From 9bdbd12c7e75f5ed50d0fec881d01a69ac7e816c Mon Sep 17 00:00:00 2001 From: Cezary Pukownik Date: Fri, 19 Jun 2020 12:46:47 +0200 Subject: [PATCH] =?UTF-8?q?Poprawiono=20przecinki,=20liter=C3=B3wki,=20b?= =?UTF-8?q?=C5=82=C4=99dy=20j=C4=99zykowe=20i=20niezrozumia=C5=82e=20fragm?= =?UTF-8?q?entu,=20ta=20wersja=20pracy=20zosta=C5=82a=20wys=C5=82ana=20do?= =?UTF-8?q?=20Promotora?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- ...uzyki przy pomocy gÅ‚Ä™bokiego uczenia.pdf | Bin 0 -> 1241654 bytes docs/document.aux | 82 ++++--- docs/document.fdb_latexmk | 29 +-- docs/document.fls | 3 + docs/document.log | 227 +++++++++--------- docs/document.pdf | Bin 1199932 -> 1241654 bytes docs/document.synctex.gz | Bin 545896 -> 548209 bytes docs/document.tex | 204 +++++++++------- docs/document.toc | 50 ++-- docs/images/general-midi.png | Bin 0 -> 39913 bytes 10 files changed, 310 insertions(+), 285 deletions(-) create mode 100644 docs/Pukownik C. - 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W teorii należaÅ‚oby zatem wybrać takÄ… funkcjÄ™ kosztu, aby byÅ‚a różniczkowalna. RozwiÄ…zać równanie $J_\theta'(h)=0$, nastÄ™pnie dla otrzymanych wyników sprawdzić powyższÄ… nierówność oraz wybrać najmniejszy wynik ze wszystkich \cite{analiza_mat}. W praktyce rozwiÄ…zanie takiego równania ze wzglÄ™du na jego zÅ‚ożoność może siÄ™ okazać niewykonalne. Aby rozwiÄ…zać ten problem powstaÅ‚y inne metody, które pozwalajÄ… szukać ekstremów funkcji, jednak nigdy nie bÄ™dziemy mieli pewnoÅ›ci, że otrzymany wynik jest minimum globalnym funkcji kosztu. @@ -292,10 +293,10 @@ The rest of this chapter discusses an example of using the proposed model to gen NastÄ™pnie policzyć wszystkie pochodne częściowe $\frac{\partial J_\theta(h)}{\partial \theta_i}$. Otrzymamy w ten sposób gradient $\nabla J_\theta(h)$, gdzie \[ - \nabla J_\theta(h) = \left[ \frac{\partial J_\theta(h)}{\partial \theta_1}, \frac{\partial J_\theta(h)}{\partial \theta_2}, ... , \frac{\partial J_\theta(h)}{\partial \theta_p} \right]. + \nabla J_\theta(h) = \left[ \frac{\partial J_\theta(h)}{\partial \theta_1}, \frac{\partial J_\theta(h)}{\partial \theta_2}, ... , \frac{\partial J_\theta(h)}{\partial \theta_p} \right], \] - NastÄ™pnie obliczyć element $\Theta_{k+1}$ ze wzoru + wtedy można obliczyć element $\Theta_{k+1}$ ze wzoru \[ \Theta_{k+1} = \Theta_{k} - \alpha\nabla J_\theta(h), @@ -453,7 +454,7 @@ The rest of this chapter discusses an example of using the proposed model to gen Podczas uczenia autoenkodera przedstawia siÄ™ dane wejÅ›ciowe jako cel. W ten sposób ta architektura stara siÄ™ odtworzyć funkcje identycznoÅ›ciowe. Zadanie nie jest trywialne jak mogÅ‚oby siÄ™ zdawać, ponieważ zazwyczaj ukryta warstwa jest mniejszego rozmiaru niż dane wejÅ›ciowe. Z tego wzglÄ™du autoenkoder jest zmuszony do wydobycia istotnych cech danych wejÅ›ciowych, skompresowania, a nastÄ™pnie jak najwierniejszego ich odtworzenia. Część kompresujÄ…ca dane nazywana jest enkoderem, natomiast część dekompresujÄ…ca dekoderem. Cechy, które zostaÅ‚y odkryte przez autoenkoder nazywane sÄ… zmiennymi utajnionymi (\textit{ang. latent variables}). Zarówno encoder jak i dekoder można wyodrÄ™bnić z autoenkodera i wykorzystywać go jako osobnÄ… sieć neuronowÄ…. - CiekawÄ… cechÄ… dekodera jest jego generatywny charakter, ponieważ dostarczajÄ…c zupeÅ‚nie nowe informacje jako zmienne wejÅ›ciowe, dekoder otworzy je na podobieÅ„stwo danych, na których zostaÅ‚ nauczony. + CiekawÄ… cechÄ… dekodera jest jego generatywny charakter, ponieważ dostarczajÄ…c zupeÅ‚nie nowe informacje jako zmienne wejÅ›ciowe, dekoder otworzy je na podobieÅ„stwo danych na, których zostaÅ‚ nauczony. \subsection{Rekurencyjne sieci neuronowe} \label{section:rnn} @@ -490,7 +491,7 @@ The rest of this chapter discusses an example of using the proposed model to gen \label{fig:lstm} \end{figure} - Główny pomysÅ‚ na funkcjonowanie komórek LSTM byÅ‚ taki, aby sieć sama mogÅ‚a siÄ™ nauczyć jakie informacje sÄ… istotne i je przechować, a które informacje można pominąć, zapomnieć. Schemat komórki LSTM przedstawiono na rysunku~\ref{fig:lstm}. Aby to osiÄ…gnąć powstaÅ‚a idea bramek (\textit{ang. gates}) oraz kontrolerów bramek (\textit{ang. gate controllers}). W komórce LSTM wyróżniamy trzy bramki. BramkÄ™ zapomnienia (\textit{ang. forget gate}) sterowanÄ… przez $f_{(t)}$, bramkÄ™ wejÅ›ciowÄ…(\textit{ang. input gate}) sterowanÄ… przez $i_{(t)}$ oraz bramkÄ™ wyjÅ›ciowÄ… (\textit{ang. output gate}), sterowanÄ… przez $o_{(t)}$. PrzepÅ‚yw danych w komórce LSTM zaczyna w miejscu, gdzie wektor wejÅ›ciowy $x_{(t)}$ i poprzedni krótkoterminowy stan $h_{(t-1)}$ trafiajÄ… do czterech warstw. GłównÄ… warstwÄ… jest ta zwracajÄ…ca $g_{(t)}$. W podstawowej komórce RNN jest tylko ta warstwa. PozostaÅ‚e trzy warstwy po przejÅ›ciu przez funkcje logistyczne trafiajÄ… do bramek. Bramka zapomnienia kontroluje, które informacje z dÅ‚ugookresowego stanu $c_{(t-1)}$ powinny zostać wykasowane. Bramka wejÅ›ciowa kontroluje jakie informacje z $g_{(t)}$ powinny zostać przekazane dalej i dodane do nastÄ™pnego stanu dÅ‚ugookresowego $c_{(t)}$. Bramka wyjÅ›ciowa odpowiada za wybranie odpowiednich elementów z stanu dÅ‚ugookresowego i przekazanie ich nastÄ™pnych kroku. Wynik komórki zostaje przekazany do wyjÅ›cia komórki $y_{(t)}$ oraz jako nastÄ™pny stan krótkoterminowy $h_{(t)}$. + Główny pomysÅ‚ na funkcjonowanie komórek LSTM byÅ‚ taki, aby sieć sama mogÅ‚a siÄ™ nauczyć jakie informacje sÄ… istotne i je przechować, a które informacje można pominąć, zapomnieć. Schemat komórki LSTM przedstawiono na rysunku~\ref{fig:lstm}. Aby to osiÄ…gnąć powstaÅ‚a idea bramek (\textit{ang. gates}) oraz kontrolerów bramek (\textit{ang. gate controllers}). W komórce LSTM wyróżniamy trzy bramki. BramkÄ™ zapomnienia (\textit{ang. forget gate}) sterowanÄ… przez $f_{(t)}$, bramkÄ™ wejÅ›ciowÄ… (\textit{ang. input gate}) sterowanÄ… przez $i_{(t)}$ oraz bramkÄ™ wyjÅ›ciowÄ… (\textit{ang. output gate}) sterowanÄ… przez $o_{(t)}$. PrzepÅ‚yw danych w komórce LSTM zaczyna w miejscu, gdzie wektor wejÅ›ciowy $x_{(t)}$ i poprzedni krótkoterminowy stan $h_{(t-1)}$ trafiajÄ… do czterech warstw. GłównÄ… warstwÄ… jest ta zwracajÄ…ca $g_{(t)}$. W podstawowej komórce RNN jest tylko ta warstwa. PozostaÅ‚e trzy warstwy po przejÅ›ciu przez funkcje logistyczne trafiajÄ… do bramek. Bramka zapomnienia kontroluje, które informacje z dÅ‚ugookresowego stanu $c_{(t-1)}$ powinny zostać wykasowane. Bramka wejÅ›ciowa kontroluje jakie informacje z $g_{(t)}$ powinny zostać przekazane dalej i dodane do nastÄ™pnego stanu dÅ‚ugookresowego $c_{(t)}$. Bramka wyjÅ›ciowa odpowiada za wybranie odpowiednich elementów z stanu dÅ‚ugookresowego i przekazanie ich nastÄ™pnych kroku. Wynik komórki zostaje przekazany do wyjÅ›cia komórki $y_{(t)}$ oraz jako nastÄ™pny stan krótkoterminowy $h_{(t)}$. Kolejne etapy komórki LSTM obliczane sÄ… zgodnie z poniższymi wzorami: \[ @@ -535,7 +536,7 @@ The rest of this chapter discusses an example of using the proposed model to gen %-model-679e04af4346 26.05.2020 14:58} Model sequence-to-sequence ma dwie części, enkoder i dekoder. Obie części sÄ… w zasadzie dwiema zupeÅ‚nie osobnymi modelami, poÅ‚Ä…czonymi ze sobÄ… w jednÄ… sieć. Schemat modelu sequence-to-sequence przedstawiono na rysunku~\ref{fig:seq2seq}. - Zadaniem enkodera, podobnie jak zostaÅ‚o to opisane w rozdziale~\ref{section:autoencoder} o autoenkoderze, jest wydobycie z wektora wejÅ›ciowego najistotniejszych informacji i skompresowanie ich. NastÄ™pnie wektor stanu enkodera jest przekazywany do dekodera, który + Zadaniem enkodera jest wydobycie z wektora wejÅ›ciowego najistotniejszych informacji i skompresowanie ich tak jak zostaÅ‚o to opisane w rozdziale~\ref{section:autoencoder}. NastÄ™pnie wektor stanu enkodera jest przekazywany do dekodera, który na jego podstawie rekonstruuje sekwencjÄ™. \begin{figure}[!htb] @@ -576,7 +577,7 @@ The rest of this chapter