus einer Animation von\newline https://github.com/vdumoulin/conv\_arithmetic/blob/master/README.md Vincent Dumoulin, Francesco Visin - A guide to convolution arithmetic for deep learning (BibTeX)}}{17}{figure.caption.17}\protected@file@percent }
\newlabel{Convolution_illustration}{{16}{17}{Eine Verbildlichung der Vorgänge in einem convolutional Layer\newline Aus einer Animation von\newline https://github.com/vdumoulin/conv\_arithmetic/blob/master/README.md\\ Vincent Dumoulin, Francesco Visin - A guide to convolution arithmetic for deep learning (BibTeX)}{figure.caption.17}{}}
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces Erkennt obere horizontale Kanten\relax }}{18}{figure.caption.18}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces Erkennt linke vertikale Kanten\relax }}{18}{figure.caption.18}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces Erkennt untere horizontale Kanten\relax }}{18}{figure.caption.18}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {20}{\ignorespaces Erkennt rechte vertikale Kanten\relax }}{18}{figure.caption.18}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {21}{\ignorespaces Das Beispielbild aus dem Mnist Datensatz\relax }}{18}{figure.caption.19}\protected@file@percent }
\newlabel{Filter_Example_raw}{{21}{18}{Das Beispielbild aus dem Mnist Datensatz\relax }{figure.caption.19}{}}
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {22}{\ignorespaces Die jeweils oben stehenden Filter wurden auf das Beispielbild angewandt.\relax }}{18}{figure.caption.20}\protected@file@percent }
\newlabel{Filter_output dargestellt}{{22}{18}{Die jeweils oben stehenden Filter wurden auf das Beispielbild angewandt.\relax }{figure.caption.20}{}}
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {23}{\ignorespaces Beispiele f\IeC {\"u}r low- mid- und high-level Features in Convolutional Neural Nets\newline Quelle: https://tvirdi.github.io/2017-10-29/cnn/}}{19}{figure.caption.21}\protected@file@percent }
\newlabel{HL_features_conv}{{23}{19}{Beispiele für low- mid- und high-level Features in Convolutional Neural Nets\newline Quelle: https://tvirdi.github.io/2017-10-29/cnn/}{figure.caption.21}{}}
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.7.2}Pooling Layers}{19}{subsubsection.3.7.2}\protected@file@percent }
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {24}{\ignorespaces Max Pooling mit $2\times 2$ gro\IeC {\ss }en Submatritzen\newline Quelle: https://computersciencewiki.org/index.php/Max-pooling\_/\_Pooling CC BY NC SA Lizenz}}{20}{figure.caption.22}\protected@file@percent }
\newlabel{Maxpool}{{24}{20}{Max Pooling mit $2\times 2$ großen Submatritzen\newline Quelle: https://computersciencewiki.org/index.php/Max-pooling\_/\_Pooling\\ CC BY NC SA Lizenz}{figure.caption.22}{}}
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {25}{\ignorespaces Average Pooling mit $2\times 2$ gro\IeC {\ss }en Submatritzen\newline Aus: Dominguez-Morales, Juan Pedro. (2018). Neuromorphic audio processing through real-time embedded spiking neural networks. Abbildung 33}}{20}{figure.caption.23}\protected@file@percent }
\newlabel{AvgPool}{{25}{20}{Average Pooling mit $2\times 2$ großen Submatritzen\newline Aus: Dominguez-Morales, Juan Pedro. (2018). Neuromorphic audio processing through real-time embedded spiking neural networks. Abbildung 33}{figure.caption.23}{}}
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {26}{\ignorespaces Gegen\IeC {\"u}berstellung von Max und Average Pooling\relax }}{21}{figure.caption.24}\protected@file@percent }
\newlabel{Pooling_Mnist}{{26}{21}{Gegenüberstellung von Max und Average Pooling\relax }{figure.caption.24}{}}
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {4}PyTorch}{22}{section.4}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Datenvorbereitung}{22}{subsection.4.1}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Definieren des Netzes}{22}{subsection.4.2}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {4.3}Trainieren des Netzes}{22}{subsection.4.3}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {5}Fallbeispiel I:\newline Ein Klassifizierungsnetzwerk f\IeC {\"u}r handgeschriebene Ziffern}{22}{section.5}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Aufgabe}{22}{subsection.5.1}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Der MNIST Datensatz}{22}{subsection.5.2}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Fragmentbasierte Erkennung}{22}{subsection.5.3}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {5.4}Ergebnis}{22}{subsection.5.4}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {6}Fallbeispiel II:\newline Eine selbsttrainierende KI f\IeC {\"u}r Tic-Tac-Toe}{22}{section.6}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {6.1}Das Prinzip}{22}{subsection.6.1}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {6.2}Chance-Tree Optimierung}{22}{subsection.6.2}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {6.3}L\IeC {\"o}sung mittels eines neuronalen Netzes}{22}{subsection.6.3}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {subsection}{\numberline {6.4}Vergleich}{22}{subsection.6.4}\protected@file@percent }
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {7}Schlusswort}{22}{section.7}\protected@file@percent }
\bibcite{1}{1}
\bibcite{2}{2}
\bibcite{3}{3}