From da252941a7e7dc19b9be71dc717de645539a77a0 Mon Sep 17 00:00:00 2001 From: CezaryPukownik Date: Mon, 15 Jun 2020 07:39:29 +0200 Subject: [PATCH] =?UTF-8?q?Poprawiono=20liter=C3=B3wki=20w=20pracy?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- docs/document.aux | 98 +-- docs/document.fdb_latexmk | 457 ++++++------ docs/document.fls | 698 +++++++++--------- docs/document.log | 513 ++++++------- docs/document.pdf | Bin 653423 -> 653226 bytes docs/document.synctex.gz | Bin 317306 -> 318235 bytes docs/document.tex | 204 ++--- docs/document.toc | 76 +- .... Resheff, and Itay Lieder (z-lib.org).pdf | Bin 0 -> 6240037 bytes poprawki_promotora_2020_06_10.pdf | Bin 0 -> 745665 bytes 10 files changed, 1023 insertions(+), 1023 deletions(-) create mode 100644 docs/sources/Learning TensorFlow A Guide to Building Deep Learning Systems by Tom Hope, Yehezkel S. 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zyskało na popularności. Zastosowania i możliwości różnych algorytmów uczenia maszynowego czasami przekraczają nasze wyobrażenie o tym co komputer może zrobić. Niektóre aplikacje potrafią wręcz zaskoczyć użytkowników tym co potrafią zrobić. Wśród takich aplikacji znajdują się takie, które potrafią przewidywać następne wartości akcji giełdowych, rozpoznawać na filmie obiekty w czasie rzeczywistym, czy nawet prowadzić samochód. Algorytmy wyuczone proponują nam spersonalizowane reklamy, czy produkty na podstawie naszych upodobań. Najczęstsze zastosowania dotyczą przetwarzania obrazów lub tekstu, natomiast zastosowania w przetwarzaniu muzyki są niszowe i rzadziej spotykane. - Celem tej pracy jest stworzenie modelu sieci neurowej, którego zadaniem bedzie generowanie krótkich multiinstrumentalnych klipów muzycznych. + Celem tej pracy jest stworzenie modelu sieci neuronowej, którego zadaniem będzie generowanie krótkich multi instrumentalnych klipów muzycznych. - 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. + W pierwszej części 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 opiszę 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. + W kolejnym rozdziale skupimy się na rezultatach pracy, przedstawię zalety i wady modelu. Przeprowadzę analizę jakie muzyczne koncepcje model się nauczył na podstawie danych oraz doprowadzę do ostatecznej konkluzji czy wygenerowana muzyka może być przyjemna dla odbiorcy. \newpage @@ -186,7 +186,7 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow 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. + Podstawą wszystkich sieci neuronowych jest regresja liniowa. W statystyce wykorzystywana, aby wyjaśnić liniowe zależności między zmiennymi. Prosty model regresji liniowej dla jednej zmiennej można opisać wzorem % \footnote{Statystyka, Mieczysław Sobczyk s.179} @@ -205,7 +205,7 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow - Zadaniem jest znalezienie takiego parametru $a\in \mathbb{R}$ oraz wyrazu wolnego $b \in \mathbb{R}$, aby dla znanych wartości $x \in \mathbb{R}$ oszacowanie 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 $x \in \mathbb{R}$ oszacowanie zmiennej objaśnianej $\hat{y} \in \mathbb{R}$ najlepiej opisywała zmienną objaśnianą $y \in \mathbb{R}$. 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] @@ -215,7 +215,7 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow \label{fig:linreg} \end{figure} - Wartość zmiennej objaśnianej $y$ można również opisać za pomocą wielu zmiennych objaśniająych. Wtedy dla zmiennych objaśniającej $x_1, x_2, ... , x_p \in \mathbb{R}$ szukamy parametrów $\theta_1, \theta_2, ... ,\theta_p \in \mathbb{R}$, gdzi $p \in \mathbb{N}$ jest liczbą cech. Otrzymany w ten sposób model nazywany jest również hipotezą i oznaczamy go $h(x)$. + Wartość zmiennej objaśnianej $y$ można również opisać za pomocą wielu zmiennych objaśniających. Wtedy dla zmiennych objaśniającej $x_1, x_2, ... , x_p \in \mathbb{R}$ szukamy parametrów $\theta_1, \theta_2, ... ,\theta_p \in \mathbb{R}$, gdzie $p \in \mathbb{N}$ jest liczbą cech. Otrzymany w ten sposób model nazywany jest również hipotezą i oznaczamy go $h(x)$. \[h(x) = b + \theta_1x_2 + \theta_2x_2 + ... + \theta_px_p + \epsilon = b + \sum_{i=1}^{p} \theta_ix_i + \epsilon.\] @@ -228,7 +228,7 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow \[ \textoperatorname{błąd} = \sum_{i=1}^m | \textoperatorname{predykcja} - \textoperatorname{rzeczywistość} |, \] - gdzie $n \in \mathbb{N}$ jest wielkością zbioru danych jakim dysponujemy. Minimalizując bład dla modelu jesteśmy wstanie znaleźć przybliżenie funkcji $h(x)$. + gdzie $n \in \mathbb{N}$ jest wielkością zbioru danych jakim dysponujemy. Minimalizując błąd dla modelu jesteśmy w stanie znaleźć przybliżenie funkcji $h(x)$. \subsection{Funkcja kosztu} @@ -241,15 +241,15 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow \subsection{Znajdowanie minimum funkcji} - 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: + 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 dziedziny funkcji $f$. Dodatkowo jeśli istnieje 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. Rozwiązać równanie $J_\theta'(h)=0$, następnie dla otrzymanych wyników sprawdzić powyższą nierówność oraz wybrać najmniejszy wynik ze wszystkich \cite{analiza_mat}. W praktyce rozwiązanie takiego 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. - % \footnote{źródlo: Analiza matematyczna, Krysicki Włodarski, s.187 }. + % \footnote{źródło: Analiza matematyczna, Krysicki Włodarski, s.187 }. \subsection{Metody gradientowe} - Metody gradientowe (\textit{ang. gradient descent}) są to iteracyjne algorytmy służące do znajdowania minimum funkcji. Aby móc skorzystać z metod gradientowych analizowana funkcja musi być ciągła oraz różniczkowalna. Sposób ich działania można intuicyjnie opisać w nastepujących krokach. + Metody gradientowe (\textit{ang. gradient descent}) są to iteracyjne algorytmy służące do znajdowania minimum funkcji. Aby móc skorzystać z metod gradientowych analizowana funkcja musi być ciągła i różniczkowalna. Sposób ich działania można intuicyjnie opisać w następujących krokach. 1. Wybierz punkt początkowy. @@ -275,7 +275,7 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow \[ \Theta_0 = \mathbf{\boldsymbol{\left[ \theta_1, \theta_2, ... ,\theta_n \right]}}. \] - Następnie policzyć wszystkie pochodne cześciowe $\frac{\partial J_\theta(h)}{\partial \theta_i}$. Otrzymamy w ten sposób gradient $\nabla J_\theta(h)$, gdzie + Następnie policzyć wszystkie pochodne częściowe $\frac{\partial J_\theta(h)}{\partial \theta_i}$. Otrzymamy w ten sposób gradient $\nabla J_\theta(h)$, gdzie \[ \nabla J_\theta(h) = \mathbf{\boldsymbol{\left[ \frac{\partial J_\theta(h)}{\partial \theta_1}, \frac{\partial J_\theta(h)}{\partial \theta_2}, ... , \frac{\partial J_\theta(h)}{\partial \theta_n} \right]}}. \] @@ -285,8 +285,8 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow \[ \Theta_{k+1} = \Theta_{k} - \alpha\nabla J_\theta(h), \] - gdzie $\alpha \in \mathbb{R}$ jest współczynnikiem uczenia (\textit{ang. learning rate}), a $k \in \mathbb{N}$ jest kolejną iteracją algorytmu. Proces ten należy powtarzać do pewnego momentu. Najczęściej 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 \cite{survay}. - % \footnote{Deep Learning techniques for music geneation - A survay s.44} + gdzie $\alpha \in \mathbb{R}$ jest współczynnikiem uczenia (\textit{ang. learning rate}), a $k \in \mathbb{N}$ jest kolejną iteracją algorytmu. Proces ten należy powtarzać do pewnego momentu. Najczęściej z góry określoną liczbę razy lub do momentu, gdy uzysk funkcji kosztu spowodowany następną iteracją jest mniejszy niż ustalona wartość. Otrzymany w ten sposób wektor parametrów $\Theta_k$ jest wynikiem algorytmu \cite{survay}. + % \footnote{Deep Learning techniques for music generation - A survey 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. @@ -319,16 +319,16 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow co jest równoważne omawianemu modelowi regresji liniowej. Węzły sieci nazywane są neuronami, a wyraz wolny modelu $b$ nazywany jest biasem (\textit{ang. 