discusses an example of using the proposed model to gen \subsection{SygnaÅ‚ dźwiÄ™kowy} - W rzeczywistoÅ›ci utwór muzyczny jest zazwyczaj kombinacjÄ… wielu fal dźwiÄ™kowych, o różnych charakterystykach i nazywany jest sygnaÅ‚em dźwiÄ™kowym. WizualizacjÄ™ sygnaÅ‚u dźwiÄ™kowego przedstawiono na Rysunku~\ref{fig:waveform} + W rzeczywistoÅ›ci utwór muzyczny jest zazwyczaj kombinacjÄ… wielu fal dźwiÄ™kowych o różnych charakterystykach i nazywany jest sygnaÅ‚em dźwiÄ™kowym. WizualizacjÄ™ sygnaÅ‚u dźwiÄ™kowego przedstawiono na Rysunku~\ref{fig:waveform} \begin{figure}[!htb] \centering @@ -587,7 +588,7 @@ The rest of this chapter discusses an example of using the proposed model to gen \subsection{Zapis nutowy} - Reprezentacja muzyki jako sygnaÅ‚u dźwiÄ™kowego przechowuje informacje o dokÅ‚adnym brzmieniu danego utworu tzn. jakie drgania należy wytworzyć, aby móc odtworzyć muzykÄ™. Taki zapis nie informuje nas bezpoÅ›rednio jakie instrumenty zostaÅ‚y użyte, jakie wysokoÅ›ci i dÅ‚ugoÅ›ci dźwiÄ™ków zostaÅ‚y wykorzystane. Dlatego ludzkość na przestrzeni wieków opracowaÅ‚a abstrakcyjne obiekty, które reprezentujÄ… utwór w czytelny dla czÅ‚owieka sposób. + Reprezentacja muzyki jako sygnaÅ‚u dźwiÄ™kowego przechowuje informacje o dokÅ‚adnym brzmieniu danego utworu tzn. jakie drgania należy wytworzyć, aby móc odtworzyć muzykÄ™. Taki zapis nie informuje nas o instrumentach, które zostaÅ‚y użyte ani jakie wysokoÅ›ci i dÅ‚ugoÅ›ci dźwiÄ™ków zostaÅ‚y zagrane. Dlatego ludzkość na przestrzeni wieków opracowaÅ‚a abstrakcyjne obiekty, które reprezentujÄ… utwór w czytelny dla czÅ‚owieka sposób. \subsubsection{Tempo} W muzyce symbolicznej tempo informuje nas o prÄ™dkoÅ›ci utworu. W muzyce klasycznej stosowaÅ‚o siÄ™ opisowy sposób dostosowywania tempa np. Allegro - Szybko lub Adagio - wolno. Jak można szybko stwierdzić sÄ… to zwroty subiektywne i nie wyznaczajÄ… tempa jednoznacznie. Obecnie wyraża siÄ™ tempo w liczbie uderzeÅ„ na minutÄ™ (\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/ @@ -608,7 +609,8 @@ The rest of this chapter discusses an example of using the proposed model to gen \newline 5 kwietnia 2020 12:46} - Tak jak pisaÅ‚em wczeÅ›niej, wysokość dźwiÄ™ku jest to czÄ™stotliwość drgaÅ„ fali dźwiÄ™kowej wyrażona w hercach. W muzyce symbolicznej dla uproszczenia wybrane czÄ™stotliwoÅ›ci zostaÅ‚y nazwane literami alfabetu C, D, E, F, G, A, H. + Tak jak pisaÅ‚em wczeÅ›niej wysokość dźwiÄ™ku jest to czÄ™stotliwość drgaÅ„ fali dźwiÄ™kowej wyrażona w hercach. Obecnie używa siÄ™ systemu równomiernie temperowanego, który wyróżnia 12 dzwiÄ™ków równo od siebie oddzielonych. SÄ… to dzwiÄ™ki C, C\#/D$\flat$, D, D\#/E$\flat$, E, F, F\#/G$\flat$, G, G\#/A$\flat$, A, A\#/B oraz H. + Każdej literze przypisana jest czÄ™stotliwość zgodnie z TabelÄ…~\ref{table:dzwieki} \begin{table}[!htb] @@ -649,7 +651,7 @@ The rest of this chapter discusses an example of using the proposed model to gen \footnotetext{https://amplitudaschool.weebly.com/lekcja-11.html 5 kwietnia 2020 13:24} \subsubsection{InterwaÅ‚} - O interwaÅ‚ach mówimy, kiedy porównujemy ze sobÄ… dwie nuty. InterwaÅ‚ jest to odlegÅ‚ość miÄ™dzy nutami, liczona w półnutach. Półnuta jest to najmniejsza odlegÅ‚ość miÄ™dzy nutami we współczesnej notacji muzycznej. Oktawa jest podzielona na 12 równych części. PomiÄ™dzy dźwiÄ™kami C i D jest odlegÅ‚ość + O interwaÅ‚ach mówimy kiedy porównujemy ze sobÄ… dwie nuty. InterwaÅ‚ jest to odlegÅ‚ość miÄ™dzy nutami liczona w półnutach. Półnuta jest to najmniejsza odlegÅ‚ość miÄ™dzy nutami we współczesnej notacji muzycznej. Oktawa jest podzielona na 12 równych części. PomiÄ™dzy dźwiÄ™kami C i D jest odlegÅ‚ość dwóch półnut, natomiast miÄ™dzy F oraz F\# jest odlegÅ‚ość jednej półnuty. Dla ludzkiego ucha w celu rozpoznania melodii istotniejsze sÄ… interwaÅ‚y miÄ™dzy kolejnymi nutami niż konkretna wysokość dźwiÄ™ków. \subsubsection{Oktawa} @@ -657,11 +659,10 @@ The rest of this chapter discusses an example of using the proposed model to gen OktawÄ… nazywamy zestaw oÅ›miu nut od C do H. Podane w Tabeli~\ref{table:dzwieki} czÄ™stotliwoÅ›ci nut odpowiadajÄ… dźwiÄ™kom w oktawie czwartej. Dlatego w indeksie dolnym nuty widnieje liczba 4. Aby utworzyć dźwiÄ™k, np. $A_5$ należy pomnożyć czÄ™stotliwość dźwiÄ™ku $A_4$ razy dwa natomiast, aby utworzyć dźwiÄ™k $A_3$, należy tÄ™ czÄ™stotliwość podzielić przez dwa. \begin{center} - $A_5$ = 2 * 440Hz = 880Hz \\ - $A_3$ = 1/2 * 440Hz = 220Hz + $A_5$ = 2 * 440Hz = 880Hz, \\ + $A_3$ = 1/2 * 440Hz = 220Hz. \end{center} - W ten sposób możemy stworzyć nieskoÅ„czenie wiele oktaw, jednak w rzeczywistoÅ›ci używa siÄ™ nut od C0 do C8. \subsubsection{Akord} @@ -669,7 +670,14 @@ The rest of this chapter discusses an example of using the proposed model to gen \subsubsection{Skala} \label{section:skala} - Skala jest to zestaw nut, które dobrze ze sobÄ… brzmiÄ…. SkalÄ™ opisujemy dwoma parametrami, tonacjÄ… oraz modem. Tonacja jest to pierwsza nuta dla skali. Mod natomiast jest to zestaw interwałów liczony od pierwszej nuty. np. C-Dur, gdzie C jest wartoÅ›ciÄ… poczÄ…tkowÄ…, a Dur opisuje sekwencjÄ™ interwałów. Możemy utworzyć inne skale, np G-Dur, używajÄ…c tych samych interwałów, ale zaczynajÄ…c od innej nuty. + Skala szereg dzwiÄ™ków uÅ‚ożonych wedÅ‚ug staÅ‚ego schematu interwałów. WspoÅ‚czeÅ›nie wyróżniamy dwa rodzaje skal, durowÄ… (Dur) oraz molowÄ… (Mol). Skala durowa odbierana jest przez sÅ‚uchacza jako "wesoÅ‚a", a skala molowa jako "smutna". SkalÄ™ tworzy siÄ™ wybierajÄ…c dowolny dzwiÄ™k poczÄ…tkowy, który bÄ™dzie pierwszym stopniem skali. NastÄ™pnie dobieramy kolejne dźwiÄ™ki zgodnie ze schematem skali. Skale durowÄ… tworzymy wedÅ‚ug nastÄ™pujÄ…cego schematu + \begin{center} + 2 2 1 2 2 2 1. + \end{center} + Schemat przedstawia liczbÄ™ półnut miÄ™dzy kolejnymi dzwiÄ™kami skali. Dla przykÅ‚adu skala C-Dur skÅ‚ada siÄ™ z dzwiÄ™ków C, D, E, F, G, A i H. + + % http://www.kwadransdlagitary.pl/skala-durowa-teoria/ + % https://pl.wikipedia.org/wiki/Skala_(muzyka) \section{Cyfrowa reprezentacja muzyki symbolicznej} @@ -706,7 +714,7 @@ 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 dźwiÄ™k nr 48 z gÅ‚oÅ›noÅ›ciÄ… 100 w momencie 0 utworu. Nie informuje nas on jednak o dÅ‚ugoÅ›ci trwania dźwiÄ™ku. Aby zakoÅ„czyć dźwiÄ™k, należy wysÅ‚ać wiadomość: + oznacza, że na kanele 0 nalezy zagrać dźwiÄ™k nr 48 z gÅ‚oÅ›noÅ›ciÄ… 100 w momencie 0 utworu. Nie informuje nas on jednak o dÅ‚ugoÅ›ci trwania dźwiÄ™ku. Aby zakoÅ„czyć dźwiÄ™k należy wysÅ‚ać wiadomość: \begin{center} note\textunderscore off, channel 0, note 48, velocity 100, time 24. \\ @@ -724,13 +732,25 @@ note_on channel=0 note=60 velocity=0 time=0 \subsubsection{Nuty} Nuty w formacie MIDI opisane sÄ… kolejnymi cyframi naturalnymi w przedziale od 0 do 127. Odpowiada to dźwiÄ™kom od $C_0$ do $C_8$. Dla przykÅ‚adu nuta 69 odpowiada $A_4$, a nuta 47 odpowiada $B_2$. - WyjÄ…tkiem sÄ… nuty z kanaÅ‚u dziewiÄ…tego, gdzie istniejÄ… tylko nuty z zakresu od 35 do 81 i każda nuta odpowiada innemu elementowi perkusyjne np. 35 to stopa (\textit{ang. kick}), a 37 to werbel {\textit{ang. snare}}. + WyjÄ…tkiem sÄ… nuty z kanaÅ‚u dziewiÄ…tego, gdzie istniejÄ… tylko nuty z zakresu od 35 do 81 i każda nuta odpowiada innemu elementowi perkusyjne, np. 35 to stopa (\textit{ang. kick}), a 37 to werbel {\textit{ang. snare}}. \subsubsection{GÅ‚oÅ›ność} Za gÅ‚oÅ›ność dźwiÄ™ku odpowiada parametr \textit{velocity}, który jest liczbÄ… z przedziaÅ‚u od 0 do 127. Im wiÄ™ksza jest wartość tym gÅ‚oÅ›niej wybrzmi dźwiÄ™k. \subsubsection{Program} - Program w kontekÅ›cie standardu MIDI oznacza instrument który ma zagrać nuty. W standardzie GM (ang. General MIDI), jest 16 grup instrumentów a w każdej z nich znajduje siÄ™ po 8 instrumentów. SÄ… to pianina, chromatyczne perkusje, organy, gitary, basy, instrumenty smyczkowe, zestawy instrumentów, instrumenty dmuchane blaszane, instrumenty dmuchane drewniane, flety, syntezatory