Dokończono rozdział I - RNN, LSTM, Seq2Seq
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||||
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||||
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||||
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||||
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||||
"/usr/share/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty" 1572595918 339 592cf35cba3d400082b8a9a5d0199d70 ""
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||||
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||||
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||||
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||||
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||||
(generated)
|
||||
"/home/altarin/praca-magisterska/docs/document.pdf"
|
||||
"document.pdf"
|
||||
"document.aux"
|
||||
"document.toc"
|
||||
"document.log"
|
||||
"/home/altarin/praca-magisterska/docs/document.log"
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||||
"document.idx"
|
||||
# Fdb version 3
|
||||
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||||
(generated)
|
||||
"document.ilg"
|
||||
"document.ind"
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
"c:/software/latex/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm" 1550339660 940 228d6584342e91276bf566bcf9716b83 ""
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||||
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||||
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||||
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||||
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||||
"c:/software/latex/texmf-dist/fonts/tfm/public/pl/plr5.tfm" 1550343089 2008 4c18492417d4ad9dae4007f662b5da21 ""
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"c:/software/latex/texmf-dist/fonts/tfm/public/pl/plr6.tfm" 1550343089 2088 aa80c569a200447488b571f8bf7b132b ""
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||||
"c:/software/latex/texmf-dist/fonts/tfm/public/pl/plr7.tfm" 1550343089 2088 3950be4df310cc88dade7a45ba964220 ""
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||||
"c:/software/latex/texmf-dist/fonts/tfm/public/pl/plr8.tfm" 1550343089 2080 290449bfe12d41e2714fa828fd909bf8 ""
|
||||
"c:/software/latex/texmf-dist/fonts/tfm/public/pl/plsy10.tfm" 1550343089 1308 adee1faadc465f51667a741ced3a8365 ""
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||||
"c:/software/latex/texmf-dist/fonts/tfm/public/pl/plsy5.tfm" 1550343089 1296 bc803ec3860b078a8e22fb7a6202aa37 ""
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||||
"c:/software/latex/texmf-dist/fonts/tfm/public/pl/plsy7.tfm" 1550343089 1304 a6a2c86c403d8bc56664eeac17804b8a ""
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||||
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||||
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||||
"c:/software/latex/texmf-dist/fonts/type1/public/cm-super/sfrm1000.pfb" 1550340374 138258 6525c253f16cededa14c7fd0da7f67b2 ""
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||||
"c:/software/latex/texmf-dist/fonts/type1/public/cm-super/sfrm1095.pfb" 1550340374 145929 5c9aebea9ba6e33fc93158c04a3bdcd8 ""
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||||
"c:/software/latex/texmf-dist/fonts/type1/public/cm-super/sfrm1200.pfb" 1550340374 136101 b18d10b3436f8cb0cd04046deb340fe7 ""
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||||
"c:/software/latex/texmf-dist/fonts/type1/public/cm-super/sfrm1440.pfb" 1550340374 131078 3adc08bf3d7686c3b3220602214807d7 ""
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"c:/software/latex/texmf-dist/fonts/type1/public/cm-super/sfti1095.pfb" 1550340374 196446 823e77efd89b89faab342901e22eb237 ""
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"c:/software/latex/texmf-dist/fonts/type1/public/pl/plmi12.pfb" 1550343089 29704 59e409fb948cf911862e0a97f2ae41a4 ""
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"c:/software/latex/texmf-dist/fonts/type1/public/pl/plmi8.pfb" 1550343089 29648 b38cd15b84b56d7bea1291ffd32de967 ""
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||||
"c:/software/latex/texmf-dist/fonts/type1/public/pl/plr12.pfb" 1550343089 27754 6f5ae55af1b64df2aab0bbeada447136 ""
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"c:/software/latex/texmf-dist/fonts/type1/public/pl/plr8.pfb" 1550343089 27613 2ab70f7885927ea178f952791c5494f9 ""
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"c:/software/latex/texmf-dist/fonts/type1/public/pl/plsy10.pfb" 1550343089 26714 6fe260cd3a16c4a700b121f4edac67f2 ""
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||||
"c:/software/latex/texmf-dist/tex/generic/oberdiek/etexcmds.sty" 1550342831 7612 729a8cc22a1ee0029997c7f74717ae05 ""
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||||
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||||
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||||
"c:/software/latex/texmf-dist/tex/generic/pgf/basiclayer/pgfcorearrows.code.tex" 1550343018 43820 bc6cf5aa959817914ace33f5c6232161 ""
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||||
"c:/software/latex/texmf-dist/tex/generic/pgf/basiclayer/pgfcoregraphicstate.code.tex" 1550343018 6038 d639d02574be9a72f3c602c2a3510e02 ""
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"c:/software/latex/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreimage.code.tex" 1550343018 6948 284bbe3c9a7ca0a826c1c03895e69b9f ""
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"c:/software/latex/texmf-dist/tex/generic/pgf/basiclayer/pgfcorelayers.code.tex" 1550343018 4883 a6f3eb1f71d8c4affaf43a169828b043 ""
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||||
"c:/software/latex/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreobjects.code.tex" 1550343018 2544 3b1b198fd49f01e328adc9162a07b213 ""
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"c:/software/latex/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathconstruct.code.tex" 1550343018 44195 134d5eb267e64d2a6b6dc75008e7c5fd ""
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Output written on /home/altarin/praca-magisterska/docs/document.pdf (35 pages, 618938 bytes).
|
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55i,12n,49p,1500b,1110s stack positions out of 5000i,500n,10000p,200000b,80000s
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Output written on j:/_MAGISTERKA/praca-magisterska/docs/document.pdf (37 pages, 702361 bytes).
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@ -10,16 +10,16 @@
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\usepackage{tikz}
|
||||
\usepackage{listings}
|
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\usepackage{subfig}
|
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\usepackage[T1]{fontenc}
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% \usepackage[utf8]{inputenc}
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% \usepackage{amsmath}
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\newcommand{\textoperatorname}[1]{%
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\operatorname{\textnormal{#1}}%
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}
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\newcommand{\tens}[1]{%
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\mathbin{\mathop{\otimes}\limits_{#1}}%
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}
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\textheight 21.1 cm
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@ -168,7 +168,7 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow
|
||||
|
||||
W pierwszej częsci swojej pracy przedstawię podstawowe koncepcje związane z muzyką oraz sposobami jej reprezentacji. Następnie opiszę w jaki sposób działają sieci neuronowe, jak się uczą oraz podstawowe architektury sieci, które pomogą zrozumieć model który wykorzystałem.