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 $\hat{y_1}, \hat{y_2}, \dots , \hat{y_q}$, który oznaczać bedziemy jako $\hat{Y}$. Model ten został 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 $\hat{y_1}, \hat{y_2}, \dots , \hat{y_q}$, który oznaczać będziemy jako $\hat{Y}$. Model ten został przedstawiony na rysunku~\ref{fig:neural_model_multi}. \begin{figure}[!htb] \centering \includegraphics[width=8cm]{images/naural_model_multi_ver2.png} - \caption{Regresja liniowa wielu zmiennych jako model sieci nauronowej} + \caption{Regresja liniowa wielu zmiennych jako model sieci neuronowej} \label{fig:neural_model_multi} \end{figure} - Dla uogólnienia pojedyncze wagi modelu zapisywać będę jako $w_{pq}$, natomiast macierz wag jako $W$. Algebricznie zapisalibyśmy ten model jako + Dla uogólnienia pojedyncze wagi modelu zapisywać będę jako $w_{pq}$, natomiast macierz wag jako $W$. Algebraicznie zapisaliśmy ten model jako \[ \mathbb{\boldsymbol{\begin{bmatrix} @@ -360,11 +360,11 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow b+XW = \hat{Y}, \] - gdzie $p$ jest liczbą zmiennych niezależnych, $q$ jest liczbą zmiennych zaleznych, $X$ jest rozszerzonym do macierzy o rozmiarach $q$ x $p$ wektorem zmiennych objaśniających, w taki sposób że $x_{i1} = x_{i2} = \dots = x_{ip}$ dla $i = 1, 2, ..., q$, $W$ jest macierzą wag o rozmiarach $p$ x $q$, natomiast $b$ jest sumą wyrazów wolnych $b_1, ... ,b_q$. 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. + gdzie $p$ jest liczbą zmiennych niezależnych, $q$ jest liczbą zmiennych zależnych, $X$ jest rozszerzonym do macierzy o rozmiarach $q$ x $p$ wektorem zmiennych objaśniających, w taki sposób że $x_{i1} = x_{i2} = \dots = x_{ip}$ dla $i = 1, 2, ..., q$, $W$ jest macierzą wag o rozmiarach $p$ x $q$, natomiast $b$ jest sumą wyrazów wolnych $b_1, ... ,b_q$. 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 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 (\textit{ang. activation function}). Istnieje wiele różnych funkcji aktywacji, a każda posiada inną charakterystykę i wpływ na model. Najpopularnijeszą grupą fukcji są funkcje sigmoidalne (\textit{ang. sigmoid functions}). Jedną z nich jest funkcja logistyczna (\textit{ang. logistic curve}) + 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 (\textit{ang. activation function}). Istnieje wiele różnych funkcji aktywacji, a każda posiada inną charakterystykę i wpływ na model. Najpopularniejszą grupą funkcji są funkcje sigmoidalne (\textit{ang. sigmoid functions}). Jedną z nich jest funkcja logistyczna (\textit{ang. logistic curve}) \[ \sigma(x) = \frac{1}{1+e^{-x}} \] @@ -387,20 +387,20 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow \sigma(b+XW) = \hat{Y} \] - W dalszych cześciach pracy, kiedy bedę używał funkcji aktywacji nie wskazując na konkretną funkcję, będe wykorzystywał oznaczenie $AF(x)$. + W dalszych częściach pracy, kiedy będę używał funkcji aktywacji nie wskazując na konkretną funkcję, będę wykorzystywał oznaczenie $AF(x)$. \section{Wielowarstwowe 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 perceptronów w jeden model, tworzymy warstwy (\textit{ang. layers}) 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 następnego podstawowego modelu. Składając ze sobą wiele perceptronów w jeden model, tworzymy warstwy (\textit{ang. layers}) sieci neuronowej. Wyróżniamy trzy rodzaje warstw: \begin{itemize} \item warstwę wejściową (\textit{ang. input layer}), która jest pierwszą warstwą modelu, - \item warstwę wyjściową (\textit{ang. output layer}), która jest ostatnią wartstwą modelu, - \item wartwy ukryte (\textit{ang. hidden layer}), które są warstwami pomiędzy warstwą wejsciową oraz wyjściową. + \item warstwę wyjściową (\textit{ang. output layer}), która jest ostatnią warstwą modelu, + \item warstwy ukryte (\textit{ang. hidden layer}), które są warstwami pomiędzy warstwą wejściową i wyjściową. \end{itemize} - Na rysunku~\ref{fig:neural_net_1} przedstawiono sieć posiadającą warstwę wejściową, dwie wartswy ukryte oraz wartswę wyjsciową. + Na rysunku~\ref{fig:neural_net_1} przedstawiono sieć posiadającą warstwę wejściową, dwie warstwy ukryte oraz warstwę wyjściową. \begin{figure}[!htb] \centering @@ -409,13 +409,13 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow \label{fig:neural_net_1} \end{figure} - Tego typu modele są głębokimi sieciami neuronowymi (\textit{ang. 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. + Tego typu modele są głębokimi sieciami neuronowymi (\textit{ang. deep neural networks}). Istnieje wiele różnych architektur głębokich sieci neuronowych, które wykorzystują te podstawowe koncepcje i rozszerzają je o dodatkowe warstwy, połączenia, funkcje aktywacji czy neurony o specjalnych właściwościach. \subsection{Jednokierunkowe sieci neuronowe} \label{section:feedforeward} - Jednokierunkowe sieci neuronowe (\textit{ang. feedforward neural networks}) są to najprostrze sieci neuronowe, które wprost czerpią z omówionych wcześniej podstawowych wartsw. Możemy się również spotkać z nazwą wielowarstwowy perceptron (\textit{ang. multi layer perceptron - MLP}) ze względu na fakt, że jest zbudowany z wielu perceptronów zaprezentoanych w rozdziale~\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 \cite{survay} %\footnote{Deep Learning techniques for music geneation - A survay s.63} + Jednokierunkowe sieci neuronowe (\textit{ang. feedforward neural networks}) są to najprostsze sieci neuronowe, które wprost czerpią z omówionych wcześniej podstawowych warstw. Możemy się również spotkać z nazwą wielowarstwowy perceptron (\textit{ang. multi layer perceptron - MLP}) ze względu na fakt, że jest zbudowany z wielu perceptronów zaprezentowanych w rozdziale~\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 \cite{survay} %\footnote{Deep Learning techniques for music generation - A survey s.63} \[ X_k = AF(b_k + W_kX_{k-1}). \] @@ -423,12 +423,12 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow \subsubsection{Propagacja wsteczna błędu} \label{section:backpropagation} - Kiedy używamy jednokierunkowych sieci neuronowych, zasilamy je danymi wejściowymi $x$ ostatecznie otrzymując predykcję $\hat{y}$. Taki sposób działania nazywa się propagcją wprzód (\textit{ang. foreward propagation}). Podczas uczenia sieci kontynuuje się ten proces obliczając koszt $J(h)$. Propagacja wsteczna (\textit{ang. 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. + Kiedy używamy jednokierunkowych sieci neuronowych, zasilamy je danymi wejściowymi $x$ ostatecznie otrzymując predykcję $\hat{y}$. Taki sposób działania nazywa się propagacją wprzód (\textit{ang. forward propagation}). Podczas uczenia sieci kontynuuje się ten proces obliczając koszt $J(h)$. Propagacja wsteczna (\textit{ang. back-propagation}) pozwala na przepływ informacji od funkcji kosztu wstecz sieci neuronowej, aby ostatecznie obliczyć gradient. Zasada działania algorytmu propagacji wstecznej błędu polega na sukcesywnym aktualizowaniu wag i biasów oraz przesyłaniu wstecz po warstwach sieci. Dzięki temu jesteśmy w stanie wyuczyć sieć oraz obliczyć optymalne wagi i biasy dla całej sieci neuronowej. - \subsection{Autoencodery} + \subsection{Autoencoder} \label{section: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}. + Autoencoder jest szczególnym przypadkiem sieci neuronowej. Posiada jedną warstwę ukrytą, a rozmiar warstwy wejściowej musi być równy rozmiarowi warstwy wyjściowej, tworząc w ten sposób symetryczną sieć, której kształt przypomina klepsydrę. Przykład autoencodera przedstawiono na rysunku~\ref{fig:autoencoder}. \begin{figure}[!htb] \centering @@ -437,7 +437,7 @@ 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 funkcje identycznościowe. 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. + Podczas uczenia autoencodera przedstawia się dane wejściowe jako cel. W ten sposób ta architektura stara się odtworzyć funkcje identycznościowe. Zadanie nie jest trywialne jak mogłoby 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. Cechy, które zostały odkryte przez autoencoder nazywane są zmiennymi utajnionymi (\textit{ang. 