prowadzÄ…ce, syntezatory uzupeÅ‚niajÄ…ce, efekty syntetyczne, instrumenty etniczne, perkusjonalia i efekty dźwiÄ™kowe. + Program w kontekÅ›cie standardu MIDI oznacza instrument, który ma zagrać nuty. W standardzie GM (\textit{ang. General MIDI}) jest 16 grup instrumentów, a w każdej z nich znajduje siÄ™ po 8 instrumentów. SÄ… to pianina, chromatyczne perkusje, organy, gitary, basy, instrumenty smyczkowe, zestawy instrumentów, instrumenty dmuchane blaszane, instrumenty dmuchane drewniane, flety, syntezatory prowadzÄ…ce, syntezatory uzupeÅ‚niajÄ…ce, efekty syntetyczne, instrumenty etniczne, perkusjonalia i efekty dźwiÄ™kowe. Szczegółowa rozpiska zostaÅ‚a przedstawiona na rysunku~\ref{fig:generalmidi} + + \begin{figure}[!htb] + \centering + \includegraphics[width=\linewidth]{images/general-midi.png} + \caption[]{Lista programów w standardzie General MIDI\footnotemark} + \label{fig:generalmidi} + \end{figure} + % https://www.midi.org/specifications-old/item/gm-level-1-sound-set + + + \footnotetext{https://alchetron.com/ 16 czerwca 2020 8:23} + % https://alchetron.com/General-MIDI#general-midi-d016a071-b750-46c2-8828-926e6d2aa12-resize-750.png \subsubsection{Åšcieżka} Åšcieżka (\textit{ang. track}) grupuje nuty, aby podzielić utwór muzyczny na różne instrumenty lub partie. Protokół MIDI pozwala, aby grać wiele Å›cieżek dźwiÄ™kowych jednoczeÅ›nie. Wtedy mówimy o muzyce polifonicznej lub multiinstrumentalnej. @@ -738,20 +758,19 @@ note_on channel=0 note=60 velocity=0 time=0 \chapter{Projekt} \label{section:project} - W tym rozdziale opiszÄ™ szczegóły dziaÅ‚ania modelu, który przygotowaÅ‚em. Najpierw przedstawiÄ™ pomysÅ‚ na model, opiszÄ™ szczegóły techniczne dotyczÄ…ce przygotowania danych uczÄ…cych dla modelu. NastÄ™pnie zdefiniuj model i rozwiÅ„ opis modelu sequence-to-sequence. W tym rozdziale bÄ™dÄ™ również zamieszczaÅ‚ fragmentu kodu napisanego w jÄ™zyku Python. + W tym rozdziale opiszÄ™ szczegóły dziaÅ‚ania modelu, który przygotowaÅ‚em. Najpierw przedstawiÄ™ pomysÅ‚ na model, opiszÄ™ szczegóły techniczne dotyczÄ…ce przygotowania danych uczÄ…cych dla modelu. NastÄ™pnie zdefiniujÄ™ i opiszÄ™ architekturÄ™ sequence-to-sequence. Fragmenty kodu zamieszoczne w pracy zostaÅ‚y napisane w jÄ™zyku Python. \section{Koncepcja} - Celem tej pracy, byÅ‚o wykonanie modelu, który przy użyciu gÅ‚Ä™bokiego uczenia bÄ™dzie w stanie generować krótkie klipy multiinstrumentalne. ZainspirowaÅ‚ mnie sposób w jaki tworzy siÄ™ muzykÄ™ w zespole. W przeciwieÅ„stwie do muzyki tworzonej przez jednego kompozytora, w zespole każda partia tworzona jest przez muzyka grajÄ…cego na danym instrumencie. PrzykÅ‚adowy sposób tworzenia utworu w zespole, np. rockowym wyglÄ…da jak nastÄ™puje. Jedna osoba tworzy (generuje) pierwszÄ… partiÄ™ muzycznÄ…, np. partiÄ™ na gitary. Ta partia zostaÅ‚a stworzona bez odniesienia do innych czÅ‚onków zespoÅ‚u. NastÄ™pnie taka partia zostaje przedstawiona zespoÅ‚owi. Każdy z czÅ‚onków zespoÅ‚u musi teraz stworzyć swoje partie w taki sposób, aby pasowaÅ‚y one muzycznie do pierwszej partii. W ten sposób powstajÄ… nam zależnoÅ›ci miÄ™dzy partiami, tworzÄ…cymi caÅ‚y utwór. + Celem tej pracy byÅ‚o wykonanie modelu, który przy użyciu gÅ‚Ä™bokiego uczenia bÄ™dzie w stanie generować krótkie klipy multiinstrumentalne. ZainspirowaÅ‚ mnie sposób w jaki tworzy siÄ™ muzykÄ™ w zespole. W przeciwieÅ„stwie do muzyki tworzonej przez jednego kompozytora, w zespole każda partia tworzona jest przez muzyka grajÄ…cego na danym instrumencie. PrzykÅ‚adowy sposób tworzenia utworu w zespole, np. rockowym wyglÄ…da jak nastÄ™puje. Jedna osoba tworzy (generuje) pierwszÄ… partiÄ™ muzycznÄ…, np. partiÄ™ na gitary. Ta partia zostaÅ‚a stworzona bez odniesienia do innych czÅ‚onków zespoÅ‚u. NastÄ™pnie taka partia zostaje przedstawiona zespoÅ‚owi. Każdy z czÅ‚onków zespoÅ‚u musi teraz stworzyć swoje partie w taki sposób, aby pasowaÅ‚y one muzycznie do pierwszej partii. W ten sposób powstajÄ… nam zależnoÅ›ci miÄ™dzy partiami tworzÄ…cymi caÅ‚y utwór. - Na podstawie tej idei postanowiÅ‚em opracować model skÅ‚adajÄ…cy siÄ™ z wielu sieci neuronowych, każda z nich odpowiadać bÄ™dzie jednej partii w utworze, muzykowi w zespole. Jedna z tych sieci bÄ™dzie generatorem. Ta sieć powinna być skonstruowana w taki sposób, aby zainicjować partiÄ™ muzycznÄ…. PozostaÅ‚e bÄ™dÄ… dopasowywać swoje partie w taki sposób, aby pasowaÅ‚y pod partiÄ™ wygenerowanÄ…. Te sieci nazywać bÄ™dÄ™ modelami akompaniujÄ…cy. DziÄ™ki temu jesteÅ›my wstanie stworzyć model wielu sieci, w którym nastÄ™pna sieć bÄ™dzie produkować swoje partie na podstawie tego, co wygenerowaÅ‚a poprzednia. + Na podstawie tej idei postanowiÅ‚em opracować model skÅ‚adajÄ…cy siÄ™ z wielu sieci neuronowych, każda z nich odpowiadać bÄ™dzie jednej partii w utworze, muzykowi w zespole. Jedna z tych sieci bÄ™dzie generatorem. Ta sieć powinna być skonstruowana w taki sposób, aby zainicjować partiÄ™ muzycznÄ…. PozostaÅ‚e bÄ™dÄ… dopasowywać swoje partie pod partiÄ™ stworzÄ…nÄ… przez generator. Te sieci nazywać bÄ™dÄ™ modelami akompaniujÄ…cy. DziÄ™ki temu jesteÅ›my wstanie stworzyć model wielu sieci, w którym nastÄ™pna sieć bÄ™dzie produkować swoje partie na podstawie tego, co wygenerowaÅ‚a poprzednia. - Kluczowe byÅ‚o zauważenie podobieÅ„stwa miÄ™dzy jÄ™zykiem naturalnym oraz muzykÄ…. Zarówno zdanie jak i partia muzyczna skÅ‚ada siÄ™ z sekwencji elementów rozmieszczonych w czasie. Elementy te sÄ… zależne od dÅ‚ugoterminowego kontekstu oraz od tego jaki element byÅ‚ ustawiony wczeÅ›niej. Dla jÄ™zyka naturalnego sÄ… to sÅ‚owa, dla muzyki sÄ… to nuty i akordy. Dodatkowo pomyÅ›laÅ‚em, że różne instrumenty można porównać do różnych jÄ™zyków Å›wiata. Wtedy, aby stworzyć melodiÄ™, np. basu tak, aby pasowaÅ‚a pod partiÄ™ gitary, należy ,,przetÅ‚umaczy'' jÄ™zyk gitary na jÄ™zyk basu. Do tÅ‚umaczeÅ„ jÄ™zyka naturalnego wykorzystuje siÄ™ modele sequence-to-sequence, dlatego postanowiÅ‚em w modelu generowania muzyki wykorzystać wÅ‚aÅ›nie tÄ… architekturÄ™. Dodatkowo modele sequence-to-sequence majÄ… tÄ™ cechÄ™, że liczba elementów sekwencji wejÅ›ciowej może być inna niż liczba elementów sekwencji wyjÅ›ciowej. Idealnie sprawdzi siÄ™ w przypadku muzyki, ponieważ o dÅ‚ugoÅ›ci trwania Å›cieżki muzycznej nie Å›wiadczy liczba nut tylko suma ich wartoÅ›ci. + Kluczowe byÅ‚o zauważenie podobieÅ„stwa miÄ™dzy jÄ™zykiem naturalnym oraz muzykÄ…. Zarówno zdanie jak i partia muzyczna skÅ‚ada siÄ™ z sekwencji elementów rozmieszczonych w czasie. Elementy te sÄ… zależne od dÅ‚ugoterminowego kontekstu oraz od tego jaki element byÅ‚ ustawiony wczeÅ›niej. Dla jÄ™zyka naturalnego sÄ… to sÅ‚owa, dla muzyki sÄ… to nuty i akordy. Dodatkowo pomyÅ›laÅ‚em, że różne instrumenty można porównać do różnych jÄ™zyków Å›wiata. Wtedy, aby stworzyć melodiÄ™, np. basu tak, żeby pasowaÅ‚a pod partiÄ™ gitary należy przetÅ‚umaczyć ,,jÄ™zyk'' gitary na ,,jÄ™zyk'' basu. Do tÅ‚umaczeÅ„ jÄ™zyka naturalnego wykorzystuje siÄ™ modele sequence-to-sequence, dlatego postanowiÅ‚em w modelu generowania muzyki wykorzystać wÅ‚aÅ›nie tÄ… architekturÄ™. Dodatkowo modele sequence-to-sequence majÄ… tÄ™ cechÄ™, że liczba elementów sekwencji wejÅ›ciowej może być inna niż liczba elementów sekwencji wyjÅ›ciowej. Idealnie sprawdzi siÄ™ w przypadku muzyki, ponieważ o dÅ‚ugoÅ›ci trwania Å›cieżki muzycznej nie Å›wiadczy liczba nut tylko suma ich wartoÅ›ci. \section{WstÄ™pne przygotowanie danych do treningu} \label{section:midi} - - \subsection{Muzyczne ,,sÅ‚owo''} + \subsection{Muzyczne sÅ‚owo} \label{section:midi_words} Na potrzeby dostosowania danych muzycznych do koncepcji słów w zdaniu zakodowaÅ‚em pojedyncze sÅ‚owo muzyczne jako @@ -762,10 +781,10 @@ note_on channel=0 note=60 velocity=0 time=0 W ten sposób byÅ‚em w stanie zakodować pojedyÅ„cze nuty i akordy. - Akord C-dur skÅ‚adajÄ…cy siÄ™ z dźwiÄ™ków C, E i G o dÅ‚ugoÅ›ci ósemki, zapisaliÅ›my w nastÄ™pujÄ…cy sposób. + Akord C-dur skÅ‚adajÄ…cy siÄ™ z dźwiÄ™ków C, E