Related papers: A Method of Incorporating Matrix Theory to Create …
To train a machine learning model is necessary to take numerous decisions about many options for each process involved, in the field of sequence generation and more specifically of music composition, the nature of the problem helps to…
In this paper polynomial maps are represented by the use of matrices whose entries are numbered by pair of multiindices and a new product of such matrices is introduced. A matrix representation of composition of polynomial maps is given. In…
The role of integrable systems in string theory is discussed. We remind old examples of the correspondence between stringy partition functions or effective actions and integrable equations, based on effective application of the matrix model…
Modelling compositionality has been a longstanding area of research in the field of vector space semantics. The categorical approach to compositionality maps grammar onto vector spaces in a principled way, but comes under fire for requiring…
Matrix syntax is a formal model of syntactic relations in language. The purpose of this paper is to explain its mathematical foundations, for an audience with some formal background. We make an axiomatic presentation, motivating each axiom…
Deep Learning models have shown very promising results in automatically composing polyphonic music pieces. However, it is very hard to control such models in order to guide the compositions towards a desired goal. We are interested in…
Automatic music transcription converts audio recordings into symbolic representations, facilitating music analysis, retrieval, and generation. A musical note is characterized by pitch, onset, and offset in an audio domain, whereas it is…
Statistical modeling of popular music presents a unique challenge due to the complexity of song structures, which cannot be easily analyzed using conventional statistical tools. However, recent advances in data science have shown that…
Repetition is a basic indicator of musical structure. This study introduces new algorithms for identifying musical phrases based on repetition. Phrases combine to form sections yielding a two-level hierarchical structure. Automatically…
Applying the word2vec technique, commonly used in language modeling, to melodies, where notes are treated as words in sentences, enables the capture of pitch information. This study examines two datasets: 20 children's songs and an excerpt…
This paper introduces a new large-scale music dataset, MusicNet, to serve as a source of supervision and evaluation of machine learning methods for music research. MusicNet consists of hundreds of freely-licensed classical music recordings…
This paper provides a new mathematical axiom system for classical harmony, which is a prescriptive rule system for composing music, introduced in the second half of the 18th century. The clearest model of classical harmony is given by the…
We analyze the set of increasingly enumerable additive submonoids of R, for instance, the set of logarithms of the positive integers with respect to a given base. We call them $\omega$-monoids. The $\omega$-monoids for which consecutive…
We study polynomial optimization problems whose objective has a composition or tensor train structure. These polynomials can be evaluated as a sequence of maps, giving rise to intermediate variables (``states'') of dimension lower than the…
In this paper, we introduce new methods and discuss results of text-based LSTM (Long Short-Term Memory) networks for automatic music composition. The proposed network is designed to learn relationships within text documents that represent…
These notes present an approach to obtaining monoid operations which are compatible with a given family of mappings in the sense that the mappings become left translations in the monoid. This can be applied to various situations such as the…
We set up an algebraic theory of multivariable integration, based on a hierarchy of Rota-Baxter operators and an action of the matrix monoid as linear substitutions. Given a suitable coefficient domain with a bialgebra structure, this…
For arbitrary F-algebra, in which the operation of addition is defined, I explore biring of matrices of mappings. The sum of matrices is determined by the sum in F-algebra, and the product of matrices is determined by the product of…
Many music AI models learn a map between music content and human-defined labels. However, many annotations, such as chords, can be naturally expressed within the music modality itself, e.g., as sequences of symbolic notes. This observation…
Algorithmic composition is the partial or total automation of the process of music composition by using computers. Since the 1950s, different computational techniques related to Artificial Intelligence have been used for algorithmic…