|
||||
|
||||
Następnie przedstawię koncepcję działania modelu, jakie idee stały za wyborami które podjąłem w projektowaniu sieci. W szczegółowy sposób opiszę sposób ekstrakcji danych, tak aby mogły być one wykorzystane przez model. Opiszę architekturę którą wybrałem oraz przedstawię i opisze fragmenty kodu w języku python.
|
||||
Następnie przedstawię koncepcję działania modelu, jakie idee stały za wyborami, które podjąłem w projektowaniu sieci. W szczegółowy sposób opiszę sposób ekstrakcji danych tak aby mogły być one wykorzystane przez model. Opiszę architekturę którą wybrałem oraz przedstawię i opisze fragmenty kodu w języku python.
|
||||
|
||||
W kolejnym rozdziale skupimy się na rezultatach pracy, przedstawie zalety i wady modelu. Przeprowadze analizę jakie muzyczne koncepcje model się nauczył na podstawie danych oraz doprowadzę do ostatecznej konkluzji czy wygenerowana muzyka może być przyjemna dla odbiorcy.
|
||||
|
||||
@ -176,28 +176,28 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow
|
||||
|
||||
\chapter{Wprowadzenie do sieci neuronowych}
|
||||
|
||||
Aby lepiej zrozumieć, w jaki sposób odpowiednio skonstruowane sieci neuronowe potrafią sprostać takiemu zadaniu jak generowanie muzyki, w tym rozdziale przedstawię od podstaw zasady działania sieci neuronowych. Opiszę w jaki sposób można od regresji liniowej przejść do prostych sieci oraz w jaki sposób uczy się sieci neuronowe. Ostatecznie przedstawię architektury które wykorzystałem w projekcie.
|
||||
Aby lepiej zrozumieć w jaki sposób odpowiednio skonstruowane sieci neuronowe potrafią sprostać takiemu zadaniu jak generowanie muzyki, w tym rozdziale przedstawię od podstaw zasady działania sieci neuronowych. Opiszę w jaki sposób można od regresji liniowej przejść do prostych sieci oraz w jaki sposób uczy się sieci neuronowe. Ostatecznie przedstawię architektury, które wykorzystałem w projekcie.
|
||||
|
||||
\section{Regresja liniowa}
|
||||
Podstawą wszystkich sieci neuronowych, jest regresja liniowa. W statystyce wykorzystywana aby wyjaśnić liniowe zalezności między zmiennymi. Wyróżnia się dwa rodzaje
|
||||
Podstawą wszystkich sieci neuronowych jest regresja liniowa. W statystyce wykorzystywana, aby wyjaśnić liniowe zalezności między zmiennymi.
|
||||
|
||||
Prosty model regresji liniowej dla jednej zmiennej można opisać wzorem.
|
||||
Prosty model regresji liniowej dla jednej zmiennej można opisać wzorem
|
||||
|
||||
\[y = ax+b+\epsilon\]
|
||||
\[y = ax+b+\epsilon,\]
|
||||
|
||||
gdzie,
|
||||
gdzie
|
||||
\begin{itemize}
|
||||
\item $y$ jest zmienną objaśnianą,
|
||||
\item $x$ jest to zmienna objaśniająca,
|
||||
\item $a$ jest parametrem modelu,
|
||||
\item $b$ jest wyrazem wolnym modelu.
|
||||
\item $b$ jest wyrazem wolnym modelu,
|
||||
\item $\epsilon$ jest składnikiem losowym.
|
||||
\end{itemize}
|
||||
\medskip
|
||||
|
||||
|
||||
|
||||
Zadaniem jest znalezienie takiego parametru $a\in \mathbb{R}$ oraz wyrazu wolnego $b \in \mathbb{R}$, aby dla znanych wartości $x \in \mathbb{R}$ estymacja zmiennej objasnianej $\hat{y} \in \mathbb{R}$ najlepiej opisywała zmienną objasnaną $y \in \mathbb{R}$. Tak zdefiniowany model, opisuje zmienną $y$ z dokładnością do składnika losowego. W praktyce oznacza to że szacowane modele będą przybliżeniem opisywanych zależności.
|
||||
Zadaniem jest znalezienie takiego parametru $a\in \mathbb{R}$ oraz wyrazu wolnego $b \in \mathbb{R}$, aby dla znanych wartości $x \in \mathbb{R}$ estymacja zmiennej objasnianej $\hat{y} \in \mathbb{R}$ najlepiej opisywała zmienną objasnaną $y \in \mathbb{R}$. Tak zdefiniowany model opisuje zmienną $y$ z dokładnością do składnika losowego. W praktyce oznacza to, że szacowane modele będą przybliżeniem opisywanych zależności.
|
||||
|
||||
\medskip
|
||||
\begin{figure}[!htb]
|
||||
@ -235,7 +235,7 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow
|
||||
Aby znaleźć minimum funkcji $f$ możemy skorzystać z analizy matematycznej. Wiemy, że jeśli funkcja $f$ jest różniczkowalna to funkcja może przyjmować minimum lokalne, gdy $f'(x_0) = 0$ dla pewnego $x_0$ z dzieniny funkcji $f$. Dodatkowo jeśli istanieje otoczenie punktu $x_0$, że dla wszystkich punktów z tego otoczenia spełniona jest nierówność:
|
||||
\[ f(x)>f(x_0) \]
|
||||
to znaleziony punkt $x_0$ jest minimum lokalnym.
|
||||
W teorii, należałoby zatem wybrać taką funkcję kosztu, aby była różniczkowalna. Obliczyć równanie $J_\theta'(h)=0$, następnie dla otrzymanych wyników sprawdzić powyższą nierówność oraz wybrać najmniejszy wynik ze wszystkich\footnote{źródlo: Analiza matematyczna, Krysicki Włodarski, s.187 }. W praktyce rozwiązanie takie równania ze względu na jego złożoność może się okazać niewykonalne. Aby rozwiązać ten problem powstały inne metody, które pozwalają szukać ekstremów funkcji, jednak nigdy nie będziemy mieli pewności że otrzymany wynik jest minimum globalnym funkcji kosztu.
|
||||
W teorii należałoby zatem wybrać taką funkcję kosztu, aby była różniczkowalna. Obliczyć równanie $J_\theta'(h)=0$, następnie dla otrzymanych wyników sprawdzić powyższą nierówność oraz wybrać najmniejszy wynik ze wszystkich\footnote{źródlo: Analiza matematyczna, Krysicki Włodarski, s.187 }. W praktyce rozwiązanie takie równania ze względu na jego złożoność może się okazać niewykonalne. Aby rozwiązać ten problem powstały inne metody, które pozwalają szukać ekstremów funkcji, jednak nigdy nie będziemy mieli pewności, że otrzymany wynik jest minimum globalnym funkcji kosztu.