i G o dÅ‚ugoÅ›ci ósemki zapisaliÅ›my w nastÄ™pujÄ…cy sposób \begin{center} - ((60, 64, 67), 0.5) + ((60, 64, 67), 0.5). \end{center} W ten sposób jesteÅ›my w stanie kodować melodiÄ™ w sekwencji słów muzycznych. Tak skonstruowane dane majÄ… niestety swoje negatywne aspekty. Nie da siÄ™ w ten sposób zapisać partii, w której zostaje grana nowa nuta, gdy poprzednia jeszcze powinna brzmieć. Nasz zapis zakÅ‚ada, że melodia jest grana element po elemencie i nowy element wymusza zakoÅ„czenie poprzedniego. Nie przechowujemy również informacji o dynamice melodii (gÅ‚oÅ›noÅ›ci). Rozszerzenie tego zapisu o informacje o gÅ‚oÅ›noÅ›ci nie jest trudne i nie bÄ™dzie wymagać przebudowy modelu, natomiast wraz ze wzrostem liczby możliwych ,,słów muzycznych'' w sÅ‚owniku i zwiÄ™ksza zÅ‚ożoność obliczeniowÄ…. ZdecydowaÅ‚em siÄ™ na niewykorzystanie tych danych w generowaniu muzyki. @@ -855,7 +874,7 @@ def parse_pretty_midi_instrument(instrument, resolution, \end{python} - Powyższa funkcja w zamienia wartoÅ›ci absolutne czasu, na wartoÅ›ci wzglÄ™dne o ustalonej rozdzielczoÅ›ci przez plik MIDI. Dodatkowo zmniejsza szczegółowość i zaokrÄ…gla czas zagrania nuty po szesnastki. Gdy w tym samym momencie, czyli jeÅ›li kilka nut posiada tÄ… samÄ… wartość start, zostajÄ… dodane do jednego sÅ‚owa muzycznego, aby utworzyć akord. Pauzy sÄ… kodowane jako $-1$. Dodatkowo jeÅ›li pauza trwa dÅ‚użej niż takt wtedy zostaje podzielona na mniejsze części o dÅ‚ugoÅ›ci \pyth{max_rest_len}. Funkcja zwraca obiekt \pyth{SingleTrack}, który jest obiektem stworzonym, aby poza nutami, przechowywać inne istotne informacje na temat Å›cieżki, którÄ… bÄ™dÄ… istotne w nastÄ™pnych częściach przetwarzania danych. Ostatecznie sekwencje słów muzycznych przechowane sÄ… w \pyth{notes}. + Powyższa funkcja zamienia wartoÅ›ci absolutne czasu na wartoÅ›ci wzglÄ™dne o ustalonej rozdzielczoÅ›ci przez plik MIDI. Dodatkowo zmniejsza szczegółowość i zaokrÄ…gla czas zagrania nuty po szesnastki. Gdy w tym samym momencie, czyli jeÅ›li kilka nut posiada tÄ… samÄ… wartość start, zostajÄ… dodane do jednego sÅ‚owa muzycznego, aby utworzyć akord. Pauzy sÄ… kodowane jako $-1$. Dodatkowo jeÅ›li pauza trwa dÅ‚użej niż takt wtedy zostaje podzielona na mniejsze części o dÅ‚ugoÅ›ci \pyth{max_rest_len}. Funkcja zwraca obiekt \pyth{SingleTrack}, który jest obiektem stworzonym, aby poza nutami przechowywać inne istotne informacje na temat Å›cieżki. BÄ™dÄ… one istotne w nastÄ™pnych częściach przetwarzania danych. Ostatecznie sekwencje słów muzycznych przechowane sÄ… w \pyth{notes}. \begin{python} >>> resolution = midi.resolution @@ -883,13 +902,13 @@ resolution, time_to_tick, key_offset=0) \subsection{Inne aspekty przygotowania danych} - Po odczytaniu danych i konwersji je do pożądanego formatu dane należy oczyÅ›cić. W mojej pracy zastosowaÅ‚em kilka operacji, w celu zwiÄ™kszenia muzycznego sensu danych. + Po odczytaniu danych i konwersji ich do pożądanego formatu dane należy oczyÅ›cić. W mojej pracy zastosowaÅ‚em kilka operacji, w celu zwiÄ™kszenia muzycznego sensu danych. \subsubsection{Unormowanie skali} W muzyce istnieje pojÄ™cie skali. Skala jest to zestaw nut, które dobrze ze sobÄ… współgrajÄ…. ZostaÅ‚o to szerzej opisane w podrozdziale~\ref{section:skala}. W uczeniu maszynowym powoduje to realny problem, ponieważ piosenki wykorzystujÄ… różne skale i sieć neuronowa bÄ™dzie preferować wybranie skali częściej używanej. Dodatkowo zmiana skali nie zmienia znacznie kontentu muzycznego utworu, tj. nawet po zmianie skali melodii czÅ‚owiek dalej jest w stanie jÄ… rozpoznać. Zmiana wysokoÅ›ci wszystkich nut bez zmiany ich wzglÄ™dnych interwałów nazywana jest transpozycjÄ…. Aby rozwiÄ…zać ten problem zaleca siÄ™ rozszerzenie danych do wszystkich możliwych skal. W mojej pracy wykorzystaÅ‚am jednak inne rozwiÄ…zanie. Zamiast rozszerzać zbiór danych sprowadziÅ‚em wszystkie Å›cieżki muzyczne do jednej skali C. DziÄ™ki temu model przyÅ‚oży wiÄ™kszÄ… uwagÄ™ na rozumienie wzajemnych relacji, zamiast uczyć siÄ™ pojÄ™cia tonacji skali \cite{survay}. \subsubsection{PodziaÅ‚ na takty} - DÅ‚ugie listy muzycznych słów zostaÅ‚y podzielone na takty (\textit{ang. bars}), o odpowiedniej dÅ‚ugoÅ›ci, domyÅ›lnie o dÅ‚ugoÅ›ci 4, co odpowiada czterem ćwierćnutom. DziÄ™ki temu utwór muzyczny zostanie podzielony na mniejsze sekwencje. Sekwencje te bÄ™dÄ… posiadaÅ‚y różnÄ… liczbÄ™ elementów, ale bÄ™dÄ… tak samo dÅ‚ugie, w kontekÅ›cie muzycznym. Głównym celem takie zabiegu, jest zapewnienie muzycznego sensu sekwenjom. Takt jest naturalnym dla muzyki podziaÅ‚em dÅ‚uższego partii na mniejsze. + DÅ‚ugie listy muzycznych słów zostaÅ‚y podzielone na takty (\textit{ang. bars}) o odpowiedniej dÅ‚ugoÅ›ci, domyÅ›lnie o dÅ‚ugoÅ›ci 4, co odpowiada czterem ćwierćnutom. DziÄ™ki temu utwór muzyczny zostanie podzielony na mniejsze sekwencje. Sekwencje te bÄ™dÄ… posiadaÅ‚y różnÄ… liczbÄ™ elementów, ale bÄ™dÄ… tak samo dÅ‚ugie w kontekÅ›cie muzycznym. Głównym celem takiego zabiegu, jest zapewnienie muzycznego sensu sekwenjom. Takt jest naturalnym podziaÅ‚em dÅ‚uższych partii na krótsze. \subsection{PodziaÅ‚ danych na dane wejÅ›ciowe i wyjÅ›ciowe} @@ -904,13 +923,13 @@ resolution, time_to_tick, key_offset=0) gdzie $n$ jest liczbÄ… taktów w partii muzycznej. Pary $(x_t, y_t)$ tworzymy wedÅ‚ug poniżej reguÅ‚y \[ \begin{array}{c} - x_t = g_t \\ + x_t = g_t, \\ y_t = g_{t+1}, \end{array} \] dla $t \in (1, n-1)$. - DziÄ™ki takiemu zdefiniowaniu danych uczÄ…cych generator bÄ™dzie uczyÅ‚ siÄ™ jak powinien wyglÄ…dać nastÄ™pny takt, na podstawie poprzedniego. W ten sposób bÄ™dziemy w stanie wykorzystać model do generowania muzyki bez danych wejÅ›ciowych. WÄ…tek zostanie rozwiniÄ™ty w dalszej części pracy. + DziÄ™ki takiemu zdefiniowaniu danych uczÄ…cych generator bÄ™dzie uczyÅ‚ siÄ™ jak powinien wyglÄ…dać nastÄ™pny takt na podstawie poprzedniego. W ten sposób bÄ™dziemy w stanie wykorzystać model do generowania muzyki bez danych wejÅ›ciowych. WÄ…tek zostanie rozwiniÄ™ty w dalszej części pracy. Implementacja w Pythonie: \begin{python} @@ -949,7 +968,7 @@ def get_data_seq2seq_melody(self, instrument_class, \subsubsection{Przygotowanie danych dla akompaniamentu} - Model akompaniujÄ…cy natomiast, bÄ™dzie na podstawie partii instrumentu tworzyć partiÄ™ na nowy instrument. + Model akompaniujÄ…cy bÄ™dzie na podstawie partii instrumentu tworzyć partiÄ™ na nowy instrument. Niech $G$, $B$ bÄ™dÄ… sekcjami muzycznymi różnych instrumentów tej samej dÅ‚ugoÅ›ci oraz niech \[ \begin{array}{c} @@ -1005,10 +1024,10 @@ def get_data_seq2seq_arrangment(self, x_instrument, W przygotowaniu danych dla modelu ważne jest, aby dostarczone dane byÅ‚y jak najlepszej jakoÅ›ci. W tym celu usunÄ…Å‚em powtarzajÄ…ce siÄ™ pary $(x, y)$ oraz usunÄ…Å‚em takty, które nie zawieraÅ‚y muzycznego kontentu. \subsubsection{Wybór programu dla instrumentu} - Podczas etapu ekstrakcji danych z plików MIDI poza informacjami o muzyce, zapamiÄ™tujÄ™ również informacje o programie partii muzycznej. Każda Å›cieżka MIDI przechowuje informacje o instrumencie (brzmieniu) danej partii. Istnieje 128 różnych programów, dla zmniejszenia szczególnoÅ›ci na potrzeby modelu wyróżniam 16 instrumentów zgodnie z grupÄ… do jakiej należą w podziale General MIDI. Dla każdej z grup, sprawdzam jaki program zostaÅ‚ najczęściej wykorzystywany i zapisujÄ™ go na przyszÅ‚ość, aby móc wygenerowanej muzyce przy kompilacji do MIDI zdefiniować brzmienie instrumentu zgodnie z najczęściej wykorzystywanym w zbiorze MIDI, który zostaÅ‚ wykorzystany do stworzenia zbioru uczÄ…cego dla modelu. + Podczas etapu ekstrakcji danych z plików MIDI poza informacjami o muzyce zapamiÄ™tujÄ™ również informacje o programie partii muzycznej. Każda Å›cieżka MIDI przechowuje informacje o instrumencie (brzmieniu) danej partii. Istnieje 128 różnych programów, dla zmniejszenia szczególnoÅ›ci na potrzeby modelu wyróżniam 16 instrumentów zgodnie z grupÄ… do jakiej należą