We will introduce a new generative model for music composition, applying Langevin dynamics to a gradient-based score matching algorithm based on Song and Ermon, 2019. Unlike implicit models such as GANs, this learns a true, explicit distribution of the input data.

Previous work has seen a success on modeling from continuous input manifolds, such high-quality image inpainting and conditional sampling from MNIST, CIFAR-10, and other datasets. However, it is an open question whether this algorithm can be adjusted to perform well on discrete domains, such as music scores.

We hope that Langevin dynamics and score matching can combine the controllability and of Markov chain Monte Carlo, with the global view and fast convergence of stochastic gradient descent, to generate high-quality structured, compositions.

DeepBach is a simple and controllable autoregressive model for Bach chorale generation, which are features that make it easy to train and use. In particular, learning Bach chorales is an interesting task because the music is highly structured (often following various "rules"), consistent, and often complex.

However, there are many instances where DeepBach is unable to capture long-term structure. Some casual listeners have remarked that the compositions "sound good but go nowhere". This could be due to a combination of vanishing LSTM gradients, and Gibbs sampling getting stuck in 1-optimal local minima.

We believe by applying enough tricks, it should be possible to produce a model that strongly avoids these local minima, while retaining controllability.

It was seen in Welling and Teh, 2011 that directing traditional MCMC algorithms with learned supervision can greatly accelerate their convergence. This is what motivates us to augment DeepBach's approach with score matching.

It's interesting to analyze other approaches that people have tried in the past:

• Generative adversarial networks: Although GANs acheive very promising results in modeling latent distributions of images, it's difficult to train them on sequence tasks (discrete tokens), as gradients need to propagate from the discrminator to the generator (Yu et al., 2016).
• Transformers: Transformers have been applied to the task of music generation and achieved state-of-the-art results on at least one dataset (Huang et al., 2018). However, transformers are computationally expensive, so they're not easily controllable through masking and iterative MCMC-like algorithms.
• Markov random fields: MRFs have been used for generative models to optimize an energy function, notably for bitmap image generation in ConvChain. This lends credence to MCMC for discrete probabilistic modeling. However, as previously mentioned, it doesn't learn global structure. Also, the alternative approach of gradient ascent is impractical due to adversarial perturbations.

We think that score matching and Langevin dynamics, by adding graded noise to the distribution of data, has the potential to perform well on generative sequence modeling tasks such as music composition, while maintaining the controllability of models like DeepBach.

This project will be successful if we can implement a score matching algorithm for music generation and evaluate its feasibility. In the best case, score matching can be used to improve long-term patterns and interpretability. However, due to the complexity of the algorithm, results are unclear, and we may need various tricks or innovations to obtian convergence.

Our goal, then, is to determine the tractability and performance of a score-matching approach in the discrete domain, which we think is very exciting.