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diff --git a/doc/main.pdf b/doc/main.pdf Binary files differnew file mode 100644 index 0000000..1a2404e --- /dev/null +++ b/doc/main.pdf diff --git a/doc/main.tex b/doc/main.tex new file mode 100644 index 0000000..00028f9 --- /dev/null +++ b/doc/main.tex @@ -0,0 +1,67 @@ +%acmart +%IEEEtran +%rbt-mathnotes-formula-sheet +\documentclass{rbt-mathnotes-formula-sheet} +\usepackage[utf8]{inputenc} +\usepackage[pdf]{graphviz} +\usepackage{derivative} +\title{Deep learning notes} + +\begin{document} + +\section{Observations} +\begin{eqnarray} + i,j,k,l,L,m,M,n,N,o \in & \mathcal{N} \\ + X \in & \mathcal{R}^{n \times o} \\ + Y \in & \mathcal{R}^{n \times m} +\end{eqnarray} + +\section{Neural Network} + +\includegraphics[width=0.3\textwidth]{net.pdf} + +\begin{eqnarray} + a^0 = & x_{1 \times p}(n) \\ + a^L = & d_{1 \times m}(n) \\ + a^l = & \varphi (z^l) \\ + z^l = & a^{l - 1} W^l +\end{eqnarray} + +\section{Gradient Descent} + +\begin{eqnarray} + e(n) = & y(n) - d(n) \\ + \xi(n) = & \frac{1}{2} e e^{\top}\\ + \xi(n) = & \frac{1}{2} \sum_{j=1}^{M} (e_j(n))^2 \\ + W_{(k + 1)} = & W_{(k)} - \nabla_{W} \xi(d,y) \\ + \xi_{avg}(n) = & \frac{1}{2n} \sum_{n=1}^N \sum_{j=1}^{M} (e_j(n))^2 \\ +\end{eqnarray} + +\section{Backpropagation} + +\begin{eqnarray} + \pdv{\xi}{\omega^l_{ij}} = & \delta_j^l \pdv{z_j^l}{\omega_{ij}} \\ + \delta_j^l = & \pdv{\xi}{z_j^l} \\ + \pdv{z_j^l}{\omega_{ij}} = & a_i^{l-1} \\ +\end{eqnarray} + +Output Layer + +\begin{eqnarray} + \delta_j^L =& \pdv{\xi}{z_j^L} = \pdv{\xi}{a_j^L} \pdv{a_j^L}{z_j^L}\\ + \delta_j^L =& \pdv{\xi}{a_j^L} \dot{\varphi}(z_j^L)\\ + =& - e_j \dot{\varphi}(z_j^L) +\end{eqnarray} + +Hidden Layer + +\begin{eqnarray} + \delta_j^l = & \pdv{\xi}{z_j^l} = \sum_k \pdv{\xi}{z_k^{l+1}} \pdv{z_k^{l+1}}{z_j^l}\\ + \delta_j^l = & \sum_k \delta_k^{l+1} \pdv{z_k^{l+1}}{z_j^l}\\ + \pdv{z_k^{l+1}}{z_j^l} = & + \frac{\partial}{\partial z_j^l} \left( \sum_j \omega_{jk}^{l+1} \varphi(z_j^l) \right)\\ + \pdv{z_k^{l+1}}{z_j^l} = & \omega_{jk} \dot{\varphi}(z_j^l)\\ + \delta_j^l = & \sum_k \delta_k^{l+1} \omega_{jk}^{l+1} \dot{\varphi}(z_j^l)\\ +\end{eqnarray} + +\end{document} diff --git a/doc/net.dot b/doc/net.dot new file mode 100644 index 0000000..d7a1bf3 --- /dev/null +++ b/doc/net.dot @@ -0,0 +1,17 @@ +digraph abc { + node [shape=circle, size=0.2]; + rankdir=LR; + + x₁ -> a₁[label = w¹]; + x₁ -> {a₂ a₃}; + x₂ -> {a₁ a₂ a₃}; + + a₁ -> d₁[label = w²]; + a₁ -> d₂; + a₂ -> {d₁ d₂}; + a₃ -> {d₁ d₂}; + + subgraph {rank=source; x₁; x₂}; + subgraph {rank=same; a₁; a₂; a₃}; + subgraph {rank=sink; d₁; d₂}; +} diff --git a/doc/net.pdf b/doc/net.pdf Binary files differnew file mode 100644 index 0000000..1ecc6cc --- /dev/null +++ b/doc/net.pdf |