w podziale General MIDI. Dla każdej z grup sprawdzam jaki program zostaÅ‚ najczęściej wykorzystywany i zapisujÄ™ go na przyszÅ‚ość. DziÄ™ki temu przy kompilacji wygenerowanej muzyki do MIDI bÄ™dzie można zdefiniować brzmienie instrumentu zgodnie z najczęściej wykorzystywanym w zbiorze uczÄ…cym. \subsubsection{Melodia} - Dodatkowym elementem procesu ekstrakcji danych jest znalezienie Å›cieżek melodii przewodnich w plikach MIDI. Åšcieżki tego typu zamiast być oznaczone nazwÄ… grupy instrumentów, do której należą oznaczone sÄ… nazwÄ… \pyth{Melody}. Melodia jest kategoriÄ… Å›cieżek z podziaÅ‚u ze wzglÄ™du na rolÄ™ partii w utworze, zamiast na instrument. IstniejÄ… też inne role instrumentów, jednak czÄ™sto rola jest w pewnym sensie definiowana przez instrument. Nie jest to zasada, bardziej prawidÅ‚owość w muzyce. UznaÅ‚em że wydobycie tej informacji na temat Å›cieżki nada wiÄ™cej muzycznego sensu danym. + Dodatkowym elementem procesu ekstrakcji danych jest znalezienie Å›cieżek melodii przewodnich w plikach MIDI. Åšcieżki tego typu zamiast być oznaczone nazwÄ… grupy instrumentów, do której należą oznaczone sÄ… nazwÄ… \pyth{Melody}. Melodia jest kategoriÄ… Å›cieżek z podziaÅ‚u ze wzglÄ™du na rolÄ™ partii w utworze, zamiast na instrument. IstniejÄ… też inne role instrumentów, jednak czÄ™sto rola jest w pewnym sensie definiowana przez instrument. Nie jest to zasada, bardziej prawidÅ‚owość w muzyce. UznaÅ‚em, że wydobycie tej informacji na temat Å›cieżki nada wiÄ™cej muzycznego sensu danym. Aby sprawdzić czy dana Å›cieżka jest melodiÄ… zastosowaÅ‚em poniższÄ… funkcjÄ™: \begin{python} @@ -1050,20 +1069,20 @@ else: return False \end{python} -Funkcja sprawdza liczbÄ™ pojedynczych nut i akordów w Å›cieżce oraz zagÄ™szczenie nut w takcie. JeÅ›li jest wiÄ™cej niż 90\% pojedynczych nut w Å›cieżce oraz jest Å›rednio wiÄ™cej nut w takcie niż dwie wtedy uznajÄ™, że partia instrumentalna utworu jest melodiÄ…. +Funkcja sprawdza liczbÄ™ pojedynczych nut i akordów w Å›cieżce oraz zagÄ™szczenie nut w takcie. JeÅ›li jest wiÄ™cej niż 90\% pojedynczych nut w Å›cieżce i jest Å›rednio wiÄ™cej nut w takcie niż dwie, wtedy uznajÄ™ że partia instrumentalna utworu jest melodiÄ…. \section{Definicja modelu} \label{section:model} Wszystkie modele sieci neuronowych zastosowane w tej pracy, zostaÅ‚y napisane z wykorzystaniem Å›rodowiska Keras. Keras jest to Å›rodowisko wyższego poziomu, sÅ‚użące do tworzenia modelu gÅ‚Ä™bokiego uczenia. -Model sequence-to-sequence, jest to model skÅ‚adajÄ…cy siÄ™ z dwóch mniejszych sieci neuronowych, enkodera i dekodera. Dodatkowo inaczej definiuje siÄ™ model, aby go uczyć a inaczej, aby dokonać predykcji. +Model sequence-to-sequence jest to model skÅ‚adajÄ…cy siÄ™ z dwóch mniejszych sieci neuronowych, enkodera i dekodera. Dodatkowo inaczej definiuje siÄ™ model aby go uczyć, a inaczej aby dokonać predykcji. \subsection{Model w trybie uczenia} \subsubsection{Definiowanie warstw enkodera} -Zadaniem enkodera jest wydobycie z przetwarzanej sekwencji kontekstu, skompresowanej informacji o danych. W tym celu zastosowana zostaÅ‚a jedna warstwa wejÅ›ciowa o rozmiarze sÅ‚ownika wejÅ›ciowego oraz warstwa LSTM. Definiowane warstwy sÄ… atrybutami caÅ‚ej klasy modelu, dlatego w prezentowanym kodzie wystÄ™puje przedrostek \pyth{self.}. +Zadaniem enkodera jest wydobycie z przetwarzanej sekwencji kontekstu skompresowanej informacji o danych. W tym celu zastosowana zostaÅ‚a jedna warstwa wejÅ›ciowa o rozmiarze sÅ‚ownika wejÅ›ciowego oraz warstwa LSTM. Definiowane warstwy sÄ… atrybutami caÅ‚ej klasy modelu, dlatego w prezentowanym kodzie wystÄ™puje przedrostek \pyth{self.}. \begin{python} self.encoder_inputs = @@ -1078,13 +1097,13 @@ self.encoder_outputs, self.state_h, self.state_c = self.encoder_states = [self.state_h, self.state_c] \end{python} -Ostatecznie jako dane wyjÅ›ciowe otrzymujemy wektor danych ukrytych \pyth{encoder_outputs} o wymiarze równym ustalonej zmiennej \pyth{latent_dim}. Dodatkowo używajÄ…c parametru \pyth{return_state=True}, warstwa LSTM zwraca wektory stanu komórek $h$ oraz $c$. Te wektory sÄ… pamiÄ™ciÄ… warstwy LSTM i posÅ‚użą jako stan wejÅ›ciowy dla modelu dekodera. +Ostatecznie jako dane wyjÅ›ciowe otrzymujemy wektor danych ukrytych \pyth{encoder_outputs} o wymiarze równym ustalonej zmiennej \pyth{latent_dim}. Dodatkowo używajÄ…c parametru \pyth{return_state=True} warstwa LSTM zwraca wektory stanu komórek $h$ oraz $c$. Te wektory sÄ… pamiÄ™ciÄ… warstwy LSTM i posÅ‚użą jako stan wejÅ›ciowy dla modelu dekodera. Oba wektory zostaÅ‚y zapisane do jednej zmiennej \pyth{self.encoder_states}. \subsubsection{Definiowanie warstw dekodera} -W części dekodera sieci sequence-to-sequence, definiujemy warstwÄ™ wejÅ›ciowÄ… o rozmiarze sÅ‚ownika wynikowego i jednÄ… warstwÄ™ LSTM o stanie komórek $h$ i $c$ w enkodera. Na koÅ„cu zostaÅ‚a zdefiniowana prosta warstwa typu \pyth{Dense} z funkcjÄ… aktywacji \pyth{softmax} w celu rozszerzenia wymiaru do wielkoÅ›ci sÅ‚ownika wyjÅ›ciowego. +W części dekodera sieci sequence-to-sequence definiujemy warstwÄ™ wejÅ›ciowÄ… o rozmiarze sÅ‚ownika wynikowego i jednÄ… warstwÄ™ LSTM o stanie komórek $h$ i $c$ enkodera. Na koÅ„cu zostaÅ‚a zdefiniowana prosta warstwa typu \pyth{Dense} z funkcjÄ… aktywacji \pyth{softmax}, w celu rozszerzenia wymiaru do wielkoÅ›ci sÅ‚ownika wyjÅ›ciowego. \begin{python} self.decoder_inputs = @@ -1110,7 +1129,7 @@ Jako wynik propagacji modelu otrzymujemy wektor o rozmiarze sÅ‚ownika wyjÅ›ciowe \subsubsection{Definicja modelu w trybie uczenia} -Ostatnim krokiem, aby otrzymać model gotowy do procesu uczenia należy poÅ‚Ä…czyć ze sobÄ… enkoder i dekoder, tworzÄ…c peÅ‚ny model. Po jego skompilowaniu model można przedstawić jako graf tak jak pokazano to na rysunku~\ref{fig:training-model} +Aby otrzymać model gotowy do procesu uczenia należy poÅ‚Ä…czyć ze sobÄ… enkoder i dekoder tworzÄ…c peÅ‚ny model. Po jego skompilowaniu model można przedstawić jako graf tak jak pokazano to na rysunku~\ref{fig:training-model} \begin{figure}[!htb] \centering @@ -1136,12 +1155,12 @@ Możemy zauważyć, że w procesie uczenia musimy zaprezentować modelowi dwa we \item \pyth{decoder_target_data}, zawierajÄ…ce sekwencje elementów wyjÅ›ciowych, które bÄ™dÄ… celem. \end{itemize} -Jest to ciekawe, że musimy dostarczyć do modelu dane, które tak naprawdÄ™ chcemy otrzymać. Jednak te dane sÄ… przesuniÄ™te o jeden element w sekwencji do przodu i pierwszy element tej sekwencji nie zawiera treÅ›ci. Dekoder uczy siÄ™ jak na podstawie aktualnego stanu enkodera oraz aktualnego elementu sekwencji wyjÅ›ciowej jaki powinien być nastÄ™pny element w sekwencji docelowej. Warto też zauważyć, że z definicji modelu nie wynika, aby model uczyÅ‚ siÄ™ przetwarzania caÅ‚ych sekwencji, tylko każdego elementu sekwencji z osobna. +Jest to ciekawe, że musimy dostarczyć do modelu dane, które tak naprawdÄ™ chcemy otrzymać. Jednak te dane sÄ… przesuniÄ™te o jeden element w sekwencji do przodu i pierwszy element tej sekwencji nie zawiera treÅ›ci. Dekoder uczy siÄ™ jak na podstawie aktualnego stanu enkodera oraz aktualnego elementu sekwencji wyjÅ›ciowej przewidzieć nastÄ™pny element w sekwencji docelowej. Warto też zauważyć, że z definicji modelu nie wynika, aby model uczyÅ‚ siÄ™ przetwarzania caÅ‚ych sekwencji tylko każdego elementu sekwencji z osobna. \subsection{Model w trybie wnioskowania} \label{section:inference-model} -To co czyni model seq2seq zdolnym do przetwarzania caÅ‚ych sekwencji jest sposób zdefiniowania metody wnioskowania (\textit{ang. inference}). Na tym etapie model w sposób rekurencyjny bÄ™dzie przewidywaÅ‚ nastÄ™pny element sekwencji, na podstawie tego co przewidziaÅ‚ wczeÅ›niej oraz aktualizowanych wektorów stanu warstwy LSTM. Musimy w tym celu zdefiniować dekoder tak, aby mógÅ‚ przyjąć swoje wyjÅ›cie jako nowe wejÅ›cie. Dlatego definicja modelu wtedy wyglÄ…da nastÄ™pujÄ…co, a graf przedstawiajÄ…cy dekoder w trybie