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. @@ -445,7 +445,7 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow \subsection{Rekurencyjne sieci neuronowe} \label{section:rnn} - Rekurencyjne sieci neuronowe (\textit{ang. recurrent neural networks; RNN}) w uproszczeniu są to MLP posiadające pamięć. Wykorzystywane są do analizawania i przewidywania sekwencji wartości uporządkowanych w czasie. Rekurencyjne sieci neuronowe znalazły zastosowanie w przetwarzaniu języka natutralnego, np. tłumaczenia na różne języki świata. Potrafią poradzić sobie z różnej długości sekwencjami od krótkich zawierających kilka elementów do bardzo długich jak próbki audio, czy tekst zawierający dziesiątki tysięcy kroków czasu. + Rekurencyjne sieci neuronowe (\textit{ang. recurrent neural networks; RNN}) w uproszczeniu są to MLP posiadające pamięć. Wykorzystywane są do analizowania i przewidywania sekwencji wartości uporządkowanych w czasie. Rekurencyjne sieci neuronowe znalazły zastosowanie w przetwarzaniu języka naturalnego, np. tłumaczenia na różne języki świata. Potrafią poradzić sobie z różnej długości sekwencjami od krótkich zawierających kilka elementów do bardzo długich jak próbki audio, czy tekst zawierający dziesiątki tysięcy kroków czasu. 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 odwiniętej w czasie (\textit{ang. unrolled through time}). @@ -456,7 +456,7 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow \label{fig:autoencoder} \end{figure} - 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 + Gdyby rozważyć całą warstwę neuronów tego typu, wtedy warstwa przyjmowała by dwie macierze wag $W_x$ oraz $W_y$. Dane wyjściowe całej warstwy zostaną obliczone wtedy zgodnie ze wzorem \[ y_{(t)} = AF(W_x^\top x_{(t)} + W_y^\top y_{(t-1)} + b) @@ -477,9 +477,9 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow \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 (\textit{ang. gates}), oraz kontrolerów bramek (\textit{ang. gate controllers}). W komórce LSTM wyróżniamy trzy bramki. Bramkę zapomnienia (\textit{ang. forget gate}) sterowaną przez $f_{(t)}$, bramkę wejściową(\textit{ang. input gate}) sterowaną przez $i_{(t)}$, oraz bramkę wyjściową (\textit{ang. 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 $h_{(t)}$. + Główny pomysł na funkcjonowanie 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 (\textit{ang. gates}), oraz kontrolerów bramek (\textit{ang. gate controllers}). W komórce LSTM wyróżniamy trzy bramki. Bramkę zapomnienia (\textit{ang. forget gate}) sterowaną przez $f_{(t)}$, bramkę wejściową(\textit{ang. input gate}) sterowaną przez $i_{(t)}$, oraz bramkę wyjściową (\textit{ang. output gate}), sterowaną przez $o_{(t)}$. Przepływ danych w komórce LSTM zaczyna w miejscu gdzie wektor wejściowy $x_{(t)}$ i poprzedni krótkoterminowy 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 warstwy 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 następnego 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: + Kolejne etapy komórki LSTM obliczane są zgodnie z poniższymi wzorami: \[ i_{(t)} = \sigma(W_{xi}^{\top}x_{(t)} + W_{hi}^{\top}h_{(t-1)} + b_i) \] @@ -501,7 +501,7 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow 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 \cite{handson}. %\footnote{Hands-on Machine Learning with Scikit-Learn, Keras, and TensorFlow s.517} - Funckja $tanh$ to tangens hiperboliczny, jedna z funkcji sigmoidalnych. Wykres funkcji $tanh$ został przedstawiony na rysunku~\ref{fig:tanh} + Funkcja $tanh$ to tangens hiperboliczny, jedna z funkcji sigmoidalnych. Wykres funkcji $tanh$ został przedstawiony na rysunku~\ref{fig:tanh} \[ tanh(x) = \frac{e^x - e^{-x}}{e^x + e^{-x}} \] @@ -518,21 +518,21 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow \subsection{Sequence-to-sequence} - Model w architekturze Sequence-to-sequance (\textit{ang. 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 \cite{seq2seq}. %\footnote{https://towardsdatascience.com/understanding-encoder-decoder-sequence-to-sequence + Model w architekturze Sequence-to-sequence (\textit{ang. 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 \cite{seq2seq}. %\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 osobnymi modelami, połączonymi ze sobą w jedną sieć. + Model sequence-to-sequence ma dwie części, encoder i decoder. Obie części są w zasadzie dwiema zupełnie osobnymi modelami, połączonymi ze sobą w jedną 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} + \caption{Architektura modelu sequence-to-sequence} \label{fig:seq2seq} \end{figure} - Więcej szczegółów technicznych dotycząych modelu sequence-to-sequence przedstawię w dalszych rozdziałach pracy. + Więcej szczegółów technicznych dotyczących modelu sequence-to-sequence przedstawię w dalszych rozdziałach pracy. \chapter{Wprowadzenie do teorii muzyki} @@ -543,15 +543,15 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow \subsection{Dźwięk muzyczny} - Drgania powietrza z otoczenia człowieka są przetwarzane w mózgu i rozumiane jako dźwięki. Takie drgania nazywamy falą dźwiękową. Dzwięk muzyczny jest to fala dźwiękowa, którą wytwarza intrument muzyczny. Dzwięk muzyczny charakteryzuje się trzema podstawowymi parametrami: + Drgania powietrza z otoczenia człowieka są przetwarzane w mózgu i rozumiane jako dźwięki. Takie drgania nazywamy falą dźwiękową. Dźwięk muzyczny jest to fala dźwiękowa, którą wytwarza instrument muzyczny. Dźwięk muzyczny charakteryzuje się trzema podstawowymi parametrami: \begin{itemize} - \item wysokością (\textit{ang. pitch}) - jest to częstotliwość drgań wyrażona w hercach. Im większa częstotliwość tym dzźięk jest rozumiany jako wyższy, + \item wysokością (\textit{ang. pitch}) - jest to częstotliwość drgań wyrażona w hercach. Im większa częstotliwość tym dźwięk jest rozumiany jako wyższy, Zakres słyszalny dla człowieka wynosi od 20Hz do 20kHz. - \item głośność (\textit{ang. velocity}) - jest to amplituda drgań fali dźwiękowej. Im większa aplituda, tym dźwięk jest odczuwany jako głosniejszy, + \item głośność (\textit{ang. velocity}) - jest to amplituda drgań fali dźwiękowej. Im większa amplituda, tym dźwięk jest odczuwany jako głośniejszy, \item długość (\textit{ang. duration}) - jest to czas z jakim dźwięk wybrzmiewa, np. 2 sekundy. \end{itemize} - % Przykład dźwięku myczynego przedstawiono na Rusynku~\ref{fig:sine} + % Przykład dźwięku muzycznego przedstawiono na Rysunku~\ref{fig:sine} % \begin{figure}[!htb] % \centering @@ -562,7 +562,7 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow \subsection{Sygnał dźwiękowy} - W rzeczywistości utwór muzyczny jest zazwyczaj kombinacją wielu fal dźwiękowych, o różnych charaketystykach i nazwywany jest sygnałem dźwiękowym. Wizualizację sygnalu dźwiękowego przedstawiono na Rysunku ~\ref{fig:waveform} + W rzeczywistości utwór muzyczny jest zazwyczaj kombinacją wielu fal dźwiękowych, o różnych charakterystykach i nazywany jest sygnałem dźwiękowym. Wizualizację sygnału dźwiękowego przedstawiono na Rysunku ~\ref{fig:waveform} \begin{figure}[!htb] \centering @@ -573,7 +573,7 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow \subsection{Zapis nutowy} - Reprezentacja muzyki jako sygnału dźwiękowego przechowuje informacje o dokładnym brzmieniu danego utworu tzn. jakie drgania należy wytworzyć, aby móc odtwozyć muzykę. Taki zapis nie informuje nas bezpośrednio jakie instrumenty zostały użyte, jakie wysokości i długości dźwięków zostały wykorzystane. Dlatego ludzkość na przestrzeni wieków opracowała abstrakcyjne objekty, które reprezentują utwór w czytelny dla człowieka sposób. + Reprezentacja muzyki jako sygnału dźwiękowego przechowuje informacje o dokładnym brzmieniu danego utworu tzn. jakie drgania należy wytworzyć, aby móc odtworzyć muzykę. Taki zapis nie informuje nas bezpośrednio jakie instrumenty zostały użyte, jakie wysokości i długości dźwięków zostały wykorzystane. Dlatego ludzkość na przestrzeni wieków opracowała abstrakcyjne obiekty, które reprezentują utwór w czytelny dla człowieka sposób. \subsubsection{Tempo} W muzyce symbolicznej tempo informuje nas o prędkości utworu. W muzyce klasycznej stosowało się opisowy sposób dostosowywania tempa np. Allegro - Szybko lub Adagio - wolno. Jak można szybko stwierdzić są to zwroty subiektywne i nie wyznaczają tempa jednoznacznie. Obecnie wyraża się tempo w liczbie uderzeń na minutę (\textit{ang. beats per minute; BPM}). I tak Allegro jest to od 120 do 168 BPM a Adagio od 66 do 76 BPM \cite{tempos}. % \footnote{źródlo: http://www.classicalmusiccity.com/search/article.php?vars=446/ @@ -581,7 +581,7 @@ 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 (\textit{ang. beat}). Ta wartość pozwala nam zrozumieć jak długo nalezy wygrywać nutę relatywnie do pozostałych nut w utworze. Jeśli obok siebie ustawimy dwie nuty o wartościach ćwirćnuty i ósemki, wiemy że tę drugą nutę powinniśmy zagrać dwa razy krócej niż pierwszą. Aby wiedzieć dokładnie jak dlugo powinna wybrzmiewać nuta musimy odwołać się do tempa utworu. 