|
||||
|
||||
\subsection{Metody gradientowe}
|
||||
|
||||
@ -261,7 +261,7 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow
|
||||
\end{figure}
|
||||
\medskip
|
||||
|
||||
Dla funkcji $h(x)$ należy ustalić wartość początkową $\Theta_0$, dla wszystkich parametrów $\theta_1$ ... $\theta_n$.
|
||||
Dla funkcji $h(x)$ należy ustalić wartość początkową $\Theta_0$ dla wszystkich parametrów $\theta_1$ ... $\theta_n$.
|
||||
|
||||
\[ \Theta_0 = \left[ \theta_1, \theta_2, ... ,\theta_n \right] \]
|
||||
|
||||
@ -270,19 +270,19 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow
|
||||
\nabla J_\theta(h) = \left[ \frac{\partial J_\theta(h)}{\partial \theta_1}, \frac{\partial J_\theta(h)}{\partial \theta_2}, ... , \frac{\partial J_\theta(h)}{\partial \theta_n} \right]
|
||||
\]
|
||||
|
||||
Następnie obliczyć element $\Theta_{k+1}$, ze wzoru
|
||||
Następnie obliczyć element $\Theta_{k+1}$ ze wzoru
|
||||
|
||||
\[
|
||||
\Theta_{k+1} = \Theta_{k} - \alpha\nabla J_\theta(h)
|
||||
\Theta_{k+1} = \Theta_{k} - \alpha\nabla J_\theta(h),
|
||||
\]
|
||||
gdzie $\alpha \in \mathbb{R}$ jest współczynnikiem uczenia (learning rate). Proces ten należy powtarzać do pewnego momentu. Najczęśćiej z góry określoną liczbę razy lub do momentu, gdy uzysk funkcji kosztu spowodowany nastepną iteracją jest mniejszy niż ustalona wartość. Otrzymany w ten sposób wektor parametrów $\Theta_k$ jest wynikiem algorytmu.\footnote{Deep Learning techniques for music geneation - A survay s.44}
|
||||
|
||||
Wykorzystując metody gradientowe, otrzymujemy wyuczony model. Parametry $\theta_i$ modelu $h(x)$, zostały ustalone w taki sposób, aby błąd między predykcją, a rzeczywistością był najmniejszy.
|
||||
Wykorzystując metody gradientowe otrzymujemy wyuczony model. Parametry $\theta_i$ modelu $h(x)$ zostały ustalone w taki sposób, aby błąd między predykcją a rzeczywistością był najmniejszy.
|
||||
|
||||
\section{Regresja liniowa jako model sieci neuronowej}
|
||||
\label{section:linreg}
|
||||
|
||||
Omawiany model regresji, możemy zapisać w sposób graficzny, tak jak przedstawiono na rysunku ~\ref{fig:neural_model_one}.
|
||||
Omawiany model regresji możemy zapisać w sposób graficzny tak jak przedstawiono na rysunku~\ref{fig:neural_model_one}.
|
||||
|
||||
\begin{figure}[!htb]
|
||||
\centering
|
||||
@ -291,7 +291,7 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow
|
||||
\label{fig:neural_model_one}
|
||||
\end{figure}
|
||||
|
||||
Każdy węzeł z lewej strony reprezentuje zmienną objaśniającą $x_i$. Połączenia nazywane są wagami i reprezentują one parametry $\theta_i$. Węzeł z prawej strony oznaczony jako $\hat{y}$, jest sumą iloczynów wag oraz wartości węzłów z prawej strony. Wtedy
|
||||
Każdy węzeł z lewej strony reprezentuje zmienną objaśniającą $x_i$. Połączenia nazywane są wagami i reprezentują one parametry $\theta_i$. Węzeł z prawej strony oznaczony jako $\hat{y}$ jest sumą iloczynów wag oraz wartości węzłów z prawej strony. Wtedy
|
||||
|
||||
\[
|
||||
\hat{y} =
|
||||
@ -306,18 +306,18 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow
|
||||
b + \sum_{i=1}^n x_i\theta_i
|
||||
\]
|
||||
|
||||
co jest równoważne omawianemu modelowi regresji liniowej. Węzły sieci nazywane są neuronami a wyraz wolny modelu $b$, nazywany jest biasem (bias).
|
||||
co jest równoważne omawianemu modelowi regresji liniowej. Węzły sieci nazywane są neuronami, a wyraz wolny modelu $b$ nazywany jest biasem (bias).
|
||||
|
||||
W łatwy sposób możemy rozbudować ten model, do regresji liniowej wielu zmiennych. Predykcją modelu nie będzie jak do tej pory jedna wartość $\hat{y}$ tylko wektor wartości $\hat{y_1}, \hat{y_2}, \dots , \hat{y_m}$, który oznaczać bedziemy jako $\hat{Y}$. Model ten zostal przedstawiony na rysunku~\ref{fig:neural_model_multi}.
|
||||
W łatwy sposób możemy rozbudować ten model do regresji liniowej wielu zmiennych. Predykcją modelu nie będzie jak do tej pory jedna wartość $\hat{y}$, tylko wektor wartości $\hat{y_1}, \hat{y_2}, \dots , \hat{y_m}$, który oznaczać bedziemy jako $\hat{Y}$. Model ten zostal przedstawiony na rysunku~\ref{fig:neural_model_multi}.
|
||||
|
||||
\begin{figure}[!htb]
|
||||
\centering
|
||||
\includegraphics[width=8cm]{images/naural_model_multi.png}
|
||||
\caption{Regresja liniowa wielu zmiennych jako model sieci nauronowej}
|
||||
\caption{Regresja liniowa wielu zmiennych jako model sieci nauronowe.j}
|
||||
\label{fig:neural_model_multi}
|
||||
\end{figure}
|
||||
|
||||
Dla uogólnienia, pojedyncze wagi modelu zapisywać będę jako $w_{nm}$, natomiast macierz wag jako $W$. Algebricznie zapisalibyśmy ten model jako
|
||||
Dla uogólnienia pojedyncze wagi modelu zapisywać będę jako $w_{nm}$, natomiast macierz wag jako $W$. Algebricznie zapisalibyśmy ten model jako
|
||||
|
||||
\[
|
||||
\begin{bmatrix}
|
||||
@ -347,11 +347,11 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow
|
||||
b+XW = \hat{Y}
|
||||
\]
|
||||
|
||||
Gdzie, $n$ jest liczbą zmiennych niezależnych, $m$ jest liczbą zmiennych zaleznych, $X$ jest rozszerzonym do macierzy o rozmiarach $m$ x $n$ wektorem zmiennych objaśniających w taki sposób, że $x_{i1} = x_{i2} = \dots = x_{in}$ dla $i = 1, 2, ..., m$, $W$ jest macierzą wag o rozmiarach $n$ x $m$ natomiast $b$ jest sumą wyrazów wolnych $b_1, ... ,b_m$ nazywaną biasem (bias). Możemy zauważyć, że model dla wielu zmiennych, jest wieloma modelami dla jednej zmiennej, gdzie każdy model operuje na tych samych danych wejściowych. Taki model może być uznany na sieć neuronową i nazywany jest perceptronem.