uczenia zostaÅ‚ przedstawiony na rysunku~\ref{fig:inference-decoder}. +To co czyni model seq2seq zdolnym do przetwarzania caÅ‚ych sekwencji jest sposób zdefiniowania metody wnioskowania (\textit{ang. inference}). Na tym etapie model w sposób rekurencyjny bÄ™dzie przewidywaÅ‚ nastÄ™pny element sekwencji, na podstawie tego co przewidziaÅ‚ wczeÅ›niej oraz aktualizowanych wektorów stanu warstwy LSTM. Musimy w tym celu zdefiniować dekoder tak, aby mógÅ‚ przyjąć swoje wyjÅ›cie jako nowe wejÅ›cie. Dlatego definicja modelu wyglÄ…da nastÄ™pujÄ…co, a graf przedstawiajÄ…cy dekoder w trybie uczenia zostaÅ‚ przedstawiony na rysunku~\ref{fig:inference-decoder}. \begin{python} @@ -1175,7 +1194,7 @@ self.decoder_model = Model( \footnotetext{machinelearningmastery.com 16 czerwca 2020 06:24} -DziÄ™ki takiej definicji, jesteÅ›my w stanie w pÄ™tli przewidywać nastÄ™pne elementy do momentu osiÄ…gniÄ™cia warunku stopu. Implementacja tego procesu wyglÄ…da tak: +DziÄ™ki takiej definicji jesteÅ›my w stanie w pÄ™tli przewidywać nastÄ™pne elementy do momentu osiÄ…gniÄ™cia warunku stopu. Implementacja tego procesu wyglÄ…da tak: \begin{python} def predict(self, input_seq=None, mode=None): @@ -1228,7 +1247,7 @@ def predict(self, input_seq=None, mode=None): Enkoder w tym trybie ma za zadanie tylko dostarczyć do dekodera wektory kontekstu dla zainicjowania procesu. Dekoder na podstawie wektorów pamiÄ™ci $h$ i $c$ przewidzi pierwszy element sekwencji i tym samym zainicjuje proces wnioskowania. -W tym miejscu mamy kontrolÄ™ twórczÄ… nad dekoderem. Aby zainicjować reakcjÄ™ wystarczÄ… wektory pamiÄ™ci, możemy wtedy podać je w dowolny sposób i zobaczyć co wygeneruje dekoder. W mojej pracy próbowaÅ‚em dwóch sposób na zainicjowanie procesu predykcji z wektorów losowych. Pierwszy polega na wygenerowaniu losowej sekwencji dla enkodera i nazywam tÄ™ metodÄ™ \pyth{from_seq}. Druga metoda polega na bezpoÅ›rednim definiowaniu stanu $h$ i $c$ \pyth{states_value} w sposób losowy tak, aby wartoÅ›ci byÅ‚y z przedziaÅ‚u [-1, 1]. +W tym miejscu mamy kontrolÄ™ twórczÄ… nad dekoderem. Aby zainicjować reakcjÄ™ wystarczÄ… wektory pamiÄ™ci, wtedy możemy podać dowolne wartoÅ›ci i zobaczyć co wygeneruje dekoder. W mojej pracy próbowaÅ‚em dwóch sposób na zainicjowanie procesu predykcji z wektorów losowych. Pierwszy polega na wygenerowaniu losowej sekwencji dla enkodera i nazywam tÄ™ metodÄ™ \pyth{from_seq}. Druga metoda polega na bezpoÅ›rednim definiowaniu stanu $h$ i $c$ \pyth{states_value} w sposób losowy tak, aby wartoÅ›ci byÅ‚y z przedziaÅ‚u [-1, 1]. \section{Transformacja danych dla modelu} @@ -1236,7 +1255,7 @@ Na podstawie definicji modelu wiemy, że należy przygotować trzy zestawy danyc \subsection{Enkodowanie one-hot} -Każdy element sekwencji jest osobnÄ… kategoriÄ…, dlatego dane należy traktować tak jak dane kategoryczne. Wykorzystamy w tym celu enkodowanie one-hot (\textit{ang. one-hot encoding}) Enkodowanie One-Hot jest wykorzystywane w uczeniu maszynowym, aby nadać liczbowÄ… wartość danych kategorycznych. Polega ona stworzeniu sÅ‚ownika, w którym każde sÅ‚owo otrzyma swój unikatowy identyfikator, nastÄ™pnie zostanie utworzony wektor o wymiarze słów w sÅ‚owniku, gdzie na pozycji odpowiadajÄ…cej indeksowi sÅ‚owa bÄ™dzie wartość 1 a na pozostaÅ‚ych bÄ™dzie wartość zero \cite{onehot}. +Każdy element sekwencji jest osobnÄ… kategoriÄ…, dlatego dane należy traktować tak jak dane kategoryczne. Wykorzystamy w tym celu enkodowanie one-hot (\textit{ang. one-hot encoding}). Enkodowanie one-hot jest wykorzystywane w uczeniu maszynowym, aby nadać liczbowÄ… wartość danych kategorycznych. Polega ona stworzeniu sÅ‚ownika, w którym każde sÅ‚owo otrzyma swój unikatowy identyfikator, nastÄ™pnie zostanie utworzony wektor o wymiarze słów w sÅ‚owniku, gdzie na pozycji odpowiadajÄ…cej indeksowi sÅ‚owa bÄ™dzie wartość 1 a na pozostaÅ‚ych bÄ™dzie wartość 0 \cite{onehot}. \subsubsection{PrzykÅ‚ad enkodowania one-hot} @@ -1262,7 +1281,7 @@ KodujÄ…c sÅ‚owo MATEMATYKA, otrzymalibyÅ›my macierz 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ \end{bmatrix} -\] +.\] \subsection{SÅ‚ownik} @@ -1273,7 +1292,7 @@ x_vocab = set([note for seq in x_train for note in seq]) y_vocab = set([note for seq in y_train for note in seq]) \end{python} -Do sÅ‚ownika dodajemy dwa dodatkowe elementy, które opiszÄ™ w nastÄ™pnym rozdziale. +Do sÅ‚ownika dodajemy dwa dodatkowe elementy, które opiszÄ™ w rozdziale~\ref{section:specialtoken}. \begin{python} self.x_vocab = sorted(list(x_vocab)) @@ -1281,7 +1300,7 @@ self.y_vocab = ['',''] self.y_vocab.extend(sorted(list(y_vocab))) \end{python} -NastÄ™pnie tworzymy obiekty typu \pyth{dictionary}, aby zmapować elementy sekwencji na liczby. W tym momencie tworzymy również sÅ‚owniki odwrotne, aby móc później otrzymane wyniki zamienić na z powrotem na muzyczne sÅ‚owa. +NastÄ™pnie tworzymy obiekty typu \pyth{dictionary}, aby zmapować elementy sekwencji na liczby oraz sÅ‚owniki odwrotne, aby móc później otrzymane wyniki zamienić z powrotem na muzyczne sÅ‚owa. \begin{python} self.x_transform_dict = dict( @@ -1295,8 +1314,9 @@ self.y_reverse_dict = dict( \end{python} \subsection{Elementy specjalne} +\label{section:specialtoken} -Dodaje siÄ™ dwóch elementów specjalnych. Te elementy majÄ… za zadanie oznaczenie poczÄ…tku i koÅ„ca sekwencji. Token poczÄ…tku sekwencji zazwyczaj oznaczany jest jako \pyth{} (\textit{ang. start of sequence}). Można spotkać również inne oznaczenia,np. \pyth{} lub \pyth{}. Ten element ma na celu wypeÅ‚nienie przestrzeni pierwszego pustego miejsca w danych wejÅ›ciowych dla dekodera. Token koÅ„ca sekwencji oznaczany jako \pyth{} (\textit{ang. start of sequence}) lub \pyth{}. Ten element jest wykorzystywany, aby wywoÅ‚ać warunek stopu w procesie predykcji opisanym w rozdziale~\ref{section:inference-model}. +Dodaje siÄ™ dwa elementy specjalne. Te elementy majÄ… za zadanie oznaczenie poczÄ…tku i koÅ„ca sekwencji. Token poczÄ…tku sekwencji zazwyczaj oznaczany jest jako \pyth{} (\textit{ang. start of sequence}). Można spotkać również inne oznaczenia, np. \pyth{} lub \pyth{}. Ten element ma na celu wypeÅ‚nienie przestrzeni pierwszego pustego miejsca w danych wejÅ›ciowych dla dekodera. Token koÅ„ca sekwencji oznaczany jako \pyth{} (\textit{ang. start of sequence}) lub \pyth{}. Ten element jest wykorzystywany, aby wywoÅ‚ać warunek stopu w procesie predykcji opisanym w rozdziale~\ref{section:inference-model}. \begin{python} _y_train = [] @@ -1330,57 +1350,57 @@ decoder_input_data = np.zeros( self.y_vocab_size), dtype='float32') -decoder_target_data = np.zeros( +decoder_target = np.zeros( (len(x_train), self.y_max_seq_length, self.y_vocab_size), dtype='float32') for i, (x_train, y_train) in enumerate(zip(x_train, y_train)): - for t, char in enumerate(x_train): - encoder_input_data[i, t, self.x_transform_dict[char]] = 1. - for t, char in enumerate(y_train): - decoder_input_data[i, t, self.y_transform_dict[char]] = 1. + for t, c in enumerate(x_train): + encoder_input_data[i, t, self.x_transform_dict[c]] = 1. + for t, c in enumerate(y_train): + decoder_input_data[i, t, self.y_transform_dict[c]] = 1. if t > 0: - decoder_target_data[i, t - 1, self.y_transform_dict[char]] = 1. + decoder_target[i, t-1, self.y_transform_dict[c]] = 1. \end{python} W ten sposób otrzymujemy trzy zestawy danych potrzebne do przeprowadzenia procesu uczenia modelu. -Warto zwrócić uwagÄ™, że przed opisanÄ… transformacjÄ… sekwencje byÅ‚y różnej dÅ‚ugoÅ›ci a po niej, rozmiar sekwencji zostaÅ‚ rozszerzony do rozmiaru sekwencji posiadajÄ…cej najwiÄ™cej elementów. Taki zabieg byÅ‚ niezbÄ™dny, ponieważ rozmiar sieci neuronowej jest staÅ‚y dla wszystkich prób ze zbioru uczÄ…cego. Nie wpÅ‚ywa to jednak na same sekwencjÄ™, ponieważ podczas predykcjÄ™ koÅ„czymy w momencie wygenerowania tokenu \pyth{}. +Warto zwrócić uwagÄ™, że przed opisanÄ… transformacjÄ… sekwencje byÅ‚y różnej dÅ‚ugoÅ›ci, a po niej rozmiar