From bf505fea0db8248cf2ab6c4483fcec7ab8011b53 Mon Sep 17 00:00:00 2001 From: Jim Pivarski Date: Mon, 8 Apr 2024 17:42:20 -0500 Subject: [PATCH] start writing talk 06 --- make-talk-06/main.tex | 81 +++++++- make-talk-06/real-neuron.pdf | Bin 0 -> 18002 bytes make-talk-06/real-neuron.svg | 390 +++++++++++++++++++++++++++++++++++ 3 files changed, 469 insertions(+), 2 deletions(-) create mode 100644 make-talk-06/real-neuron.pdf create mode 100644 make-talk-06/real-neuron.svg diff --git a/make-talk-06/main.tex b/make-talk-06/main.tex index 13fd204..d207ab1 100644 --- a/make-talk-06/main.tex +++ b/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} diff --git a/make-talk-06/real-neuron.pdf b/make-talk-06/real-neuron.pdf new file mode 100644 index 0000000000000000000000000000000000000000..eb2df7d4f0a8c8f93975484d3253ed15557f5796 GIT binary patch literal 18002 zcmbTe1#lb7*0!6NnPNtnV`h+AF zCC!Z1nqJ+jyEUp(zmJAgPDq4?ftDGDwCTM11%??w53n_`fZ^f-&`BBFm^zsOSUy|| zFaQ96PQ={G$=KoJXr=FDEM#nGYh(<=!vo{!?<=oTTQZ#u!jg09W#2+utp7y2tf#Y!6bk4VD>bZww zZSiKgBNH(vx`)8S^?cR@`#D9~bLIRs$978hl_zV<%aa80wdQ?c%Vh0&`iZXVCF%FC zl)aXo`8B8CJ7$M9(>*yWIm7Rk2bmHbA}6M0`{n1aP6u4~-n22cJUs3V&n!1TmCe(Q zCMyb`en#$TooZ0<;w5Uf&1rRdXq|@YOnOZ+@bs`x#W#ArT}|%9%3$CGM%HCPo zNTK_YdiDH#qE$Lk6x9f&RV1NDgDPhSPgYwFm39#=e5vZ@)B2e2{!1Cg3%hI2T{hae zrh4+q_vtFh(|F#)6YeC-B*z-dlsxkArKu)lY1tPEV|?=X#Ixfjo2kP})wtPo6?65D zIRnS%mz5@}b9;{q^LM<-4C8C9G+N!Nx;8ImYX{m2wXIu7_sMeArR;R4^RDFSXKM$m zb4}X9>6l_`t0w_kLU=L?9CFL$`Z0P(i7sz#31aG*c9leq_RiS1U$_jBQL(jSwsCYA 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