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. + 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 (\textit{ang. beat}). Ta wartość pozwala nam zrozumieć jak długo należy wygrywać nutę relatywnie do pozostałych nut w utworze. Jeśli obok siebie ustawimy dwie nuty o wartościach ćwierćnuty i ósemki, wiemy że tę drugą nutę powinniśmy zagrać dwa razy krócej niż pierwszą. Aby wiedzieć dokładnie jak długo powinna wybrzmiewać nuta musimy odwołać się do tempa utworu. Dla przykładu w tempie 60 BPM w ciągu minuty zagramy dokładnie 60 ćwierćnut. 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 ćwierćnuty, a szesnastka połowę ósemki itd. \begin{figure}[!htb] \centering @@ -590,7 +590,7 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow \label{fig:waveform} \end{figure} - \footnotetext{źródlo: https://www.infomusic.pl/poradnik/46934,poradnik-teoria-muzyki-rytm + \footnotetext{źródło: https://www.infomusic.pl/poradnik/46934,poradnik-teoria-muzyki-rytm \newline 5 kwietnia 2020 12:46} @@ -601,7 +601,7 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow \centering \begin{tabular}{||c | c||} \hline - Dzwięk & Ćzęstotliwość \\ [0.5ex] + Dźwięk & Częstotliwość \\ [0.5ex] \hline\hline $C_4$ & 261,6\\ \hline @@ -618,17 +618,17 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow $H_4$ & 493,9\\ \hline \end{tabular} - \caption{Dźwięki symboliczne oraz ich częstosliwości} + \caption{Dźwięki symboliczne oraz ich częstotliwości} \label{table:dzwieki} \end{table} - W zapisie nutowym aby nucie nadać wysokość, umieszcza się ją w odpowiednim miejscu na pięciolonii. Przedstawione powyżej dźwięki zapisalibyśmy w taki sposób jak przedstawiono na Rysunku~\ref{fig:pieciolinia} + W zapisie nutowym aby nucie nadać wysokość, umieszcza się ją w odpowiednim miejscu na pięciolinii. Przedstawione powyżej dźwięki zapisaliśmy w taki sposób jak przedstawiono na Rysunku~\ref{fig:pieciolinia} \begin{figure}[!htb] \centering \includegraphics[width=\linewidth]{images/nuty_linia.png} - \caption{źródlo: https://amplitudaschool.weebly.com/lekcja-11.html 5 kwietnia 2020 13:24} + \caption{źródło: https://amplitudaschool.weebly.com/lekcja-11.html 5 kwietnia 2020 13:24} \label{fig:pieciolinia} \end{figure} @@ -643,20 +643,20 @@ Jednocześnie przyjmuję do wiadomości, że przypisanie sobie, w pracy dyplomow \[ A_5 = 440Hz * 2 = 880Hz \] \[ A_3 = 440Hz / 2 = 220Hz \] - W ten sposób możemy utworzyć nieskończenie wiele oktaw, jednak w rzeczywistości używa się nut od C0 do C8. + W ten sposób możemy stworzyć nieskończenie wiele oktaw, jednak w rzeczywistości używa się nut od C0 do C8. \subsubsection{Akord} Gdy w jednym momencie zabrzmią dwie lub więcej różnych nut, wtedy mówimy o akordzie. Akord potrafi dodać emocje do brzmienia całego utworu. \subsubsection{Skala} \label{section:skala} - Do opisu, czym jest skala. -> Skala jest to zestaw nut, które dobrze ze sobą brzmią. Skalę opisujemy dwoma parametrami. Tonację, oraz modem. Tonacja jest to nuta startowa, dla skali. Mod nastomiast jest to zestaw interwałów liczony od pierwszej nuty. np. C-Dur, gdzie C jest wartością początkową, a Dur opisuje interwału, Możemu utorzyć inne skale, np G-Dur, używając tych samych interwałów, ale zaczynając od innej nuty. + Do opisu, czym jest skala. -> Skala jest to zestaw nut, które dobrze ze sobą brzmią. Skalę opisujemy dwoma parametrami. Tonację, oraz modem. Tonacja jest to nuta startowa, dla skali. Mod natomiast jest to zestaw interwałów liczony od pierwszej nuty. np. C-Dur, gdzie C jest wartością początkową, a Dur opisuje interwału, Możemy utworzyć inne skale, np G-Dur, używając tych samych interwałów, ale zaczynając od innej nuty. \section{Cyfrowa reprezentacja muzyki symbolicznej} \subsection{Standard MIDI} - Standrd MIDI (ang. Musical Instrument Digital Interface) został stworzony w 1983 aby umożliwić synchronizację i wymianę informacji między elektronicznymi urządzeniami muzycznymi takimi jak syntezatory, keyboardy czy sekwencery. + Standard MIDI (ang. Musical Instrument Digital Interface) został stworzony w 1983 aby umożliwić synchronizację i wymianę informacji między elektronicznymi urządzeniami muzycznymi takimi jak syntezatory, keyboardy czy sekwencery. W późniejszych latach został on zaadaptowany do środowiska komputerowego jako cyfrowa reprezentacja muzyki symbolicznej. \begin{figure}[!htb] @@ -688,7 +688,7 @@ note_on channel=0 note=60 velocity=0 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: + oznacza aby na kanele 0 zagrać dźwięk nr 48 z głośnością 100 w momencie 0 utworu. Nie informuje nas on jednak o długości trwania dźwięku. Aby zakończyć dźwięk, należy wysłać wiadomość: \begin{center} note\textunderscore off, channel 0, note 48, velocity 100, time 24. \\ @@ -698,43 +698,43 @@ note_on channel=0 note=60 velocity=0 time=0 Co oznacza ćwierćnutę. \subsubsection{Rozdzielczość} - Czas w MIDI jest reprezentowany jako liczba naturalna i jest on zależny od ustalonego tempa utworu. Standardowa rozdzielczość pliku MIDI to 24. Oznacza to, że jedna jednostka czasu odpowiada jednej dwudziestejczwartej jednego udeżenia. + Czas w MIDI jest reprezentowany jako liczba naturalna i jest on zależny od ustalonego tempa utworu. Standardowa rozdzielczość pliku MIDI to 24. Oznacza to, że jedna jednostka czasu odpowiada jednej dwudziestej czwartej jednego uderzenia. \subsubsection{Kanały} - Plik MIDI posiada 16 kanałów numerowanych od 0 do 15. Każdy kanał odpowiada intrumentowi lub ścieżce. Kanał 9 jest kanałem zarezerwowanym na intrumenty perkusyjne. + Plik MIDI posiada 16 kanałów numerowanych od 0 do 15. Każdy kanał odpowiada instrumentowi lub ścieżce. Kanał 9 jest kanałem zarezerwowanym na instrumenty perkusyjne. \subsubsection{Nuty} - Nuty w formacie MIDI opisane są kolejnymi cyframi naturalnymi w przedziale od 0 do 127. Odpowiada to dźwękom od $C_0$ do $C_8$. Dla przykładu nuta 69 odpowiada $A_4$, a nuta 47 odpowiada $B_2$. + Nuty w formacie MIDI opisane są kolejnymi cyframi naturalnymi w przedziale od 0 do 127. Odpowiada to dźwiękom od $C_0$ do $C_8$. Dla przykładu nuta 69 odpowiada $A_4$, a nuta 47 odpowiada $B_2$. - Wyjątkiem są nuty z kanału dziewiątego, gdzie istnieją tylko nuty z zakresu od 35 do 81 i każda nuta odpowiada innemu elementowi perkusyjnemu np. 35 to stopa (\textit{kick}), a 37 to werbel {\textit{snare}}. + Wyjątkiem są nuty z kanału dziewiątego, gdzie istnieją tylko nuty z zakresu od 35 do 81 i każda nuta odpowiada innemu elementowi perkusyjne np. 35 to stopa (\textit{kick}), a 37 to werbel {\textit{snare}}. \subsubsection{Głośność} - Za głośność dźwęku odpowiada parametr \textit{velocity}, który jest liczbą z przedziału od 0 do 127. Im większa jest wartość tym głośniej wybrzmi dźwęk. + Za głośność dźwięku odpowiada parametr \textit{velocity}, który jest liczbą z przedziału od 0 do 127. Im większa jest wartość tym głośniej wybrzmi dźwięk. \subsubsection{Program} - Program w kontekscie standardu MIDI oznacza instrument który ma zagrać nuty. W standardzie GM (ang. General MIDI), jest 16 grup intrumenów a w każdej z nich znajduje się po 8 intrumentów. Są to piania, chromatyczne perkusje, organy, gitary, basy, intrumenty smyczkowe, zestawy intrumentów, intrumenty dmuchane blaszane, intrumenty dmuchane drewniane, flety, syntezatory prowadzące, syntezatory uzupełniające, efekty syntetyczne, instrumenty etniczne, perkusjonalia i efekty dzwiekowe. + Program w kontekście standardu MIDI oznacza instrument który ma zagrać nuty. W standardzie GM (ang. General MIDI), jest 16 grup instrumentów a w każdej z nich znajduje się po 8 instrumentów. Są