sekwencji zostaÅ‚ rozszerzony do rozmiaru najdÅ‚uższej sekwencji. Taki zabieg byÅ‚ niezbÄ™dny, ponieważ rozmiar sieci neuronowej jest staÅ‚y dla wszystkich prób ze zbioru uczÄ…cego. Nie wpÅ‚ywa to jednak na same sekwencjÄ™, ponieważ podczas predykcjÄ™ koÅ„czymy w momencie wygenerowania tokenu \pyth{}. \section{Ekperyment} -W tej części pokażę jak wykorzystać oprogramowanie, które stworzyÅ‚em, aby wygenerować muzykÄ™ na przykÅ‚adzie. OmówiÄ™ caÅ‚y proces, nastÄ™pnie zademonstrujÄ™ wyniki. +W tej części pokażę jak wykorzystać oprogramowanie, które stworzyÅ‚em, aby wygenerować muzykÄ™ na konkretnym przykÅ‚adzie. OmówiÄ™ caÅ‚y proces oraz przedstawiÄ™ wyniki pracy. \subsection{Oprogramowanie} -Stworzone przeze mnie oprogramowanie, napisane w jÄ™zyku Python, skÅ‚ada siÄ™ z 2 bibliotek oraz 3 skryptów. +Stworzone przeze mnie oprogramowanie skÅ‚ada siÄ™ z 2 bibliotek oraz 3 skryptów: \begin{itemize} - \item \pyth{midi_procesing.py} - zawiera funkcjÄ™ potrzebne do pracy w plikami midi. - \item \pyth{model.py} - zawiera definicjÄ™ modelu sieci neuronowej - \item \pyth{extract.py} - sÅ‚uży do wydobycia w plików midi zbioru danych w postaci sekwencji. - \item \pyth{train.py} - wykonujÄ…c ten skrypt wykorzystujemy wygenerowane dane, aby wytrenować zestaw sieci neuronowych. + \item \pyth{midi_procesing.py} - zawiera funkcjÄ™ potrzebne do pracy w plikami midi, + \item \pyth{model.py} - zawiera definicjÄ™ modelu sieci neuronowej, + \item \pyth{extract.py} - sÅ‚uży do wydobycia w plików midi zbioru danych w postaci sekwencji, + \item \pyth{train.py} - wykonujÄ…c ten skrypt wykorzystujemy wygenerowane dane, aby wytrenować zestaw sieci neuronowych, \item \pyth{generate.py} - wykorzystuje wytrenowane modele, aby wygenerować ostatecznie plik midi. \end{itemize} -Fragmenty bilbiotek \pyth{midi_procesing.py} i \pyth{model.py} zostaÅ‚y szczegółowo omówione w rozdziaÅ‚ach ~\ref{section:midi} i ~\ref{section:model}. Natomiast skrypty \pyth{extract.py}, \pyth{train.py} i \pyth{generate.py} zostaÅ‚y napisane, aby uÅ‚atwić proces generowania oraz zapewniajÄ… powtarzalność i skalowalność prowadzonych eksperymentów. +Fragmenty bilbiotek \pyth{midi_procesing.py} i \pyth{model.py} zostaÅ‚y szczegółowo omówione w rozdziaÅ‚ach ~\ref{section:midi} i ~\ref{section:model}. Natomiast skrypty \pyth{extract.py}, \pyth{train.py} i \pyth{generate.py} zostaÅ‚y napisane, aby uÅ‚atwić proces generowania. Dodatkowo zapewniajÄ… powtarzalność i skalowalność prowadzonych eksperymentów. \subsection{Zbiór danych} -W omawianym przykÅ‚adzie wykorzystaÅ‚em zbiór wybranych utworów midi zespoÅ‚u The Offspring. ZostaÅ‚ on skompletowany ze źródeÅ‚ dostÄ™pnych na stronie internetowej https://www.midiworld.com/. SkÅ‚ada siÄ™ z 7 utworów. +W omawianym przykÅ‚adzie wykorzystaÅ‚em zbiór wybranych utworów midi zespoÅ‚u The Offspring. ZostaÅ‚ on skompletowany ze źródeÅ‚ dostÄ™pnych na stronie internetowej https://www.midiworld.com/. SkÅ‚ada siÄ™ z 7 utworów: \begin{itemize} - \item The Offspring - All I Want.mid - \item The Offspring - Change the World.mid - \item The Offspring - Nitro.mid - \item The Offspring - Original Prankster.mid - \item The Offspring - Self Esteem.mid - \item The Offspring - The Kids Arent Alright.mid - \item The Offspring - Why Dont You Get a Job.mid + \item The Offspring - All I Want.mid, + \item The Offspring - Change the World.mid, + \item The Offspring - Nitro.mid, + \item The Offspring - Original Prankster.mid, + \item The Offspring - Self Esteem.mid, + \item The Offspring - The Kids Arent Alright.mid, + \item The Offspring - Why Dont You Get a Job.mid. \end{itemize} \subsection{Wydobycie danych} -Aby wydobyć dane z plików midi wykorzystamy skypt \pyth{extract.py}. Można użyć flagi \pyth{-a}, aby najpierw zapoznać siÄ™ z zawartoÅ›ciÄ… muzycznÄ… zbioru plików midi. +Aby wydobyć dane z plików MIDI wykorzystamy skypt \pyth{extract.py}. Można użyć flagi \pyth{-a}, aby najpierw zapoznać siÄ™ z zawartoÅ›ciÄ… muzycznÄ… zbioru danych. % 100\%|███████████████████████████████████| 7/7 [00:01<00:00, 3.67it/s] \begin{python} @@ -1392,11 +1412,11 @@ Aby wydobyć dane z plików midi wykorzystamy skypt \pyth{extract.py}. Można u 1 of Organ \end{python} - DziÄ™ki temu możemy zaobserwować że w zbiorze danych jest 1098 taktów perkusji, 1037 taktów gitar, 704 melodii, 528 basu oraz 1 takt organ. + DziÄ™ki temu możemy zaobserwować, że w zbiorze danych jest 1098 taktów perkusji, 1037 taktów gitar, 704 melodii, 528 basu oraz 1 takt organ. Na tym etapie musimy zdecydować, który instrument bÄ™dzie generatorem oraz jakie bÄ™dÄ… zależnoÅ›ci miÄ™dzy partiami w zespole sieci neuronowych. - W tym przykÅ‚adzie, zdecydowaÅ‚em że gitara bÄ™dzie generowana na podstawie losowego wektora, a melodia, bas oraz perkusja bÄ™dÄ™ tworzone na podstawie gitary. + W tym przykÅ‚adzie zdecydowaÅ‚em, że gitara bÄ™dzie generowana na podstawie losowego wektora, a melodia, bas oraz perkusja bÄ™dÄ… tworzone na podstawie partii gitary. Uruchamiajać skrypt \pyth{extract.py} bez flagi \pyth{-a} zdefiniujemy omawiany przepÅ‚yw za pomocÄ… prostego konfiguratora. @@ -1425,7 +1445,7 @@ Done. %Exporting: ('Guitar', 'Drums'): 100\%||███████████████████████████████████| 7/7 [00:01<00:00, 3.79it/s] %Exporting: ('Guitar', 'Bass'): 100\%||███████████████████████████████████| 7/7 [00:01<00:00, 3.81it/s] -Po tym etapie zostaÅ‚y utworzony pliki zawierajÄ…ce oczyszczone pary sekwencji dla każdej sieci neuronowej. ZostaÅ‚o wygenerowanych +Po tym etapie zostanÄ… utworzone pliki zawierajÄ…ce oczyszczone pary sekwencji dla każdej sieci neuronowej. ZostaÅ‚y wygenerowane: \begin{itemize} \item 263 próby dla modelu gitary, @@ -1434,7 +1454,7 @@ Po tym etapie zostaÅ‚y utworzony pliki zawierajÄ…ce oczyszczone pary sekwencji d \item 385 prób par basu i gitary. \end{itemize} -Na podstawie takiego zbioru danych, w nastÄ™pnym kroku zostanÄ… wytrenowane cztery sieci neuronowe, po jednej dla każdego instrumentu. +Na podstawie takiego zbioru danych w nastÄ™pnym kroku zostanÄ… wytrenowane cztery sieci neuronowe, po jednej dla każdego instrumentu. \subsection{Trenowanie modelu} @@ -1467,7 +1487,7 @@ Epoch 1/1 - 4s 12ms/step - loss: 2.2721 - val_loss: 1.7813 \end{python} -Na potrzeby badaÅ„ trenowaÅ‚em i generowaÅ‚em klipy muzyczne dla epok 1, 10, 25, 50, 75, 100, 150. DziÄ™ki temu mogÄ™ porównać ze sobÄ… poszczególne etapy treningu sieci neuronowych. Wykresy funkcji kosztów dla zbioru uczÄ…cego i testowego zaprezentowane zostaÅ‚y na rysunku~\ref{fig:losses}. +Sieci neuronowe zostaÅ‚y trenowane przez 150 epok. Na potrzeby badaÅ„ generowaÅ‚em klipy muzyczne dla epok 1, 10, 25, 50, 75, 100, 150. DziÄ™ki temu mogÅ‚em porównać ze sobÄ… poszczególne etapy treningu sieci neuronowych. Wykresy funkcji kosztów dla zbioru uczÄ…cego i testowego zaprezentowane zostaÅ‚y na rysunku~\ref{fig:losses}. \begin{figure}[!htb] \centering @@ -1478,7 +1498,7 @@ Na potrzeby badaÅ„ trenowaÅ‚em i generowaÅ‚em klipy muzyczne dla epok 1, 10, 25, \subsection{Generowanie muzyki przy pomocy wytrenowanych modeli} -Gdy zdefiniowane modele zostanÄ… wytrenowane możemy wykorzystać skrypt \pyth{generate.py}, wtedy generujÄ…ca sieć neuonowa zostanie zasilona losowym wektorem, aby wygenerować partiÄ™. W tym przykÅ‚adzie gitary a wygenerowana partia posÅ‚uży jako dane wejÅ›ciowe na pozostaÅ‚ych modeli. Ostatecznie otrzymane sekwencje zostanÄ… skompilowane do pliku MIDI. W tym momencie zostajÄ… wykorzystane informacje o programach dla każdego z instrumentów, a tempo utworu domyÅ›lnie ustawione jest na 120 BPM. Możemy również zdecydować, czy zasilanie dekodera modelu generujÄ…cego odbÄ™dzie siÄ™ za pomocÄ… losowej sekwencji elementów ze sÅ‚ownika (\textit{from\textunderscore seq}), czy losowy wektor zasili bezpoÅ›rednio stany wewnÄ™trzne dekodera $h$ i $c$ (\textit{from\textunderscore state}). +Gdy zdefiniowane modele zostanÄ… wytrenowane możemy wykorzystać skrypt \pyth{generate.py}, wtedy