Section: New Results
Music Content Processing and Information Retrieval
Music structure, music language modeling, System & Contrast model, complexity
Current work developed in our research group in the domain of music content processing and information retrieval explore various informationtheoretic frameworks for music structure analysis and description [58], in particular the System & Contrast model [1].
Modeling music by Polytopic Graphs of Latent Relations (PGLR)
Participants : Corentin Louboutin, Frédéric Bimbot.
The musical content observed at a given instant within a music segment obviously tends to share privileged relationships with its immediate past, hence the sequential perception of the music flow. But local music content also relates with distant events which have occurred in the longer term past, especially at instants which are metrically homologous (in previous bars, motifs, phrases, etc.) This is particularly evident in strongly “patterned” music, such as pop music, where recurrence and regularity play a central role in the design of cyclic musical repetitions, anticipations and surprises.
The web of musical elements can be described as a Polytopic Graph of Latent Relations (PGLR) which models relationships developing predominantly between homologous elements within the metrical grid.
For regular segments the PGLR lives on an $n$dimensional cube(square, cube, tesseract, etc...), $n$ being the number of scales considered simultaneously in the multiscale model. By extension, the PGLR can be generalized to a more or less regular $n$dimensional polytopes.
Each vertex in the polytope corresponds to a lowscale musical element, each edge represents a relationship between two vertices and each face forms an elementary system of relationships.
The estimation of the PGLR structure of a musical segment can be obtained computationally as the joint estimation of the description of the polytope, the nesting configuration of the graph over the polytope (reflecting the flow of dependencies and interactions between the elements within the musical segment) and the set of relations between the nodes of the graph, with potentially multiple possibilities.
If musical elements are chords, relations can be inferred by minimal transport [79] defined as the shortest displacement of notes, in semitones, between a pair of chords. Other chord representations and relations are possible, as studied in [81] where the PGLR approach is presented conceptually and algorithmically, together with an extensive evaluation on a large set of chord sequences from the RWC Pop corpus (100 pop songs).
Specific graph configurations, called Primer Preserving Permutations (PPP) are extensively studied in [80] and are related to 6 main redundant sequences which can be viewed as canonical multiscale structural patterns.
In parallel, recent work has also been dedicated to modeling melodic and rhythmic motifs in order to extend the polytopic model to multiple musical dimensions.
Results obtained in this framework illustrate the efficiency of the proposed model in capturing structural information within musical data and support the view that musical content can be delinearised in order to better describe its structure. Extensive results are included in Corentin Louboutin's PhD [13], defended in March 2019 and which was awarded the Prix Jeune Chercheur Science et Musique, in October.
Exploring Structural Dependencies in Melodic Sequences using Neural Networks
Participants : Nathan Libermann, Frédéric Bimbot.
This work is carried out in the framework of a PhD, codirected by Emmanuel Vincent (InriaNancy).
In order to be able to generate structured melodic phrases and section, we explore various schemes for modeling dependencies between notes within melodies, using deep learning frameworks.
A a first set of experiments, we have considered a GRUbased sequential learning model, studied under different learning scenarios in order to better understand the optimal architectures in this context that can achieve satisfactory results. By this means, we wish to explore different hypotheses relating to temporal noninvariance relationships between notes within a structural segment (motif, phrase, section).
We have defined three types of recursive architectures corresponding to different ways to exploit the local history of a musical note, in terms of information encoding and generalization capabilities.
Initially conducted on the Lakh MIDI dataset, experiments have switched to the Meertens Tune Collections data set (Dutch traditional melodies) and confirm the trends observed in [78], w.r.t. the utility of nonergodic models for the generation of melodic segments.
Ongoing work is extending these findings to the design of specific NN architectures, which incorporate attention models, to account for this noninvariance of information across musical segments.
Graph Signal Processing for Multiscale Representations of Music Similarity
Participants : Valentin Gillot, Frédéric Bimbot.
“Music Similarity” is a multifaceted concept at the core of Music Information Retrieval (MIR). Among the wide range of possible definitions and approaches to this notion, a popular one is the computation of a socalled contentbased similarity matrix (S), in which each coefficient is a similarity measure between descriptors of short time frames at different instants within a music piece or a collection of pieces.
Matrix S can be seen as the adjacency matrix of an underlying graph, embodying the local and nonlocal similarities between parts of the music material. Considering the nodes of this graph as a new set of indices for the original music frames or pieces opens the door to a “delinearized” representation of music, emphasizing its structure and its semiotic content.
Graph Signal Processing (GSP) is an emerging topic devoted to extend usual signal processing tools (Fourier analysis, filtering, denoising, compression, ...) to signals “living” on graphs rather than on the time line, and to exploit mathematical and algorithmic tools on usual graphs, in order to better represent and manipulate these signals. Toy applications of GSP concepts on music content in music resequencing and music inpainting are illustrating this trend.
From exploratory experiments, first observations point towards the following hypotheses :

local and nonlocal structures of a piece are highlighted in the adjacency matrix built from a simple timefrequency representation of the piece,

the first eigenvectors of the graph Laplacian provide a rough structural segmentation of the piece,

clusters of frames built from the eigenvectors contain similar, repetitive sound sequences.
The goal of Valentin Gillot's PhD is to consolidate these hypotheses and investigate further the topic of Graph Signal Processing for music, with more powerful conceptual tools and experiments at a larger scale.
The core of the work will consist in designing a methodology and implement an evaluation framework so as to (i) compare different descriptors and similarity measures and their capacity to capture relevant structural information in music pieces or collection of pieces, (ii) explore the structure of musical pieces by refining the frame clustering process, in particular with a multiresolution approach, (iii) identify salient characteristics of graphs in relation to midlevel structure models and (iv) perform statistics on the typical properties of the similarity graphs on a large corpus of music in relation to music genres and/or composers.
By the end of the PhD, we expect the release of a specific toolbox for music composition, remixing and repurposing using the concepts and algorithms developed during the PhD. First results obtained this year in music recomposition have proven very conclusive [32].