Povratne neuronske mreže i primjene

master's thesis

• Title (english): Recurrent neural networks and applications
• Author: Stipe Kabić
• Mentor: Zvonimir Bujanović (mentor)
• Committee member: Ivica Nakić (predsjednik povjerenstva)
• Committee member: Hrvoje Šikić (član povjerenstva)
• Committee member: Nenad Antonić (član povjerenstva)
• Committee member: Pavle Goldstein (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-03-02, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu dali smo osnovni teorijski uvod u neuronske mreže i motivirali njihovo korištenje. Nakon toga smo precizno izveli algoritam za njihovo treniranje nad podacima. Zatim smo detaljnije obradili povratne neuronske mreže, analizirali glavne probleme koji se javljaju prilikom njihovog treniranja te predstavili naprednije verzije takvih mreža koje rješavaju te probleme, a to su LSTM i GRU mreže. Nakon toga, predstavili smo problem separacije instrumenata iz glazbe te ga matematički opisali. Nadalje, prikazali smo osnovne rezultate o Fourierovim transformacijama koji su nam omogućili jednostavnije modeliranje tog problema. Također smo izveli algoritam za brzo računanje diskretne Fourierove transformacije koji nam je olakšao praktičnu primjenu iste. Ti su nas rezultati doveli do pojma spektrograma koji predstavlja prikladan način zapisa zvučnih podataka s ciljem primjene neuronskih mreža na njih. Konačno, predložili smo arhitekturu neuronske mreže koja je temeljena na povratnim mrežama i primijenili ju na problem separacije. Na samom kraju prikazali smo rezultate ovog modela i ukratko ih analizirali.

Abstract (english)

In this thesis we gave a basic theoretical introduction to neural networks and motivated their practical use. After that, we precisely worked out an alogorithm for training these networks on data. Next, we analyzed recurrent neural networks in more detail, worked out the main problems with their training and introduced more advanced versions of these networks which are the LSTM and GRU networks. Afterwards, we introduced the problem of music source separation and described it mathematically. We introduced basic results about Fourier transformations which allowed us to model this problem more easily. We also derived an algorithm for faster calculation of the discrete Fourier transform which made practical use of this transformation easier. These results led us to the definition of the spectrogram as an appropriate way of describing audio data with the goal of training neural networks on it. Finally, we defined a neural network architecture based on recurrent networks and applied it to the problem of music source separation. At the very end, we described the results of this model and briefly analyzed them.

• Keywords: neuronska mreža; LSTM; GRU mreža; separacija instrumenata iz glazbe; Fourierove transformacije; spektrogram
• Keywords (english): neural network; LSTM; GRU networks; music source separation; Fourier transformations; spectrogram
• Language: croatian
• URN:NBN: urn:nbn:hr:217:857092
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2023-07-25 12:27:35