|
||||
gdzie $n$ jest liczbą zmiennych niezależnych, $m$ jest liczbą zmiennych zaleznych, $X$ jest rozszerzonym do macierzy o rozmiarach $m$ x $n$ wektorem zmiennych objaśniających, w taki sposób że $x_{i1} = x_{i2} = \dots = x_{in}$ dla $i = 1, 2, ..., m$, $W$ jest macierzą wag o rozmiarach $n$ x $m$, natomiast $b$ jest sumą wyrazów wolnych $b_1, ... ,b_m$. Możemy zauważyć, że model dla wielu zmiennych jest wieloma modelami dla jednej zmiennej, gdzie każdy model operuje na tych samych danych wejściowych. Taki model może być uznany za sieć neuronową i nazywany jest perceptronem.
|
||||
|
||||
\section{Funkcje aktywacji}
|
||||
|
||||
Omawiany model służy rozwiązywaniu problemu regresji. Ponieważ wartości predykcji nie są uregulowane, moga przyjmować wartości z $\mathbb{R}$. Aby przekształcić ten model aby móc go wykorzystać do rozwiązania problemu klasifikacji, należy dodatkowo na otrzymanym wektorze $\hat{Y}$ wykonać pewną funkcję, która przekształci wynik. W tym celu uzywamy funkcji aktywacji (activation function). Istnieje wiele rodzaji funkcji aktywacji, każda posiada inny wpływ na model. Najpopularnijeszą grupą fukcji są funkcje sigmoidalne (sigmoid functions). Jedną z nich jest funkcja logistyczna (logistic curve) o wzrorze
|
||||
Omawiany model służy rozwiązywaniu problemu regresji, ponieważ wartości predykcji nie są uregulowane i mogą przyjmować wartości z $\mathbb{R}$. W celu przekształcenia tego modelu, aby móc go wykorzystać do rozwiązania problemu klasyfikacji, należy dodatkowo na otrzymanym wektorze $\hat{Y}$ wykonać pewną funkcję, która przekształci wynik. W tym celu używamy funkcji aktywacji (activation function). Istnieje wiele różnych funkcji aktywacji, a każda posiada inną charakterystykę i wpływ na model. Najpopularnijeszą grupą fukcji są funkcje sigmoidalne (sigmoid functions). Jedną z nich jest funkcja logistyczna (logistic curve) o wzrorze
|
||||
\[
|
||||
\sigma(x) = \frac{1}{1+e^{-x}}
|
||||
\]
|
||||
@ -364,25 +364,25 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow
|
||||
\label{fig:sigmoid}
|
||||
\end{figure}
|
||||
|
||||
Funkcja logistyczna, ma pewne użyteczne właściwości, które pozwolą kontrolować wartości węzłów, oraz zamienić wartości z całego $\mathbb{R}$ do wartości z przedziału $(0,1)$. Dzięki tej własciwości, funkcja logistyczna jest często uzywana aby otrzymać prawdopodobieństwo wystąpienia pewnego zdarzenia. Dodatkowo funkcja logistyczna szybko przyjmuje wartości skrajne, co oznacza że dla bardzo dużych wartości ujemnych i bardzo dużych wartości dodatnich, funkcja staje się mało wrażliwa na zmiany wartości, wraz ze zmianą wartości argumentu. \footnote{Deep Learning Book, s.66}
|
||||
Funkcja logistyczna ma pewne użyteczne właściwości, które pozwolą kontrolować wartości węzłów oraz rzutować wartości z całego $\mathbb{R}$ do wartości z przedziału $(0,1)$. Dzięki tej właściwości funkcja logistyczna jest często używana, aby otrzymać prawdopodobieństwo wystąpienia pewnego zdarzenia. Dodatkowo funkcja logistyczna szybko przyjmuje wartości skrajne, co oznacza że dla bardzo dużych wartości ujemnych i bardzo dużych wartości dodatnich funkcja staje się mało wrażliwa na zmiany wartości wraz ze zmianą wartości argumentu. \footnote{Deep Learning Book, s.66}
|
||||
|
||||
W ten sposób, możemy w łatwy sposób zmienić model regresji liniowej, na model regresji logistycznej.
|
||||
W ten sposób możemy w łatwy sposób zmienić model regresji liniowej na model regresji logistycznej.
|
||||
|
||||
\[
|
||||
\sigma(b+XW) = \hat{Y}
|
||||
\]
|
||||
|
||||
W dalszych cześciach pracy, kiedy bedę używał funcji aktywacji, nie wskazując na konkretną funckcję będe wykorzystywał oznaczenie $AF(x)$.
|
||||
W dalszych cześciach pracy, kiedy bedę używał funckji aktywacji nie wskazując na konkretną funckcję, będe wykorzystywał oznaczenie $AF(x)$.
|
||||
|
||||
\section{Głębokie sieci neuronowe}
|
||||
|
||||
Model omawiany wcześniej może posłużyć jako podstawowy element do budowania bardziej skomplikowanych modeli. Aby to zrobić, należy potraktować otrzymany wektor $\hat{Y}$ jako wektor wejściowy do następngo podstawowego modelu. Składając ze sobą wiele modeli, mówimy o warstwach (layers) modelu sieci neuronowej.
|
||||
Model omawiany wcześniej może posłużyć jako podstawowy element do budowania bardziej skomplikowanych modeli. Aby to zrobić, należy potraktować otrzymany wektor $\hat{Y}$ jako wektor wejściowy do następngo podstawowego modelu. Składając ze sobą wiele perceptronów w jeden model, tworzymy warstwy (layers) sieci neuronowej.
|
||||
|
||||
Wyróżniamy trzy rodzaje warstw:
|
||||
\begin{itemize}
|
||||
\item warstwa wejściowa (input layer) jest pierwszą warstwą modelu,
|
||||
\item warstwa wyjściowa (output layer) jest ostatnią wartstwą modelu
|
||||
\item wartwa ukryta (hidden layer) jest warswą pomiędzy warstwą wejsciową oraz wyjściową.
|
||||
\item warstwę wejściową (input layer), która jest pierwszą warstwą modelu,
|
||||
\item warstwę wyjściową (output layer), która jest ostatnią wartstwą modelu,
|
||||
\item wartwy ukryte (hidden layer), które są warstwami pomiędzy warstwą wejsciową oraz wyjściową.
