VAEs (Variational AutoEncoders) have proved to be powerful in the context of density modeling and have been used in a variety of contexts for creative purposes. In many settings, the data we model possesses continuous attributes that we would like to take into account at generation time. We propose in this paper GLSR-VAE, a Geodesic Latent Space Regularization for the Variational AutoEncoder architecture and its generalizations which allows a fine control on the embedding of the data into the latent space. When augmenting the VAE loss with this regularization, changes in the learned latent space reflects changes of the attributes of the data. This deeper understanding of the VAE latent space structure offers the possibility to modulate the attributes of the generated data in a continuous way. We demonstrate its efficiency on a monophonic music generation task where we manage to generate variations of discrete sequences in an intended and playful way.

This paper introduces DeepBach, a graphical model aimed at modeling polyphonic music and specifically hymn-like pieces. We claim that, after being trained on the chorale harmonizations by Johann Sebastian Bach, our model is capable of generating highly convincing chorales in the style of Bach. DeepBach's strength comes from the use of pseudo-Gibbs sampling coupled with an adapted representation of musical data. This is in contrast with many automatic music composition approaches which tend to compose music sequentially. Our model is also steerable in the sense that a user can constrain the generation by imposing positional constraints such as notes, rhythms or cadences in the generated score. We also provide a plugin on top of the MuseScore music editor making the interaction with DeepBach easy to use.

We introduce a Maximum Entropy model able to capture the statistics of melodies in music. The model can be used to generate new melodies that emulate the style of the musical corpus which was used to train it. Instead of using the $n-$body interactions of $(n-1)-$order Markov models, traditionally used in automatic music generation, we use a $k-$nearest neighbour model with pairwise interactions only. In that way, we keep the number of parameters low and avoid over-fitting problems typical of Markov models. We show that long-range musical phrases don't need to be explicitly enforced using high-order Markov interactions, but can instead emerge from multiple, competing, pairwise interactions. We validate our Maximum Entropy model by contrasting how much the generated sequences capture the style of the original corpus without plagiarizing it. To this end we use a data-compression approach to discriminate the levels of borrowing and innovation featured by the artificial sequences. The results show that our modelling scheme outperforms both fixed-order and variable-order Markov models. This shows that, despite being based only on pairwise interactions, this Maximum Entropy scheme opens the possibility to generate musically sensible alterations of the original phrases, providing a way to generate innovation.

Markov processes are widely used to generate sequences that imitate a given style, using random walk. Random walk generates sequences by iteratively concatenating states to prefixes of length equal or less than the given Markov order}. However, at higher orders, Markov chains tend to replicate chunks of the corpus with a size possibly higher than the order, a primary form of plagiarism. The Markov order defines a maximum length for training but not for generation. In the framework of constraint satisfaction (CSP), we introduce MaxOrder. This global constraint ensures that generated sequences do not include chunks larger than a given maximum order. We exhibit an automaton that recognises the solution set, with a size linear in the size of the corpus. We propose a linear-time procedure to generate this automaton from a corpus and a given max order. We then use this automaton to achieve generalised arc consistency for the MaxOrder constraint, holding on a sequence of size n, in O(n.T) time, where T is the size of the automaton. We illustrate our approach by generating text sequences from text corpora with a maximum order guarantee, effectively controlling plagiarism.