generujÄ…ca sieć neuonowa zostanie zasilona losowym wektorem, aby wygenerować partiÄ™ muzycznÄ…. W omawianym przykÅ‚adzie bÄ™dzie to partia gitary. NastÄ™pnie ta partia posÅ‚uży jako dane wejÅ›ciowe dla pozostaÅ‚ych modeli. Ostatecznie otrzymane sekwencje zostanÄ… skompilowane do pliku MIDI. W tym momencie zostajÄ… wykorzystane informacje o programach dla każdego z instrumentów, a tempo utworu domyÅ›lnie ustawione jest na 120 BPM. Możemy również zdecydować, czy zasilanie dekodera modelu generujÄ…cego odbÄ™dzie siÄ™ za pomocÄ… losowej sekwencji elementów ze sÅ‚ownika (\textit{from\textunderscore seq}), czy losowy wektor zasili bezpoÅ›rednio stany wewnÄ™trzne dekodera $h$ i $c$ (\textit{from\textunderscore state}). \begin{python} >>> python generate.py offspring --i 10 --m from_state @@ -1489,7 +1509,7 @@ Generating music... Done. \end{python} -Parametr \pyth{--i} sÅ‚uży do okreÅ›lenia liczby wygenerowanych utworów a parametr \pyth{--m} pozwala zdefiniować metodÄ™ generowania, omówionÄ… wyżej. +Parametr \pyth{--i} sÅ‚uży do okreÅ›lenia liczby wygenerowanych utworów, a parametr \pyth{--m} pozwala zdefiniować metodÄ™ generowania omówionÄ… wyżej. Przekazywanie wygenerowanych partii to odpowiednich modeli wykonywane jest przy pomocy poniższego fragmentu kodu. @@ -1546,7 +1566,7 @@ Utwór przedstawiony na rysunku~\ref{fig:score1} zostaÅ‚ wygenerowany po pierwsz \label{fig:score1} \end{figure} -Po dziesiÄ™ciu epokach treningu melodia dalej wyglÄ…da na bardzo powtarzalnÄ…, jednak teraz jest bardziej spójna. Na przedstawionej na rysunku~\ref{fig:score10} partyturze widać, że model wygenerowaÅ‚ partiÄ™ gitary. Jednostajnie, co ćwierćnutÄ™ gra akord C-G-C (tzw. Power Chord) popularnie stosowany w muzyce rockowej. Perkusja wybija tylko jednÄ… perkusjonaliÄ™, hi-hat. Melodia gra dźwiÄ™k C, ale oktawÄ™ wyżej niż poprzednio, podobnie jak bas, tylko bas gra oktawÄ™ niżej niż poprzednio. CaÅ‚y utwór oparty jest na dźwiÄ™ku C, co pomimo monotonnej i maÅ‚o ciekawej aranżacji jest muzycznie poprawnie i nie powoduje faÅ‚szu ani dysonansu w odbiorze. +Po dziesiÄ™ciu epokach treningu melodia dalej wyglÄ…da na bardzo powtarzalnÄ…, jednak teraz jest bardziej spójna. Na przedstawionej na rysunku~\ref{fig:score10} partyturze widać, że model wygenerowaÅ‚ partiÄ™ gitary. Jednostajnie co ćwierćnutÄ™ gra akord C-G-C (tzw. Power Chord) popularnie stosowany w muzyce rockowej. Perkusja wybija tylko hi-hat. Melodia gra dźwiÄ™k C, ale oktawÄ™ wyżej niż poprzednio, podobnie jak bas, tylko bas gra oktawÄ™ niżej. CaÅ‚y utwór oparty jest na dźwiÄ™ku C, co pomimo monotonnej i maÅ‚o ciekawej aranżacji jest muzycznie poprawne i nie powoduje faÅ‚szu ani dysonansu w odbiorze. \begin{figure}[!htb] \centering @@ -1564,7 +1584,7 @@ PiÄ™tnaÅ›cie epok później, na rysunku~\ref{fig:score25} model generujÄ…cy gita \label{fig:score25} \end{figure} -Na rysunku~\ref{fig:score50} przedstawiono utwór po pięćdziesiÄ™ciu epokach. W tym momencie partia gitary zaczyna wykorzystywać dwa akordy. Daje to prostÄ… progresjÄ™ akordów a to mocno urozmaica utwór. Perkusja staÅ‚a siÄ™ bardziej jednolita a melodia ciekawsza. Bas w dalszym ciÄ…gu monotonnie wygrywa dźwiÄ™k C nawet w momentach, gdzie gitara gra akord B$\flat$. Lepsze w tej sytuacji byÅ‚o by zagranie B$\flat$ również na basie. +Na rysunku~\ref{fig:score50} przedstawiono utwór po pięćdziesiÄ™ciu epokach. W tym momencie partia gitary zaczyna wykorzystywać dwa akordy. Daje to prostÄ… progresjÄ™ akordów co mocno urozmaica utwór. Perkusja staÅ‚a siÄ™ bardziej jednolita a melodia ciekawsza. Bas w dalszym ciÄ…gu monotonnie wygrywa dźwiÄ™k C nawet w momentach, gdzie gitara gra akord B$\flat$. Lepsze w tej sytuacji byÅ‚oby zagranie B$\flat$ również na basie. \begin{figure}[!htb] \centering @@ -1573,7 +1593,7 @@ Na rysunku~\ref{fig:score50} przedstawiono utwór po pięćdziesiÄ™ciu epokach. \label{fig:score50} \end{figure} -Po siedemdziesiÄ™ciu piÄ™ciu epokach uczenia, generowany utwory zaczęły być o wiele ciekawsze, ale też bardziej chaotyczne. Partia gitary staÅ‚a siÄ™ melodyczna. W partii perkusji widzimy talerze a bas zaczÄ…Å‚ podążać za gitarÄ…. Pokazano opisanÄ… sytuacjÄ™ na rysunku~\ref{fig:score75}. +Po siedemdziesiÄ™ciu piÄ™ciu epokach uczenia, generowane utwory zaczęły być o wiele ciekawsze, ale też bardziej chaotyczne. Partia gitary staÅ‚a siÄ™ melodyczna. W partii perkusji widzimy talerze a bas zaczÄ…Å‚ podążać za gitarÄ…. Pokazano opisanÄ… sytuacjÄ™ na rysunku~\ref{fig:score75}. \begin{figure}[!htb] \centering @@ -1600,11 +1620,11 @@ Na rysunku~\ref{fig:score100} i rysunku~\ref{fig:score150} przedstawiono odpowie \chapter*{Podsumowanie} - Celem pracy byÅ‚o zaprezentowanie modelu, który byÅ‚by w stanie generować krótkie multiinstrumentalne utwory muzyczne. SÄ…dzÄ™ że cel pracy zostaÅ‚ osiÄ…gniÄ™ty. Model potrafi uczyć siÄ™ z plików MIDI oraz reprodukować muzykÄ™ podobnÄ… do tej, z której siÄ™ uczyÅ‚. Ocenienie jakoÅ›ci generowanej muzyki jest trudne i subiektywne, ale sÄ…dzÄ™ że przy odpowiednio dobranym zbiorze uczÄ…cym i konfiguracji można wygenerować ciekawe rezultaty. + Celem pracy byÅ‚o zaprezentowanie modelu, który byÅ‚by w stanie generować krótkie multiinstrumentalne utwory muzyczne. SÄ…dzÄ™, że cel pracy zostaÅ‚ osiÄ…gniÄ™ty. Model potrafi uczyć siÄ™ z plików MIDI oraz reprodukować muzykÄ™ podobnÄ… do tej, z której siÄ™ uczyÅ‚. Ocena jakoÅ›ci generowanej muzyki jest trudna i subiektywna. Uważam jednak, że przy odpowiednio dobranym zbiorze uczÄ…cym i dostosowanej konfiguracji można wygenerować ciekawe rezultaty. Pomimo, że zaprezentowany przeze mnie model posiada potencjaÅ‚ nie sÄ…dzÄ™, aby mógÅ‚ on zastÄ…pić ludzi w produkcji muzyki. Natomiast uważam, że mógÅ‚by zainspirować muzyków krótkim utworem, który nastÄ™pnie mógÅ‚by zostać rozbudowany przez nich do peÅ‚nego utworu. - Temat produkcji muzyki przez sztucznÄ… inteligencjÄ™ jest temat ciekawym jak również mocno zÅ‚ożonym i skomplikowanym. Istnieje wiele kwestii, które nie zostaÅ‚y poruszone w pracy jak generowanie tekstu piosenki, dobranie brzmienia instrumentów czy struktury utworu a z którymi muzycy potrafiÄ… sobie Å›wietnie dać radÄ™. Dlatego jest jeszcze miejsce na rozwój tej dziedziny sztucznej inteligencji w przyszÅ‚oÅ›ci. + Temat produkcji muzyki przez sztucznÄ… inteligencjÄ™ jest tematem ciekawym, jak również mocno zÅ‚ożonym i skomplikowanym. Istnieje wiele kwestii, które nie zostaÅ‚y poruszone w pracy, np. generowanie tekstu piosenki, dobranie brzmienia instrumentów czy struktury utworu, a z którymi muzycy potrafiÄ… sobie Å›wietnie radzić. Dlatego jest jeszcze miejsce na rozwój tej dziedziny sztucznej inteligencji w przyszÅ‚oÅ›ci. \begin{thebibliography}{99} diff --git a/docs/document.toc b/docs/document.toc index 8579afb..8d20ecb 100644 --- a/docs/document.toc +++ b/docs/document.toc @@ -22,28 +22,28 @@ \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 }Muzyczne ,,s\IeC {\l }owo''}{34}% -\contentsline {subsection}{\numberline {3.2.2\relax .\leavevmode@ifvmode \kern .5em }Konwersja MIDI na sekwencje s\IeC {\l }\IeC {\'o}w muzycznych}{34}% -\contentsline {subsection}{\numberline {3.2.3\relax .\leavevmode@ifvmode \kern .5em }Inne aspekty przygotowania danych}{37}% -\contentsline {subsection}{\numberline {3.2.4\relax .\leavevmode@ifvmode \kern .5em }Podzia\IeC {\l } danych na dane wej\IeC {\'s}ciowe i wyj\IeC {\'s}ciowe}{38}% -\contentsline {subsection}{\numberline {3.2.5\relax .\leavevmode@ifvmode \kern .5em }Inne aspekty przygotowania zbioru ucz\IeC {\k a}cego}{40}% -\contentsline {section}{\numberline {3.3\relax .\leavevmode@ifvmode \kern .5em }Definicja modelu}{42}% -\contentsline {subsection}{\numberline {3.3.1\relax .\leavevmode@ifvmode \kern .5em }Model w trybie uczenia}{42}% -\contentsline {subsection}{\numberline {3.3.2\relax .\leavevmode@ifvmode \kern .5em }Model w trybie wnioskowania}{44}% 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