|
||||
\end{itemize}
|
||||
|
||||
Na rysunku~\ref{fig:neural_net_1} przedstawiono przykład posiadający warswę wejściową, dwie wartswy ukryte oraz wartswę wyjsciową.
|
||||
@ -394,9 +394,10 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow
|
||||
\label{fig:neural_net_1}
|
||||
\end{figure}
|
||||
|
||||
Tego typu modele są głębokimi sieciami neuronowymi (deep neural networks). Istnieje wiele różnich architektur głębokich sieci neuronowych, które wykorzystują te podstawowe koncepcje i rozszerzają je o dodatkowe warstwy, połącznia, funkcje aktywacji czy specjalne komórki (węzły).
|
||||
Tego typu modele są głębokimi sieciami neuronowymi (deep neural networks). Istnieje wiele różnich architektur głębokich sieci neuronowych, które wykorzystują te podstawowe koncepcje i rozszerzają je o dodatkowe warstwy, połącznia, funkcje aktywacji czy neurony o specjalnych właściwościach.
|
||||
|
||||
\subsection{Jednokierunkowe sieci neuronowe}
|
||||
\label{section:feedforeward}
|
||||
|
||||
Jednokierunkowe sieci neuronowe (feedforward neural networks) są to najprostrze sieci neuronowe, które wprost czerpią z omówionych wcześniej podstawowych wartsw. Możemy się również spotkać z nazwą wielowarstwowy perceptron (multi layer perceptron - MLP) ze względu na fakt, że jest zbudowany z wielu perceptronów zaprezentoanych w części~\ref{section:linreg}. Działają one w taki sposób, że zasila się je danymi do warstwy wejściowej, następnie sukcesywnie wykonuje się obliczenia do momentu dotarcia do końca sieci.
|
||||
Każdy krok z warstwy $k-1$ do warstwy $k$ obliczany jest zgodnie ze wzorem \footnote{Deep Learning techniques for music geneation - A survay s.63}
|
||||
@ -405,13 +406,15 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow
|
||||
X_k = AF(b_k + W_kX_{k-1})
|
||||
\]
|
||||
|
||||
\subsection{Propagacja wsteczna błędu}
|
||||
\subsubsection{Propagacja wsteczna błędu}
|
||||
\label{section:backpropagation}
|
||||
|
||||
Kiedy uzywamy jednokierunkowych sieci neuronowych, zasilamy je danymi wejściowymi $x$ ostatecznie otrzymując predykcję $\hat(y)$. Taki sposób działania nazywa się propagcją wprzód (foreward propagation). Podczas uczenia sieci kontynuuje się ten proces obliczając koszt $J(h)$. Propagacja wsteczna (back-propagation), pozwala na przepływ informacji od funkcji kosztu wstecz sieci neuronowej aby ostatecznie obliczyć gradient. Zasada działania algorytmu propagacji wsteczniej błędu, polega na sukcesywnym aktualizowaniu wag i biasów, oraz przesyłaniu wstecz po warstwach sieci. Dzięki temu jesteśmy wstanie wyuczyć sieć oraz obliczyć optymalne wagi i biasy dla całej sieci.
|
||||
Kiedy używamy jednokierunkowych sieci neuronowych, zasilamy je danymi wejściowymi $x$ ostatecznie otrzymując predykcję $\hat{y}$. Taki sposób działania nazywa się propagcją wprzód (foreward propagation). Podczas uczenia sieci kontynuuje się ten proces obliczając koszt $J(h)$. Propagacja wsteczna (back-propagation) pozwala na przepływ informacji od funkcji kosztu wstecz sieci neuronowej, aby ostatecznie obliczyć gradient. Zasada działania algorytmu propagacji wsteczniej błędu polega na sukcesywnym aktualizowaniu wag i biasów oraz przesyłaniu wstecz po warstwach sieci. Dzięki temu jesteśmy wstanie wyuczyć sieć oraz obliczyć optymalne wagi i biasy dla całej sieci neuronowej.
|
||||
|
||||
\subsection{Autoencodery}
|
||||
\label{section:autoencoder}
|
||||
|
||||
Autoencoder jest to rodzaj głębokiej sieci neuronowej, zbudowany z jednej warstwy ukrytej. Dodatkowo rozmiar wartwy wejściowej musi być równy rozmiarowi wartwy wyjściowej, tworząc w ten sposób symetryczną sieć, której kształt przypomina klepsydrę. Przykład autoencodera przedstawiono na rysunku ~\ref{fig:autoencoder}.
|
||||
Autoencoder jest szczególnym przypadkiem sieci neuronowej. Posiada jedną warstwę ukrytą, a rozmiar wartwy wejściowej musi być równy rozmiarowi wartwy wyjściowej, tworząc w ten sposób symetryczną sieć, której kształt przypomina klepsydrę. Przykład autoencodera przedstawiono na rysunku ~\ref{fig:autoencoder}.
|
||||
|
||||
\begin{figure}[!htb]
|
||||
\centering
|
||||
@ -420,21 +423,90 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow
|
||||
\label{fig:autoencoder}
|
||||
\end{figure}
|
||||
|
||||
Podczas uczenia autoencodera, przedstawia się dane wejściowe jako cel. W ten sposób ta architektura stara się odtworzyć funckje identyczności. Zadanie nie jest trywialne jak mogło by się zdawać ponieważ zazwyczaj ukryta warstwa jest mniejszego rozmiaru niż dane wejściowe. Przez to autoencoder jest zmuszony do wydobycia istotnych cech danych wejściowych, skompresowania a następnie jak najwierniejszego ich odtworzenia. Część kompresująca dane nazywana jest encoderem, natomiast część dekompresująca decoderem.
|
||||
Podczas uczenia autoencodera przedstawia się dane wejściowe jako cel. W ten sposób ta architektura stara się odtworzyć funckje identyczności. Zadanie nie jest trywialne jak mogło by się zdawać, ponieważ zazwyczaj ukryta warstwa jest mniejszego rozmiaru niż dane wejściowe. Z tego względu autoencoder jest zmuszony do wydobycia istotnych cech danych wejściowych, skompresowania, a następnie jak najwierniejszego ich odtworzenia. Część kompresująca dane nazywana jest encoderem, natomiast część dekompresująca decoderem.
|
||||
Wektor cech, które zostały odkryte przez autoencoder nazywane są zmiennymi utajnionymi (latent variables). Zarówno encoder jak i dekoder można wyodrębnić z autoencodera i wykorzystywać go jako osobną sieć neuronową.
|
||||
Ciekawą cechą decodera, jest jego generatywny charakter, ponieważ dostarczając zupełnie nowe informacje jako zmienne wejściowe, decoder odtworzy je na podobieństwo danych, na których został nauczony.
