Related papers: Melody and Variation Generation Through KAM Theory

We consider a class of "harmonic variations" for nonsingular curves, obtained as asymptotic degenerations along bitangents. On a geometric level, we obtain an attractive relationship between the class and the genus of $C$. The distribution…

Automatic melody generation has been a long-time aspiration for both AI researchers and musicians. However, learning to generate euphonious melodies has turned out to be highly challenging. This paper introduces 1) a new variant of…

Machine-learning techniques have been recently used with spectacular results to generate artefacts such as music or text. However, these techniques are still unable to capture and generate artefacts that are convincingly structured. In this…

We argue that the mathematical structure, enabling certain cascading and emergent phenomena to intuitively emerge, coincides with Galois connections. We introduce the notion of generative effects to formally capture such phenomena. We…

In this note, we investigate the dynamics of invariant circles in area-preserving twist maps. The invariant circles under consideration lie beyond the applicability of classical KAM theory, as the perturbations involved exceed the scope of…

In this work, we propose a symbolic music generation model with the song structure graph analysis network. We construct a graph that uses information such as note sequence and instrument as node features, while the correlation between note…

Our goal is to be able to build a generative model from a deep neural network architecture to try to create music that has both harmony and melody and is passable as music composed by humans. Previous work in music generation has mainly…

Multi-modal music generation, using multiple modalities like text, images, and video alongside musical scores and audio as guidance, is an emerging research area with broad applications. This paper reviews this field, categorizing music…

We prove an abstract KAM theorem adapted to space-multidimensional hamiltonian PDEs with regularizing nonlinearities. It applies in particular to the singular perturbation problem studied in the first part of this work.

We prove that there is an invariant torus with given Diophantine frequency vector for a class of Hamiltonian systems defined by an integrable large Hamiltonian function with a large non-autonomous Hamiltonian perturbation. As for…

This study proposes a system designed to enumerate the process of collaborative composition among humans, using automatic music composition technology. By integrating multiple Recurrent Neural Network (RNN) models, the system provides an…

Attempts to use generative models for music generation have been common in recent years, and some of them have achieved good results. Pieces generated by some of these models are almost indistinguishable from those being composed by human…

A model of music needs to have the ability to recall past details and have a clear, coherent understanding of musical structure. Detailed in the paper is a deep reinforcement learning architecture that predicts and generates polyphonic…

We describe a system based on deep learning that generates drum patterns in the electronic dance music domain. Experimental results reveal that generated patterns can be employed to produce musically sound and creative transitions between…

Most music generation models directly generate a single music mixture. To allow for more flexible and controllable generation, the Multi-Source Diffusion Model (MSDM) has been proposed to model music as a mixture of multiple instrumental…

We shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non-analytic perturbation (the latter will be assumed to have continuous derivatives up to a sufficiently large order). We shall…

In this paper, we propose a generic technique to model temporal dependencies and sequences using a combination of a recurrent neural network and a Deep Belief Network. Our technique, RNN-DBN, is an amalgamation of the memory state of the…

We provide a symplectic reduction of a partially integrable Hamiltonian system to a completely integrable one. The KAM theorem is applied to this reduced completely integrable Hamiltonian system. Its KAM perturbation generates a…

The use of deep learning to solve problems in literary arts has been a recent trend that has gained a lot of attention and automated generation of music has been an active area. This project deals with the generation of music using raw…

In this paper we describe how to derive the expressions for the higher nonlinear generation of waves, their transmission and reflection for the case of a normal incidence plane wave by direct superposition of nonlinear dipoles. We describe…