to pianina, chromatyczne perkusje, organy, gitary, basy, instrumenty smyczkowe, zestawy instrumentów, instrumenty dmuchane blaszane, instrumenty dmuchane drewniane, flety, syntezatory prowadzące, syntezatory uzupełniające, efekty syntetyczne, instrumenty etniczne, perkusjonalia i efekty dźwiękowe. \subsubsection{Ścieżka} - Ścieżka (ang. Track) grupuje nuty aby podzielić utwór muzyczny na różne intrumenty lub partie. Protokół MIDI pozwala aby grać wiele ścieżek dzwiękowych jednocześnie, wtedy mówimy o muzyce polifonicznej lub multiintrumentalnej. + Ścieżka (ang. Track) grupuje nuty aby podzielić utwór muzyczny na różne instrumenty lub partie. Protokół MIDI pozwala aby grać wiele ścieżek dźwiękowych jednocześnie, wtedy mówimy o muzyce polifonicznej lub multiinstrumentalnej. \chapter{Projekt} - W tym rozdzialę opiszę w jaki sposób zbudowałem swój własny geneator muzyki, jak przechodził proces uczenia, jakie próbki udało mi się wygenrować. Opis kodu który napisałem. + W tym rozdziale opiszę w jaki sposób zbudowałem swój własny generator muzyki, jak przechodził proces uczenia, jakie próbki udało mi się wygenerować. Opis kodu który napisałem. \section{Koncepcja} - Celem tej pracy, było wykonanie modelu, który przy użyciu głębokiego uczenia będzie w stanie generować krótkie klipy multiinstrumentalne. Zainspirował mnie sposób w jaki tworzy się muzykę w zespole. W przeciwieństwie do muzyki tworzonej przez jednego kompozytora, w zespole każda partia tworzona jest przez muzyka grającego na danym instrumencie. Przykładowy sposób tworzenia utworu w zepole, np. rockowym wygląda jak następuje. Jedna osoba tworzy (generuje) pierwszą patrię muzyczną, np partię na gitary. Ta partia została stworzona bez odniesienia do innych członków zespołu. Następnie taka partia zostaje przedstawiona zespołowi. Każdy z członków zespołu musi teraz stworzyć swoje partie w taki sposób, aby pasowały one muzycznie do pierwszej partii. W ten sposób powstają nam zalezności między partiami, tworzącymi cały utwór. + Celem tej pracy, było wykonanie modelu, który przy użyciu głębokiego uczenia będzie w stanie generować krótkie klipy multiinstrumentalne. Zainspirował mnie sposób w jaki tworzy się muzykę w zespole. W przeciwieństwie do muzyki tworzonej przez jednego kompozytora, w zespole każda partia tworzona jest przez muzyka grającego na danym instrumencie. Przykładowy sposób tworzenia utworu w zespole, np. rockowym wygląda jak następuje. Jedna osoba tworzy (generuje) pierwszą partię muzyczną, np partię na gitary. Ta partia została stworzona bez odniesienia do innych członków zespołu. Następnie taka partia zostaje przedstawiona zespołowi. Każdy z członków zespołu musi teraz stworzyć swoje partie w taki sposób, aby pasowały one muzycznie do pierwszej partii. W ten sposób powstają nam zależności między partiami, tworzącymi cały utwór. - Na podstawie tej ideii postanowiłem opracować model składający się z wielu sieci nauronowych, każda z nich odpowiadać będzie jednej partii w utworze, muzykowi w zespole. Jedna z tych sieci będzie generatorem. Ta sieć powinna być skonstuowana w taki sposób aby zainicjować partię muzyczną. Pozostałe będą dopasowywać swoje partie w taki sposób aby pasowaly pod partię wygenerowaną. Te sieci nawywać bedę modelami akompaniującymi. Dzieki temu jesteśmy wstanie stworzyć model wielu sieci, w którym następna sieć, będzie produkować swoje partie na podstawie tego co wygenerowała poprzednia. + Na podstawie tej idei postanowiłem opracować model składający się z wielu sieci neuronowych, każda z nich odpowiadać będzie jednej partii w utworze, muzykowi w zespole. Jedna z tych sieci będzie generatorem. Ta sieć powinna być skonstruowana w taki sposób aby zainicjować partię muzyczną. Pozostałe będą dopasowywać swoje partie w taki sposób aby pasowały pod partię wygenerowaną. Te sieci nazywać będę modelami akompaniującymi. Dzięki temu jesteśmy wstanie stworzyć model wielu sieci, w którym następna sieć będzie produkować swoje partie na podstawie tego co wygenerowała poprzednia. - Kluczone było zauważenie podobieństwa między językiem naturalnym oraz muzyką. Zarówno zdanie, jak i partia muzyczna składa się z sekwencji elementów rozmieszczonych w czasie. Elementy te są zależne od długoterminowego kontekstu, oraz od tego jaki element był ustawiony wcześniej. Dla języka naturalnego są to słowa, na muzyki są to nuty i akordy. Dodatkowo pomyslałem, że różne instrumenty można porównać do róznych języków świata. Wtedy, aby stworzyć melodię np. basu tak aby pasowała pod partę gitary, nalezy "przetłumaczyć" język gitary na język basu. Do tłumaczeń języka naturalnego wykorzystuje się modele sequence-to-sequence, dlatego postanowiłem w modelu generowania muzyki wykorzystać właśnie tą architekturę. Dodatkowo modele sequance-to-sequance mają tę cechę, że liczba elementów sekwencji wejściowej, może być inna niż liczba elementów sekwencji wyjściowej. Idealnie sprawdzi się w przypadku muzyki, ponieważ o długości trwania ścieżki muzycznej nie świadczy liczba nut, tylko suma ich wartości. + Kluczowe było zauważenie podobieństwa między językiem naturalnym oraz muzyką. Zarówno zdanie jak i partia muzyczna składa się z sekwencji elementów rozmieszczonych w czasie. Elementy te są zależne od długoterminowego kontekstu, oraz od tego jaki element był ustawiony wcześniej. Dla języka naturalnego są to słowa, dla muzyki są to nuty i akordy. Dodatkowo pomyślałem, że różne instrumenty można porównać do różnych języków świata. Wtedy aby stworzyć melodię, np. basu, tak aby pasowała pod partię gitary, należy "przetłumaczyć" język gitary na język basu. Do tłumaczeń języka naturalnego wykorzystuje się modele sequence-to-sequence, dlatego postanowiłem w modelu generowania muzyki wykorzystać właśnie tą architekturę. Dodatkowo modele sequence-to-sequence mają tę cechę, że liczba elementów sekwencji wejściowej może być inna niż liczba elementów sekwencji wyjściowej. Idealnie sprawdzi się w przypadku muzyki, ponieważ o długości trwania ścieżki muzycznej nie świadczy liczba nut tylko suma ich wartości. \section{Wstępne przygotowanie danych do treningu} - Aby móc przedstawić sieci neuronowej muzykę, aby mogła być ona przez niego zrozumiana nalezy zamienić ją na liczby, wektory i macierze. Istenieje wiele technik umożliwiających osiągnięcie tego celu. W mojej pracy wykorzystałem technikę o nazwie one-hot encoding. Enkodowanie One-Hot jest wykorzystywane w uczeniu maszynowym aby nadać liczbową wartość danych kategorycznych. Polega ona stworzeniu słownika, w ktorym każde słowo otrzyma swój unikatowy identyfikator, następnie zostanie utworzony wektor o wymiarze słów w słowniku, gdzie na pozycji odpowiadającej indeksowi słowa bedzie wartość 1 a na pozostałych bedzie watość zero \cite{onehot}. %\footnote{https://deepai.org/machine-learning-glossary-and-terms/one-hot-encoding 28 maja 2020 12:24} + Aby móc przedstawić sieci neuronowej muzykę, aby mogła być ona przez niego zrozumiana należy zamienić ją na liczby, wektory i macierze. Istnieje wiele technik umożliwiających osiągnięcie tego celu. W mojej pracy wykorzystałam technikę o nazwie one-hot encoding. Enkodowanie One-Hot jest wykorzystywane w uczeniu maszynowym aby nadać liczbową wartość danych kategorycznych. Polega ona stworzeniu słownika, w którym każde słowo otrzyma swój unikatowy identyfikator, następnie zostanie utworzony wektor o wymiarze słów w słowniku, gdzie na pozycji odpowiadającej indeksowi słowa będzie wartość 1 a na pozostałych będzie wartość zero \cite{onehot}. %\footnote{https://deepai.org/machine-learning-glossary-and-terms/one-hot-encoding 28 maja 2020 12:24} \subsection{Przykład działania One-Hot Encoding} - Weźmy sekwencję liter w słowie MATEMATYKA. Znajdźmy unikatowe elementy tej sekwencji, oraz nadajmy im unikatowy indentyfikator. Kolejność nie ma znaczenia. + Weźmy sekwencję liter w słowie MATEMATYKA. Znajdźmy unikatowe elementy tej sekwencji, oraz nadajmy im unikatowy identyfikator. Kolejność nie ma znaczenia. \begin{center} M - 0, @@ -745,7 +745,7 @@ note_on channel=0 note=60 velocity=0 time=0 K - 5. \end{center} - Kodując słowo MATEMATYKA, otrzymalibysmy macierz + Kodując słowo MATEMATYKA, otrzymalibyśmy macierz \[ \mathbb{\boldsymbol{ @@ -761,27 +761,27 @@ note_on channel=0 note=60 velocity=0 time=0 \subsection{Muzyczne "słowo"} - Na potrzeby dostosowania danych muzycznych do koncepcji słów w zdaniu, zakodowałem pojedyncze słowo muzyczne jako + Na potrzeby dostosowania danych muzycznych do koncepcji słów w zdaniu zakodowałem pojedyncze słowo muzyczne jako \[ ((zbiór wysokości), długość) \] - W ten sposób byłem w stanie zakodować podedyjcze nuty oraz akordy. + W ten sposób byłem w stanie zakodować pojedyńcze nuty i akordy. - Akord C-dur składojący się z dzwięków C, E i G o długości ósemki, zapisalibyśmy w następujący sposób. + Akord C-dur składający się z dźwięków C, E i G o długości ósemki, zapisaliśmy w następujący sposób. \[ ((60, 64, 67), 0.5) \] - W ten sposób jesteśmy wstanie kodować melodię w sekwencji słów muzycznych. Tak skonstruowane dane, mają niestety swoje negatywne aspekty. Nie da się w ten sposób zapisać partii, w której zostaje grana nowa nuta gdy poprzednia jeszcze powinna brzmieć. Nasz zapis zakłąda, że melodia, jest grana element po elemencie, i nowy element wymusza zakończenie poprzedniego. Nie przechowujemy również informacji o dynamice melodii (głośności). Rozszerzenie tego zapisu o informacje o głośności nie jest trudne i nie będzie wymagać przebudowania modelu, natomiast zwiększy liczbę możliwych "słów muzycznych" w słowniku i zwiększy złożoność obliczeniową. Zdecydowałem się na niewykorzystanie tych danych w generowaniu muzyki. + W ten sposób jesteśmy w stanie kodować melodię w sekwencji słów muzycznych. Tak skonstruowane dane mają niestety swoje negatywne aspekty. Nie da się w ten sposób zapisać partii, w której zostaje grana nowa nuta gdy poprzednia jeszcze powinna brzmieć. Nasz zapis zakłada, że melodia jest grana element po elemencie i nowy element wymusza zakończenie poprzedniego. Nie przechowujemy również informacji o dynamice melodii (głośności). Rozszerzenie tego zapisu o informacje o głośności nie jest trudne i nie będzie wymagać przebudowy modelu, natomiast zwiększy liczbę możliwych "słów muzycznych" w słowniku i zwiększy złożoność obliczeniową. Zdecydowałem się na niewykorzystanie tych danych w generowaniu muzyki. \subsection{Konwersja MIDI na sekwencje słów muzycznych} - Powrzechny sposób przechowywania muzyki symbolicznej w formie cyfrowej to pliki *.mid lub *.midi które przechowuja informację o potoku wiadomości protokołu MIDI. Aby odczytać wiadomości plików MIDI, wykorzystałem bibliotekę \pyth{pretty_midi}, która zawiera wiele funcji pozwalających na edycję plików MIDI. + Powszechny sposób przechowywania muzyki symbolicznej w formie cyfrowej to pliki *.mid lub *.midi które przechowują informację o potoku wiadomości protokołu MIDI. Aby odczytać wiadomości plików MIDI wykorzystałem bibliotekę \pyth{pretty_midi}, która zawiera wiele funkcji pozwalających na edycję plików MIDI. - Aby otworzyć pliki midi za pomocą bilbioteli \pyth{pretty_midi} należy skorzystać z poniższej skłądni. + Aby otworzyć pliki midi za pomocą biblioteki \pyth{pretty_midi}, należy skorzystać z poniższej składni. \begin{python} >>> import pretty_midi as pm @@ -801,7 +801,7 @@ note_on channel=0 note=60 velocity=0 time=0 ...] \end{python} - Dzięki bibliotece \pyth{pretty_midi}, plik midi został odczytany i przechwany w objecie \pyth{PrettyMIDI}. Ten objekt posiada atrybut \pyth{instruments}, który jest listą ścieżek pliku MIDI. Objekt ścieżki posiada atrubut \pyth{notes}, który jest listą nut tej ścieżki. Możemy zobaczyć, że biblioteka \pyth{pretty_midi} zamieniła potok sygnałów protokołu MIDI na konkretne nuty posiadajace parametry $start$, $end$, $pitch$ orac $velocity$. Aby otrzymać sekwencję danych w takim formacie w jakim potrzebujemy możemy zastosować na obiekcie \pyth{Instrument} poniższą funkcję. + Dzięki bibliotece \pyth{pretty_midi} plik midi został odczytany i przechowany w obiekcie \pyth{PrettyMIDI}. Ten obiekt posiada atrybut \pyth{instruments}, który jest listą ścieżek pliku MIDI. Obiekt ścieżki posiada atrybut \pyth{notes}, który jest listą nut tej ścieżki. Możemy zobaczyć, że biblioteka \pyth{pretty_midi} zamieniła potok sygnałów protokołu MIDI na konkretne nuty posiadające parametry $start$, $end$, $pitch$ orac $velocity$. Aby otrzymać sekwencję danych w takim formacie w jakim potrzebujemy możemy zastosować na obiekcie \pyth{Instrument} poniższą funkcję. \begin{python} def parse_pretty_midi_instrument(instrument, resolution, @@ -862,14 +862,14 @@ def parse_pretty_midi_instrument(instrument, resolution, \end{python} - Powyższa funkcja w zamienia wartości absolutne czasu, na wartości względne o ustalonej rozdzielczości przez plik MIDI. Dodatkowo zmniejsza szczegółowość, i zaokrągla czas zagrania nuty po szesnastki. Gdy w tym samym momencie, czyli jeśli kilka nut posiada tą samą wartość start, zostają dodane do jednego słowa muzycznego aby utworzyć akord. Pauzy są kodowane jako $-1$. Dodatkowo jeśli pauza trwa dłużej niż takt wtedy zostaje podzielona na mniejsze części o długości \pyth{max_rest_len}. Funkcja zwraca obiekt \pyth{SingleTrack}, który jest obiektem stworzonym aby poza nutami, przechowywać inne istotne informacje na temat ściezki, którą będą istotne w następnych częściach przetwarzania danych. Ostatecznie sekwencje słów muzycznych przechowane są w \pyth{notes}. + Powyższa funkcja w zamienia wartości absolutne czasu, na wartości względne o ustalonej rozdzielczości przez plik MIDI. Dodatkowo zmniejsza szczegółowość, i zaokrągla czas zagrania nuty po szesnastki. Gdy w tym samym momencie, czyli jeśli kilka nut posiada tą samą wartość start, zostają dodane do jednego słowa muzycznego aby utworzyć akord. Pauzy są kodowane jako $-1$. Dodatkowo jeśli pauza trwa dłużej niż takt wtedy zostaje podzielona na mniejsze części o długości \pyth{max_rest_len}. Funkcja zwraca obiekt \pyth{SingleTrack}, który jest obiektem stworzonym aby poza nutami, przechowywać inne istotne informacje na temat ścieżki, którą będą istotne w następnych częściach przetwarzania danych. Ostatecznie sekwencje słów muzycznych przechowane są w \pyth{notes}. \begin{python} >>> resolution = midi.resolution >>> time_to_tick = midi.time_to_tick ->>> intrument = melody +>>> instrument = melody ->>> single_track = parse_pretty_midi_instrument(intrument, +>>> single_track = parse_pretty_midi_instrument(instrument, resolution, time_to_tick, key_offset=0) >>> single_track.stream.notes @@ -890,21 +890,21 @@ resolution, time_to_tick, key_offset=0) \subsection{Inne aspekty przygotowania danych} - Po odczytaniu danych i konwersji je do pożądanego formatu dane należy oczyścić. W mojej pracy zastowowałem kilka operacji, w celu zwiększenia muzycznego sensu danych. + Po odczytaniu danych i konwersji je do pożądanego formatu dane należy oczyścić. W mojej pracy zastosowałem kilka operacji, w celu zwiększenia muzycznego sensu danych. \subsubsection{Unormowanie skali} - W muzyce istenieje pojęcie skali. Skala jest to zestaw nut, które dobrze ze sobą wspołgrają. Zostało to szerzej opiswane w podrozdziale~\ref{section:skala}. W uczeniu maszynowym powodouje to realny problem, ponieważ piosenki wykorzystują różne skale, i sieć neuronowa będzie preferować wybranie skali częściej używanej. Dodatkowo zmiana skali, nie zmienia drastycznie kontenku muzycznego utworu. Zmiana wysokości przyskich nut, bez zmiany ich względnych interwałów nazywana jest transpozycją. Aby rozwiązać ten problem zaleca się agmentację danych, do wszystkich mozliwych skal. W mojej pracy wykorzystalem jednak inne rozwiązanie. Zamiast rozszerzać zbiór danych, sprowadziłem wszystkie ścieżki muzyczne do jednej skali C. Dzięki temu model przyłoży większą uwagę na rozumienie wzajemnych relacji, zamiast uczyć się pojęcia tonacji skali \cite{survay}. + W muzyce istnieje pojęcie skali. Skala jest to zestaw nut, które dobrze ze sobą współgrają. Zostało to szerzej opisane w podrozdziale~\ref{section:skala}. W uczeniu maszynowym powoduje to realny problem, ponieważ piosenki wykorzystują różne skale i sieć neuronowa będzie preferować wybranie skali częściej używanej. Dodatkowo zmiana skali nie zmienia znacznie kontentu muzycznego utworu, tj. nawet po zmianie skali melodii człowiek dalej jest w stanie ją