|
||||
|
||||
Ciekawą cechą decodera jest jego generatywny charakter, ponieważ dostarczając zupełnie nowe informacje jako zmienne wejściowe, decoder odtworzy je na podobieństwo danych, na których został nauczony.
|
||||
|
||||
\subsection{Rekurencyjne sieci neuronowe}
|
||||
\label{section:rnn}
|
||||
|
||||
Rekurencyjne sieci neuronowe (recurrent neural networks - RNN) w uproszczeniu, są to MLP posiadające pamięć. Neurony tego typu sieci, różnią się od zwykłych neuronów ponieważ posiadają one dwa parametry zmiast jednego, obecny stan oraz poprzednią predycję.
|
||||
Rekurencyjne sieci neuronowe (recurrent neural networks - RNN) w uproszczeniu są to MLP posiadające pamięć. Wykorzystywane są do analizawania i przewidywania sekwencji wartości uporządkowanych w czasie. Rekurencyjnych sieci neuronowe znalazły zastosowanie w przetwarzaniu języka natutralnego, np. tłumaczenia na różne języki świata. Potrafią poradziac sobie z różnej długości sekwencjami od krótkich zawierających kilka elementów do bardzo długich jak próbki audio, czy tekst zawierający dziesiątki tysięcy kroków czasu.
|
||||
|
||||
\subsection{Długa pamięć krótkotrwała}
|
||||
Rekurencyjne sieci neuronowe działają podobnie do omawianych w sekcji~\ref{section:feedforeward} sieci jednokierunkowych z tym wyjątkiem, że kierunek przepływu informacji płynie również wstecz sieci. Jeden neuron sieci RNN otrzymuje dane wejściowe $x_{(t)}$, wytwarza dane wyjściowe $y_{(t)}$, a następnie wysyła te dane wyjściowe z powrotem do samego siebie. W ten sposób neuron RNN posiada dwa wejścia $x_{(t)}$ oraz $y_{(t-1)}$. Możemy również zaprezentować sieć RNN w postaci udwiniętej w czasie (unrolled through time).
|
||||
|
||||
LSTM
|
||||
\begin{figure}[!htb]
|
||||
\centering
|
||||
\includegraphics[width=\linewidth]{images/rnn.png}
|
||||
\caption{Rekurencyjny neuron (po lewej) odwinięty w czasie (po prawej)}
|
||||
\label{fig:autoencoder}
|
||||
\end{figure}
|
||||
|
||||
\subsection{Model sieci seq2seq}
|
||||
Gdyby rozważyć całą warstwę neuronów tego typu, wtedy wartswa przyjmowała by dwie macierze wag $W_x$ oraz $W_y$. Dane wyjściowe całej warstwy zostaną obliczone wtedy zgodnie ze wzorem
|
||||
|
||||
Seq2Seq
|
||||
\[
|
||||
y_{(t)} = AF(W_x^\top x_{(t)} + W_y^\top y_{(t-1)} + b)
|
||||
\]
|
||||
|
||||
|
||||
Aby wytrenować sieć neuronową stosuje się propagację wsteczną w czasie (backpropagation through time - BPTT). Polega ona na odwinięciu sieci RNN, a następnie zastosowania zwykłej metody wstecznej propagacji. \footnote{Hands-on machine learning with scikit-learn, keras and TensorFlow s.497}
|
||||
|
||||
|
||||
\subsection{LSTM}
|
||||
|
||||
Komórki LSTM (long-short term memory) są rozszerzeniem neuronów sieci rekurencyjnych. Pozwalają wykrywać zależności w danych w długim okresie. Posiadają dwa wektory opisujące stan neuronu. Wektor $h_{(t)}$ określa stan krótkookresowy i wektor $c_{(t)}$ określa stan długookresowy.
|
||||
|
||||
\begin{figure}[!htb]
|
||||
\centering
|
||||
\includegraphics[width=\linewidth]{images/lstm_cell2.png}
|
||||
\caption{Komórka LSTM}
|
||||
\label{fig:lstm}
|
||||
\end{figure}
|
||||
|
||||
Główny pomysł na funcjonowanie komórek LSTM był taki, aby sieć sama mogła się nauczyć jakie informacje są istotne i je przechować, a które informacje można pominąć, zapomnieć. Schemat komórki LSTM przedstawiono na rysunku~\ref{fig:lstm}. Aby to osiągnąć powstała idea bramek (gates), oraz kontrolerów bramek (gate controllers). W komórce LSTM wyróżniamy trzy bramki. Bramkę zapomnienia (forget gate) sterowaną przez $f_{(t)}$, bramkę wejściową(input gate) sterowaną przez $i_{(t)}$, oraz bramkę wyjściową (output gate), sterowaną przez $o_{(t)}$. Przepływ danych w komórce LSTM zaczyna w miejscu gdzie wektor wejściowy $x_{(t)}$ i poprzedni którkoterminowy stan $h_{(t-1)}$ trafiają do czterech warstw. Główną warstwą jest ta zwracająca $g_{(t)}$. W podstawowej komórce RNN jest tylko ta warstwa. Pozostałe trzy wartswy po przejściu przez funkcje logistyczne trafiają do bramek. Bramka zapomnienia kontroluje, które informacje z długookresowego stanu $c_{(t-1)}$ powinny zostać wykasowane. Bramka wejściowa kontroluje jakie informacje z $g_{(t)}$ powinny zostać przekazane dalej i dodane do nastepnego stanu długookresowego $c_{(t)}$. Bramka wyjściowa odpowiada za wybranie odpowiednich elementów z stanu długookresowego i przekazanie ich następnych kroku. Wynik komórki zostaje przekazany do wyjścia komórki $y_{(t)}$ oraz jako następny stan krótkoterminowy $h_{(t)}$.
