start writing talk 06

make-talk-06/main.tex

@@ -57,8 +57,85 @@
 
 % START START START START START START START START START START START START START
 
-\begin{frame}{TITLE}
-CONTENT
+\begin{frame}{\only<1>{Equation of a line (fitting $a$ and $b$ to measurements $y$ versus $x$)}\only<2>{Equation of a plane (height $y$ versus 2D coordinates $x_1$ and $x_2$)}\only<3>{Equation of a hyperplane (N-dimensional)}\only<4>{General linear transformation: many inputs, many outputs}\only<5>{Pass through function $f$ to make it non-linear (more on that later)}}
+\begin{columns}
+\column{1.1\linewidth}
+\renewcommand{\arraystretch}{1.5}
+\scriptsize
+\[ \uncover<5->{f \left[} \mbox{\hspace{0.25 cm}} \underbrace{\uncover<2->{\left(} \begin{array}{c c c c}
+\only<2->{\uncover<4->{a_{1,1}} & \uncover<4->{a_{1,2}} & \uncover<4->{\ldots} & \uncover<4->{a_{1,10}} \\}
+\only<2->{\uncover<4->{a_{2,1}} & \uncover<4->{a_{2,2}} & \uncover<4->{\ldots} & \uncover<4->{a_{2,10}} \\}
+\only<2->{\only<2-3>{a_1}\only<4->{a_{3,1}} & \only<2-3>{a_2}\only<4->{a_{3,2}} & \uncover<3->{\ldots} & \uncover<3->{\only<1-3>{a_{10}}}\only<4->{a_{3,10}} \\}
+\only<2->{\uncover<4->{a_{4,1}} & \uncover<4->{a_{4,2}} & \uncover<4->{\ldots} & \uncover<4->{a_{4,10}} \\}
+\only<2->{\uncover<4->{a_{5,1}} & \uncover<4->{a_{5,2}} & \uncover<4->{\ldots} & \uncover<4->{a_{5,10}} \\}
+\end{array}\only<1>{\mbox{\hspace{0.5 cm}}a\mbox{\hspace{0.5 cm}}} \vphantom{\vbox to 1.5cm{}} \uncover<2->{\right)}}_{\text{free parameters in the fit}} \cdot \underbrace{\uncover<2->{\left(} \only<1>{x}\begin{array}{c}
+\only<2->{\uncover<2->{x_1} \\}
+\only<2->{\uncover<2->{x_2} \\}
+\only<2->{\uncover<3->{\vdots} \\}
+\only<2->{\uncover<3->{x_{10}} \\}
+\end{array} \vphantom{\vbox to 1.5cm{}} \uncover<2->{\right)}}_{\text{input values}} + \underbrace{\uncover<4->{\left(} \begin{array}{c}
+\uncover<4->{b_1} \\
+\uncover<4->{b_2} \\
+\only<1-3>{b}\only<4->{b_3} \\
+\uncover<4->{b_4} \\
+\uncover<4->{b_5} \\
+\end{array} \vphantom{\vbox to 1.5cm{}} \uncover<4->{\right)}}_{\text{free parameters}} \mbox{\hspace{0.25 cm}} \uncover<5->{\right]} = \underbrace{\uncover<4->{\left(} \begin{array}{c}
+\uncover<4->{y_1} \\
+\uncover<4->{y_2} \\
+\only<1-3>{y}\only<4->{y_3} \\
+\uncover<4->{y_4} \\
+\uncover<4->{y_5} \\
+\end{array} \vphantom{\vbox to 1.5cm{}} \uncover<4->{\right)}}_{\text{output values}} = \begin{array}{c}
+\uncover<5->{f[} \uncover<4->{a_{1,1}x_1 + a_{1,2}x_2 + \ldots a_{1,10}x_{10} + b_1} \uncover<5->{]} \\
+\uncover<5->{f[} \uncover<4->{a_{2,1}x_1 + a_{2,2}x_2 + \ldots a_{2,10}x_{10} + b_2} \uncover<5->{]} \\
+\uncover<5->{f[} \only<1>{ax + b}\only<2-3>{a_{1}x_1 + a_{2}x_2 \uncover<3->{+ \ldots a_{10}x_{10}} + b}\only<4->{a_{3,1}x_1 + a_{3,2}x_2 + \ldots a_{3,10}x_{10} + b_3} \uncover<5->{]} \\
+\uncover<5->{f[} \uncover<4->{a_{4,1}x_1 + a_{4,2}x_2 + \ldots a_{4,10}x_{10} + b_4} \uncover<5->{]} \\
+\uncover<5->{f[} \uncover<4->{a_{5,1}x_1 + a_{5,2}x_2 + \ldots a_{5,10}x_{10} + b_5} \uncover<5->{]} \\
+\end{array} \]
+\end{columns}
+\end{frame}
+
+\begin{frame}{Neural networks take inspiration from neurons in the brain}
+\begin{center}
+\includegraphics[width=0.9\linewidth]{real-neuron.pdf}
+\end{center}
+
+\vspace{-1cm}
+\begin{columns}
+\column{1.1\linewidth}
+\renewcommand{\arraystretch}{1.5}
+\scriptsize
+\[ f \left[ \mbox{\hspace{0.25 cm}} \underbrace{\left( \begin{array}{c c c c}
+a_{1,1} & a_{1,2} & \ldots & a_{1,10} \\
+a_{2,1} & a_{2,2} & \ldots & a_{2,10} \\
+a_{3,1} & a_{3,2} & \ldots & a_{3,10} \\
+a_{4,1} & a_{4,2} & \ldots & a_{4,10} \\
+a_{5,1} & a_{5,2} & \ldots & a_{5,10} \\
+\end{array} \vphantom{\vbox to 1.5cm{}} \right)}_{\text{free parameters in the fit}} \cdot \underbrace{\left( \begin{array}{c}
+x_1 \\
+x_2 \\
+\vdots \\
+x_{10} \\
+\end{array} \vphantom{\vbox to 1.5cm{}} \right)}_{\text{input values}} + \underbrace{\left( \begin{array}{c}
+b_1 \\
+b_2 \\
+b_3 \\
+b_4 \\
+b_5 \\
+\end{array} \vphantom{\vbox to 1.5cm{}} \right)}_{\text{free parameters}} \mbox{\hspace{0.25 cm}} \right] = \underbrace{\left( \begin{array}{c}
+y_1 \\
+y_2 \\
+y_3 \\
+y_4 \\
+y_5 \\
+\end{array} \vphantom{\vbox to 1.5cm{}} \right)}_{\text{output values}} = \begin{array}{c}
+f[ a_{1,1}x_1 + a_{1,2}x_2 + \ldots a_{1,10}x_{10} + b_1 ] \\
+f[ a_{2,1}x_1 + a_{2,2}x_2 + \ldots a_{2,10}x_{10} + b_2 ] \\
+f[ a_{3,1}x_1 + a_{3,2}x_2 + \ldots a_{3,10}x_{10} + b_3 ] \\
+f[ a_{4,1}x_1 + a_{4,2}x_2 + \ldots a_{4,10}x_{10} + b_4 ] \\
+f[ a_{5,1}x_1 + a_{5,2}x_2 + \ldots a_{5,10}x_{10} + b_5 ] \\
+\end{array} \]
+\end{columns}
 \end{frame}
 
 \end{document}