rozpoznać. Zmiana wysokości wszystkich nut bez zmiany ich względnych interwałów nazywana jest transpozycją. Aby rozwiązać ten problem zaleca się rozszerzenie danych, do wszystkich możliwych skal. W mojej pracy wykorzystałam jednak inne rozwiązanie. Zamiast rozszerzać zbiór danych sprowadziłem wszystkie ścieżki muzyczne do jednej skali C. Dzięki temu model przyłoży większą uwagę na rozumienie wzajemnych relacji, zamiast uczyć się pojęcia tonacji skali \cite{survay}. \subsubsection{Podział na takty} - Długie listy muzycznych słów zostały podzielone na takty (\textit{bars}), o odpowiedniej długości, domyslnie o długości 4, co odpowiada czterem ćwierćnutom. Dzięki temu utwór muzyczny zostanie podzielony na mniejsze sekwencje. Sekwencje te będą posidały różną liczbę elementów, ale będą tak samo długie, w kontekcie muzycznym. Głównym celem takie zabiegu, jest zapewnienie muzycznego sensu sekwenjom. Takt jest naturalnym dla muzyki podziałem dłuższegej pratii na mniejsze. + Długie listy muzycznych słów zostały podzielone na takty (\textit{bars}), o odpowiedniej długości, domyślnie o długości 4, co odpowiada czterem ćwierćnutom. Dzięki temu utwór muzyczny zostanie podzielony na mniejsze sekwencje. Sekwencje te będą posiadały różną liczbę elementów, ale będą tak samo długie, w kontekście muzycznym. Głównym celem takie zabiegu, jest zapewnienie muzycznego sensu sekwenjom. Takt jest naturalnym dla muzyki podziałem dłuższego partii na mniejsze. \subsection{Podział danych na dane wejściowe i wyjściowe} - Na podstawie przetworzonych danych, należy przygotować dane wejściowe $X$ i wyjściowe $Y$ dla sieci neurowonych, aby przeprowadzić proces uczenia. W tym celu będziemy rozważać pary sekwencji $(x, y)$, gdzie $x \in X$ i $y \in Y$. Każda senwencja zawierać bedzie omówione wcześniej słowa muzyczne. W przygotowanym przeze mnie modelu, występują dwa rodzaje sieci neuronowych, sieć generująca oraz sieć akompaniująca. + Na podstawie przetworzonych danych, należy przygotować dane wejściowe $X$ i wyjściowe $Y$ dla sieci neuronowych, aby przeprowadzić proces uczenia. W tym celu będziemy rozważać pary sekwencji $(x, y)$, gdzie $x \in X$ i $y \in Y$. Każda sekwencja zawierać będzie omówione wcześniej słowa muzyczne. W przygotowanym przeze mnie modelu, występują dwa rodzaje sieci neuronowych, sieć generująca oraz sieć akompaniująca. \subsubsection{Przygotowanie danych dla generatora} - Model generatywny będzie tworzył partie muzyczne, na podstawie poprzeprzednich sekwencji tego samego intrumentu. Weźmy parię muzyczną $G$, która jest uporządkowaną listą elementów $g$ w czasie. Każdy element $g$ jest taktem składających sie ze słów muzycznych. + Model generatywny będzie tworzył partie muzyczne, na podstawie poprzednich sekwencji tego samego instrumentu. Weźmy partię muzyczną $G$, która jest uporządkowaną listą elementów $g$ w czasie. Każdy element $g$ jest taktem składających się ze słów muzycznych. \[ G = \left[g_1, g_2, g_n \right], \] @@ -917,14 +917,14 @@ resolution, time_to_tick, key_offset=0) \] dla $t \in (1, n-1)$. - Dzięki takiemu zdefiniowaniu danych uczacych generator będzie uczył sie jak powinien wyglądać następny takt, na podstawie poprzedniego. W ten sposób będziemy wstanie wykorzystać model, do generowania muzyki bez danych wejściowych. Wątek zostanie rozwinięty w dalejszej części pracy. + Dzięki takiemu zdefiniowaniu danych uczących generator będzie uczył się jak powinien wyglądać następny takt, na podstawie poprzedniego. W ten sposób będziemy w stanie wykorzystać model, do generowania muzyki bez danych wejściowych. Wątek zostanie rozwinięty w dalszej części pracy. Implementacja w pythonie: \begin{python} def get_data_seq2seq_melody(self, instrument_class, x_seq_len=4): '''return a list of bars with content for every track - with given instrument class for melody generaiton + with given instrument class for melody generation x_seq_len and y_seq_len x previous sentence, y next sentence of the same melody line @@ -954,7 +954,7 @@ def get_data_seq2seq_melody(self, instrument_class, return x_seq, y_seq \end{python} - \subsubsection{Przygotowanie danych dla akomaniamentu} + \subsubsection{Przygotowanie danych dla akompaniamentu} Model akompaniujący natomiast, będzie na podstawie partii jednego tworzyć partię na nowy instrument, dla tego samego kroku czasu. Niech $G, B$ będą sekcjami muzycznymi różnych instrumentów tej samej długości oraz niech @@ -964,7 +964,7 @@ def get_data_seq2seq_melody(self, instrument_class, B = \left[b_1, b_2, ..., b_k \right], \end{array} \] - wówczas pary dla zbioru uczącego tworzymy w nastęujący sposób + wówczas pary dla zbioru uczącego tworzymy w następujący sposób \[ \begin{array}{c} @@ -980,10 +980,10 @@ def get_data_seq2seq_melody(self, instrument_class, \begin{python} def get_data_seq2seq_arrangment(self, x_instrument, y_instrument, bars_in_seq=4): - '''this method is returning a sequances of given lenth - by rolling this lists of x and y for arrangemt generation - x and y has the same bar lenth, and represent the - same musical phrase played mb difrent instruments (tracks) + '''this method is returning a sequences of given length + by rolling this lists of x and y for arrangement generation + x and y has the same bar length, and represent the + same musical phrase played mb different instruments (tracks) ''' x_seq = [] @@ -1006,16 +1006,16 @@ def get_data_seq2seq_arrangment(self, x_instrument, \end{python} -\subsection{Inne apekty przygotowania zbioru uczącego} +\subsection{Inne aspekty przygotowania zbioru uczącego} \subsubsection{Oczyszczenie danych} W przygotowaniu danych dla modelu, ważne jest aby dostarczone dane były jak najlepszej jakości. W tym celu zastosowałem jeszcze deduplikację par $(x, y)$ oraz usunąłem takty które nie zawierały muzycznego kontentu. - \subsubsection{Wybór programu dla intrumentu} - Podczas etapu ekstracji danych z plików MIDI poza informacjami o muzyce, zapamiętuję również informacje o programie partii muzycznej. Każda ścieżka MIDI przechowuje informacje o intrumencie (brzmieniu) danej partii. Istenieje 128 rówznych programów, dla zmniejszenia szczegółwości na potrzeby modelu wyróżniam 16 intrumentów zgodnie z grupą do jakiej należą w podziale General MIDI. Dla każdej z grup, sprawdzam jaki program został najczęściej wykorzystywany i zapisuję go na przyszłość, aby móc wygenrowanej muzyce przy kompilacji do MIDI zdefiniować brzmienie intrumentu zgodnie z najczęściej wykorzystywanym w zbiorze MIDI, który został wykorzystany do stworzenia zbioru uczacego dla modelu. + \subsubsection{Wybór programu dla instrumentu} + Podczas etapu ekstrakcji danych z plików MIDI poza informacjami o muzyce, zapamiętuję również informacje o programie partii muzycznej. Każda ścieżka MIDI przechowuje informacje o instrumencie (brzmieniu) danej partii. Istnieje 128 różnych programów, dla zmniejszenia szczególności na potrzeby modelu wyróżniam 16 instrumentów zgodnie z grupą do jakiej należą w podziale General MIDI. Dla każdej z grup, sprawdzam jaki program został najczęściej wykorzystywany i zapisuję go na przyszłość, aby móc wygenerowanej muzyce przy kompilacji do MIDI zdefiniować brzmienie instrumentu zgodnie z najczęściej wykorzystywanym w zbiorze MIDI, który został wykorzystany do stworzenia zbioru uczącego dla modelu. \subsubsection{Melodia} - Dodatkowym elementem procesu ektracji danych jest znaleniezie ścieżek melodii przewodnich w plikach MIDI. Ścieżki tego typu zamiast być oznaczone nazwą grupy intrumentów do której należą oznaczone są nazwą \pyth{Melody}. Melodia jest kategorią ścieżek z podziału ze względu na rolę partii w utworze, zamiast na intrument. Istnieją też inne role intrumentów, jednak często rola jest w pewnym sensie definiowana przez instrument. Nie jest to zasada, bardziej prawidłowość w muzyce. Uznazłem że wydobycie ten informacji na temat ścieżki nada więcej muzycznego sensu danym. + Dodatkowym elementem procesu ekstrakcji danych jest znalezienie ścieżek melodii przewodnich w plikach MIDI. Ścieżki tego typu zamiast być oznaczone nazwą grupy instrumentów do której należą oznaczone są nazwą \pyth{Melody}. Melodia jest kategorią ścieżek z podziału ze względu na rolę partii