|
||||
|
||||
Kolejne etapy komórki LSTM obliczane są zgodnie z poniższymy wzorami:
|
||||
\[
|
||||
i_{(t)} = \sigma(W_{xi}^{\top}x_{(t)} + W_{hi}^{\top}h_{(t-1)} + b_i)
|
||||
\]
|
||||
\[
|
||||
f_{(t)} = \sigma(W_{xf}^{\top}x_{(t)} + W_{hf}^{\top}h_{(t-1)} + b_f)
|
||||
\]
|
||||
\[
|
||||
o_{(t)} = \sigma(W_{xo}^{\top}x_{(t)} + W_{ho}^{\top}h_{(t-1)} + b_o)
|
||||
\]
|
||||
\[
|
||||
g_{(t)} = \sigma(W_{xg}^{\top}x_{(t)} + W_{hg}^{\top}h_{(t-1)} + b_g)
|
||||
\]
|
||||
\[
|
||||
c_{(t)} = f_{(t)}\tens{} c_{(t-1)} + i_{(t)}\tens{} g_{(t)}
|
||||
\]
|
||||
\[
|
||||
y_{(t)} = h_{(t)} = o_{(t)} \tens{} tanh \left( c_{(t)} \right),
|
||||
\]
|
||||
|
||||
gdzie $W_{xi}$, $W_{xf}$, $W_{xo}$, $W_{xg}$ są to macierze wag dla każdej w czterech warstw połączonych z wektorem wejściowym $x_{(t)}$, $W_{hi}$, $W_{hf}$, $W_{ho}$, $W_{hg}$ są to macierze wag dla każdej w czterech warstw połączonych z poprzednim krótkookresowym stanem $h_{(t-1)}$ a $b_i$, $b_f$, $b_o$, $b_g$to biasy dla każdej z tych warstw. \footnote{Hands-on Machine Learning with Scikit-Learn, Keras, and TensorFlow s.517}
|
||||
|
||||
Funckja $tanh$ to tangens hiperboliczny, jedna z funkcji sigmoidalnych. To co różni funkcję $tanh$ od $\sigma$ to zakres przyjmowanych wartości. Tangens hiperboliczny przyjmuje wartości z przedziału $(-1, 1)$
|
||||
|
||||
|
||||
\subsection{Sequance-to-sequance}
|
||||
|
||||
Model w architekturze Sequence-to-sequance (seq2seq) został wynaleziony z myślą o tłumaczeniu maszynowym języków, ale zastosowanie dla niego znaleziono również w rozpoznawaniu mowy, opisywaniu wideo, czy tworzeniu chatbotów. Jego główną zaletą jest przetwarzanie sekwencji elementów o różnych długościach. Jest to naturalne, ponieważ tłumacząc z języka na język często tą samą sentencję można wyrazić różną liczbę słów. Dla przykładu zdanie po Polsku "Co dzisiaj robisz?" zawiera trzy słowa, natomiast przetłumaczone na Angielski "What are you doing today?" zawiera pięć słów. Nie można tego osiągnąć zwykłą siecią LSTM, dlatego model seq2seq został zaprojektowany, aby móc go zastosować do tego typu problemów. \footnote{https://towardsdatascience.com/understanding-encoder-decoder-sequence-to-sequence
|
||||
-model-679e04af4346 26.05.2020 14:58}
|
||||
|
||||
Model sequence to sequance ma dwie części, encoder i decoder. Obie czeście są w zasadzie dwiema zupełnie innymi modelami, połączonymi ze sobą w jedną wielką sieć.
|
||||
Zadaniem encodera, podobnie jak zostało to opisane w rozdziale~\ref{section:autoencoder} o autoencoderze, jest wydobycie z wektora wejściowego najistotniejszych informacji i skompresowanie ich. Następnie wektor stanu encodera jest przekazywany do decodera, który
|
||||
na jego podstawie rekonstruuje sekwencję.
|
||||
|
||||
\begin{figure}[!htb]
|
||||
\centering
|
||||
\includegraphics[width=\linewidth]{images/seq2seq2.png}
|
||||
\caption{Architektura modelu sequance-to-sequance}
|
||||
\label{fig:seq2seq}
|
||||
\end{figure}
|
||||
|
||||
Więcej szczegółów technicznych dotycząych modelu sequance-to-sequance przedstawię w dalszych rozdziałach pracy.
|
||||
|
||||
|
||||
\chapter{Reprezentacja danych muzycznych}
|
||||
@ -485,7 +557,6 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow
|
||||
\subsubsection{Nuta}
|
||||
Nuta jest to graficzna reprezentacja dźwięku muzycznego. Informuje nas ona o dwóch parametrach dźwięku, wysokości oraz długości dźwięku. Długość dźwięku nazywa się jej wartością. Podstawową wartością nuty jest ćwierćnuta, odpowiada ona jednemu uderzeniu. Dla przykładu w tempie 60 BPM w ciągu minuty zagramy dokładnie 60 ćwierć nut. Kolejne wartości tworzone poprzez sumowanie lub podział długości ćwierćnuty. Półnuta trwa tyle co dwie ćwierćnuty, cała nuta tyle co dwie półnuty, ósemka trwa połowę czasu ćwiercnuty, a szesnastka połowę ósemki itd.
|
||||
|
||||
|
||||
\begin{figure}[!htb]
|
||||
\centering
|
||||
\includegraphics[width=\linewidth]{images/wartosc_nut.jpg}
|
||||
@ -553,7 +624,7 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow
|
||||
|
||||
\begin{figure}[!htb]
|
||||
\centering
|
||||
\begin{lstlisting}
|
||||
\begin{lstlisting}[backgroundcolor = \color{lightgray}]
|
||||
note_on channel=0 note=48 velocity=100 time=0
|
||||
note_on channel=0 note=53 velocity=100 time=0
|
||||
note_on channel=0 note=60 velocity=100 time=0
|
||||
@ -577,7 +648,7 @@ note_on channel=0 note=60 velocity=0 time=0
|
||||
Dla przykładu wiadomość:
|
||||
|
||||
\begin{center}
|
||||
note\textunderscore on, channel 0, note 48, velocity 100, time 0. \\
|
||||
note\textunderscore on channel 0 note 48 velocity 100 time 0 \\
|
||||
\end{center}
|
||||
|
||||
oznacza aby na kanele 0 zagrać dźwięk nr 48 z głośnością 100 w momencie 0 utworu. Nie informuje nas on jednak o długości trwania dźwęku. Aby zakończyć dźwęk, należy wysłac wiadomość:
|
||||
|
@ -1,28 +1,27 @@
|
||||
\contentsline {chapter}{Streszczenie}{7}%
|
||||
\contentsline {chapter}{Abstract}{9}%
|
||||
\contentsline {chapter}{Wstęp}{11}%
|
||||
\contentsline {chapter}{Rozdzia\PlPrIeC {\l }\ 1\relax .\enspace Wprowadzenie do sieci neuronowych}{13}%
|
||||
\contentsline {section}{\numberline {1.1\relax .\enspace }Regresja liniowa}{13}%
