Markov constraints: steerable generation of Markov sequences

Abstract

Markov chains are a well known tool to model temporal properties of many phenomena, from text structure to fluctuations in economics. Because they are easy to generate, Markovian sequences, i.e. temporal sequences having the Markov property, are also used for content generation applications such as text or music generation that imitate a given style. However, Markov sequences are traditionally generated using greedy, left-to-right algorithms. While this approach is computationally cheap, it is fundamentally unsuited for interactive control. This paper addresses the issue of generating steerable Markovian sequences. We target interactive applications such as games, in which users want to control, through simple input devices, the way the system generates a Markovian sequence, such as a text, a musical sequence or a drawing. To this aim, we propose to revisit Markov sequence generation as a branch and bound constraint satisfaction problem (CSP). We propose a CSP formulation of the basic Markovian hypothesis as elementary Markov Constraints (EMC). We propose algorithms that achieve domain-consistency for the propagators of EMCs, in an event-based implementation of CSP. We show how EMCs can be combined to estimate the global Markovian probability of a whole sequence, and accommodate for different species of Markov generation such as fixed order, variable-order, or smoothing. Such a formulation, although more costly than traditional greedy generation algorithms, yields the immense advantage of being naturally steerable, since control specifications can be represented by arbitrary additional constraints, without any modification of the generation algorithm. We illustrate our approach on simple yet combinatorial chord sequence and melody generation problems and give some performance results.

Neural Melody Composition from Lyrics

“…Chan, Potter, and Schubert (2006) design rules from music theory to use music clips to stitch them together in a reasonable way. With the development of machine learning and the increase of public music data, data-driven methods such as Markov chains model (Pachet and Roy 2011) and graphic model (Pachet, Papadopoulos, and Roy 2017) have been introduced to compose music. Recently, deep learning has been revealed the potentials for musical creation.…”

A Viewpoint Approach to Symbolic Music Transformation

“…Another possible constraint consists in generating sequences respecting a given structure (i.e., controlling how chords repeat along the sequence). The idea of constraining some chords along the generation process has also been explored by [14,10]. The structure constraint is interesting in our context of transformation since it enables the conservation of the harmonic structure of the template piece.…”

Multidisciplinary Contributions to the Science of Creative Thinking

“…The description of these techniques is outside the scope of this paper and the interested reader is referred to Pachet and Roy (2011) and Roy and Pachet (2013). The project has produced novel techniques to solve this problem in the sequential domain.…”