w utworze, zamiast na instrument. Istnieją też inne role instrumentów, jednak często rola jest w pewnym sensie definiowana przez instrument. Nie jest to zasada, bardziej prawidłowość w muzyce. Uznałem że wydobycie ten informacji na temat ścieżki nada więcej muzycznego sensu danym. Aby sprawdzić czy dana ścieżka jest melodią, zastosowałem poniższą funkcję: \begin{python} @@ -1023,7 +1023,7 @@ def check_if_melody(self): '''checks if Track object could be a melody it checks if percentage of single notes in - Track.stream.notes is higher than treshold + Track.stream.notes is higher than threshold of 90 and there is at least 2 notes in bar per average ''' @@ -1057,9 +1057,9 @@ else: return False \end{python} -Funkcja sprawdza liczbę pojedynczych nut i akordów w ścieżce, oraz zagęszczenie nut w takcie. Jeśli jest więcej niż 90 pojedynczych nut w ścieżce oraz jest średnio więcej nut w takcie niż dwie, wtedy uznaję że partia intrumentalna utworu jest melodią. +Funkcja sprawdza liczbę pojedynczych nut i akordów w ścieżce, oraz zagęszczenie nut w takcie. Jeśli jest więcej niż 90 pojedynczych nut w ścieżce oraz jest średnio więcej nut w takcie niż dwie, wtedy uznaję że partia instrumentalna utworu jest melodią. - \section{Tranformacja danych dla modelu} + \section{Transformacja danych dla modelu} @@ -1078,7 +1078,7 @@ Funkcja sprawdza liczbę pojedynczych nut i akordów w ścieżce, oraz zagęszcz \chapter{Podsumowanie} - Ostateczne wnioski, czy muzyka generowana komputerowa da się lubić? Czy to pozytywnie wpłynie na przemysł muzyczny? Tak i nie. Może złużyć jako inspiracja dla muzyków, proces wspierający. Z drugiej strony może obnizy koszty produkowania muzyki pop, która i tak jest już bardzo powtarzalna. Czy sieci neuronowe nauczą się produkować Hity? + Ostateczne wnioski, czy muzyka generowana komputerowa da się lubić? Czy to pozytywnie wpłynie na przemysł muzyczny? Tak i nie. Może służyć jako inspiracja dla muzyków, proces wspierający. Z drugiej strony może obniży koszty produkowania muzyki pop, która i tak jest już bardzo powtarzalna. Czy sieci neuronowe nauczą się produkować Hity? \begin{thebibliography}{99} @@ -1120,3 +1120,5 @@ Funkcja sprawdza liczbę pojedynczych nut i akordów w ścieżce, oraz zagęszcz \printindex \end{document} + + diff --git a/docs/document.toc b/docs/document.toc index 138e45e..ca2c6fd 100644 --- a/docs/document.toc +++ b/docs/document.toc @@ -1,41 +1,41 @@ \contentsline {chapter}{Streszczenie}{7}% \contentsline {chapter}{Abstract}{9}% -\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 }Wielowarstwowe sieci neuronowe}{19}% -\contentsline {subsection}{\numberline {1.5.1\relax .\leavevmode@ifvmode \kern .5em }Jednokierunkowe sieci neuronowe}{20}% -\contentsline {subsection}{\numberline {1.5.2\relax .\leavevmode@ifvmode \kern .5em }Autoencodery}{21}% -\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 }Sequence-to-sequence}{25}% -\contentsline {chapter}{Rozdzia\PlPrIeC {\l }\ 2\relax .\leavevmode@ifvmode \kern .5em Wprowadzenie do teorii muzyki}{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}{31}% -\contentsline {subsection}{\numberline {2.2.1\relax .\leavevmode@ifvmode \kern .5em }Standard MIDI}{31}% -\contentsline {chapter}{Rozdzia\PlPrIeC {\l }\ 3\relax .\leavevmode@ifvmode \kern .5em Projekt}{33}% -\contentsline {section}{\numberline {3.1\relax .\leavevmode@ifvmode \kern .5em }Koncepcja}{33}% -\contentsline {section}{\numberline {3.2\relax .\leavevmode@ifvmode \kern .5em }Wst\IeC {\k e}pne przygotowanie danych do treningu}{34}% -\contentsline {subsection}{\numberline {3.2.1\relax .\leavevmode@ifvmode \kern .5em }Przyk\IeC {\l }ad dzia\IeC {\l }ania One-Hot Encoding}{34}% -\contentsline {subsection}{\numberline {3.2.2\relax .\leavevmode@ifvmode \kern .5em }Muzyczne "s\IeC {\l }owo"}{34}% -\contentsline {subsection}{\numberline {3.2.3\relax .\leavevmode@ifvmode \kern .5em }Konwersja MIDI na sekwencje s\IeC {\l }\IeC {\'o}w muzycznych}{35}% -\contentsline {subsection}{\numberline {3.2.4\relax .\leavevmode@ifvmode \kern .5em }Inne aspekty przygotowania danych}{38}% -\contentsline {subsection}{\numberline {3.2.5\relax .\leavevmode@ifvmode \kern .5em }Podzia\IeC {\l } danych na dane wej\IeC {\'s}ciowe i wyj\IeC {\'s}ciowe}{38}% -\contentsline {subsection}{\numberline {3.2.6\relax .\leavevmode@ifvmode \kern .5em }Inne apekty przygotowania zbioru ucz\IeC {\k a}cego}{41}% -\contentsline {section}{\numberline {3.3\relax .\leavevmode@ifvmode \kern .5em }Tranformacja danych dla modelu}{43}% -\contentsline {section}{\numberline {3.4\relax .\leavevmode@ifvmode \kern .5em }Definicja modelu}{43}% -\contentsline {section}{\numberline {3.5\relax .\leavevmode@ifvmode \kern .5em }Uczenie modelu}{43}% -\contentsline {section}{\numberline {3.6\relax .\leavevmode@ifvmode \kern .5em }Generowanie muzyki przy pomocy wytrenowanego modelu}{43}% -\contentsline {section}{\numberline {3.7\relax .\leavevmode@ifvmode \kern .5em }Wyniki}{43}% -\contentsline {section}{\numberline {3.8\relax .\leavevmode@ifvmode \kern .5em }Wnioski}{43}% -\contentsline {chapter}{Rozdzia\PlPrIeC {\l }\ 4\relax .\leavevmode@ifvmode \kern .5em Podsumowanie}{45}% +\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 }Wielowarstwowe sieci neuronowe}{19}% +\contentsline {subsection}{\numberline {1.5.1\relax .\enspace }Jednokierunkowe sieci neuronowe}{20}% +\contentsline {subsection}{\numberline {1.5.2\relax .\enspace }Autoencoder}{21}% +\contentsline {subsection}{\numberline {1.5.3\relax .\enspace }Rekurencyjne sieci neuronowe}{22}% +\contentsline {subsection}{\numberline {1.5.4\relax .\enspace }LSTM}{23}% +\contentsline {subsection}{\numberline {1.5.5\relax .\enspace }Sequence-to-sequence}{25}% +\contentsline {chapter}{Rozdzia\PlPrIeC {\l }\ 2\relax .\enspace Wprowadzenie do teorii muzyki}{27}% +\contentsline {section}{\numberline {2.1\relax .\enspace }Podstawowe koncepcje}{27}% +\contentsline {subsection}{\numberline {2.1.1\relax .\enspace }Dźwięk muzyczny}{27}% +\contentsline {subsection}{\numberline {2.1.2\relax .\enspace }Sygnał dźwiękowy}{27}% +\contentsline {subsection}{\numberline {2.1.3\relax .\enspace }Zapis nutowy}{27}% +\contentsline {section}{\numberline {2.2\relax .\enspace }Cyfrowa reprezentacja muzyki symbolicznej}{31}% +\contentsline {subsection}{\numberline {2.2.1\relax .\enspace }Standard MIDI}{31}% +\contentsline {chapter}{Rozdzia\PlPrIeC {\l }\ 3\relax .\enspace Projekt}{33}% +\contentsline {section}{\numberline {3.1\relax .\enspace }Koncepcja}{33}% +\contentsline {section}{\numberline {3.2\relax .\enspace }Wstępne przygotowanie danych do treningu}{34}% +\contentsline {subsection}{\numberline {3.2.1\relax .\enspace }Przykład działania One-Hot Encoding}{34}% +\contentsline {subsection}{\numberline {3.2.2\relax .\enspace }Muzyczne "słowo"}{34}% +\contentsline {subsection}{\numberline {3.2.3\relax .\enspace }Konwersja MIDI na sekwencje słów muzycznych}{35}% +\contentsline {subsection}{\numberline {3.2.4\relax .\enspace }Inne aspekty przygotowania danych}{38}% +\contentsline {subsection}{\numberline {3.2.5\relax .\enspace }Podział danych na dane wejściowe i wyjściowe}{38}% +\contentsline {subsection}{\numberline {3.2.6\relax .\enspace }Inne aspekty przygotowania zbioru uczącego}{41}% +\contentsline {section}{\numberline {3.3\relax .\enspace }Transformacja danych dla modelu}{43}% +\contentsline {section}{\numberline {3.4\relax .\enspace }Definicja modelu}{43}% +\contentsline {section}{\numberline {3.5\relax .\enspace }Uczenie modelu}{43}% +\contentsline {section}{\numberline {3.6\relax .\enspace }Generowanie muzyki przy pomocy wytrenowanego modelu}{43}% +\contentsline {section}{\numberline {3.7\relax .\enspace }Wyniki}{43}% +\contentsline {section}{\numberline {3.8\relax .\enspace }Wnioski}{43}% +\contentsline {chapter}{Rozdzia\PlPrIeC {\l }\ 4\relax .\enspace Podsumowanie}{45}% \contentsline {chapter}{Bibliografia}{47}% diff --git a/docs/sources/Learning TensorFlow A Guide to Building Deep Learning Systems by Tom Hope, Yehezkel S. Resheff, and Itay Lieder (z-lib.org).pdf b/docs/sources/Learning TensorFlow A Guide to Building Deep Learning Systems by Tom Hope, Yehezkel S. 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