|
||||
\contentsline {section}{\numberline {1.2\relax .\enspace }Uczenie modelu}{14}%
|
||||
\contentsline {subsection}{\numberline {1.2.1\relax .\enspace }Funkcja kosztu}{15}%
|
||||
\contentsline {subsection}{\numberline {1.2.2\relax .\enspace }Znajdowanie minimum funkcji}{15}%
|
||||
\contentsline {subsection}{\numberline {1.2.3\relax .\enspace }Metody gradientowe}{15}%
|
||||
\contentsline {section}{\numberline {1.3\relax .\enspace }Regresja liniowa jako model sieci neuronowej}{17}%
|
||||
\contentsline {section}{\numberline {1.4\relax .\enspace }Funkcje aktywacji}{19}%
|
||||
\contentsline {section}{\numberline {1.5\relax .\enspace }Głębokie sieci neuronowe}{20}%
|
||||
\contentsline {subsection}{\numberline {1.5.1\relax .\enspace }Jednokierunkowe sieci neuronowe}{21}%
|
||||
\contentsline {subsection}{\numberline {1.5.2\relax .\enspace }Propagacja wsteczna błędu}{21}%
|
||||
\contentsline {subsection}{\numberline {1.5.3\relax .\enspace }Autoencodery}{22}%
|
||||
\contentsline {subsection}{\numberline {1.5.4\relax .\enspace }Rekurencyjne sieci neuronowe}{23}%
|
||||
\contentsline {subsection}{\numberline {1.5.5\relax .\enspace }Długa pamięć krótkotrwała}{23}%
|
||||
\contentsline {subsection}{\numberline {1.5.6\relax .\enspace }Model sieci seq2seq}{23}%
|
||||
\contentsline {chapter}{Rozdzia\PlPrIeC {\l }\ 2\relax .\enspace Reprezentacja danych muzycznych}{25}%
|
||||
\contentsline {section}{\numberline {2.1\relax .\enspace }Podstawowe koncepcje}{25}%
|
||||
\contentsline {subsection}{\numberline {2.1.1\relax .\enspace }Dźwięk muzyczny}{25}%
|
||||
\contentsline {subsection}{\numberline {2.1.2\relax .\enspace }Sygnał dźwiękowy}{25}%
|
||||
\contentsline {subsection}{\numberline {2.1.3\relax .\enspace }Zapis nutowy}{25}%
|
||||
\contentsline {section}{\numberline {2.2\relax .\enspace }Cyfrowa reprezentacja muzyki symbolicznej}{28}%
|
||||
\contentsline {subsection}{\numberline {2.2.1\relax .\enspace }Standard MIDI}{28}%
|
||||
\contentsline {chapter}{Rozdzia\PlPrIeC {\l }\ 3\relax .\enspace Projekt}{31}%
|
||||
\contentsline {chapter}{Rozdzia\PlPrIeC {\l }\ 4\relax .\enspace Podsumowanie}{33}%
|
||||
\contentsline {chapter}{Bibliografia}{35}%
|
||||
\contentsline {chapter}{Wst\IeC {\k e}p}{11}%
|
||||
\contentsline {chapter}{Rozdzia\PlPrIeC {\l }\ 1\relax .\leavevmode@ifvmode \kern .5em Wprowadzenie do sieci neuronowych}{13}%
|
||||
\contentsline {section}{\numberline {1.1\relax .\leavevmode@ifvmode \kern .5em }Regresja liniowa}{13}%
|
||||
\contentsline {section}{\numberline {1.2\relax .\leavevmode@ifvmode \kern .5em }Uczenie modelu}{14}%
|
||||
\contentsline {subsection}{\numberline {1.2.1\relax .\leavevmode@ifvmode \kern .5em }Funkcja kosztu}{15}%
|
||||
\contentsline {subsection}{\numberline {1.2.2\relax .\leavevmode@ifvmode \kern .5em }Znajdowanie minimum funkcji}{15}%
|
||||
\contentsline {subsection}{\numberline {1.2.3\relax .\leavevmode@ifvmode \kern .5em }Metody gradientowe}{15}%
|
||||
\contentsline {section}{\numberline {1.3\relax .\leavevmode@ifvmode \kern .5em }Regresja liniowa jako model sieci neuronowej}{17}%
|
||||
\contentsline {section}{\numberline {1.4\relax .\leavevmode@ifvmode \kern .5em }Funkcje aktywacji}{19}%
|
||||
\contentsline {section}{\numberline {1.5\relax .\leavevmode@ifvmode \kern .5em }G\IeC {\l }\IeC {\k e}bokie sieci neuronowe}{20}%
|
||||
\contentsline {subsection}{\numberline {1.5.1\relax .\leavevmode@ifvmode \kern .5em }Jednokierunkowe sieci neuronowe}{21}%
|
||||
\contentsline {subsection}{\numberline {1.5.2\relax .\leavevmode@ifvmode \kern .5em }Autoencodery}{22}%
|
||||
\contentsline {subsection}{\numberline {1.5.3\relax .\leavevmode@ifvmode \kern .5em }Rekurencyjne sieci neuronowe}{22}%
|
||||
\contentsline {subsection}{\numberline {1.5.4\relax .\leavevmode@ifvmode \kern .5em }LSTM}{23}%
|
||||
\contentsline {subsection}{\numberline {1.5.5\relax .\leavevmode@ifvmode \kern .5em }Sequance-to-sequance}{25}%
|
||||
\contentsline {chapter}{Rozdzia\PlPrIeC {\l }\ 2\relax .\leavevmode@ifvmode \kern .5em Reprezentacja danych muzycznych}{27}%
|
||||
\contentsline {section}{\numberline {2.1\relax .\leavevmode@ifvmode \kern .5em }Podstawowe koncepcje}{27}%
|
||||
\contentsline {subsection}{\numberline {2.1.1\relax .\leavevmode@ifvmode \kern .5em }D\IeC {\'z}wi\IeC {\k e}k muzyczny}{27}%
|
||||
\contentsline {subsection}{\numberline {2.1.2\relax .\leavevmode@ifvmode \kern .5em }Sygna\IeC {\l } d\IeC {\'z}wi\IeC {\k e}kowy}{27}%
|
||||
\contentsline {subsection}{\numberline {2.1.3\relax .\leavevmode@ifvmode \kern .5em }Zapis nutowy}{27}%
|
||||
\contentsline {section}{\numberline {2.2\relax .\leavevmode@ifvmode \kern .5em }Cyfrowa reprezentacja muzyki symbolicznej}{30}%
|
||||
\contentsline {subsection}{\numberline {2.2.1\relax .\leavevmode@ifvmode \kern .5em }Standard MIDI}{30}%
|
||||
\contentsline {chapter}{Rozdzia\PlPrIeC {\l }\ 3\relax .\leavevmode@ifvmode \kern .5em Projekt}{33}%
|
||||
\contentsline {chapter}{Rozdzia\PlPrIeC {\l }\ 4\relax .\leavevmode@ifvmode \kern .5em Podsumowanie}{35}%
|
||||
\contentsline {chapter}{Bibliografia}{37}%
|
||||
|
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Reference in New Issue
Block a user