# Notochord: a Flexible Probabilistic Model for Real-Time MIDI Performance

arXiv: https://arxiv.org/abs/2403.12000 · HTML: https://mlsanity.com/paper/2403.12000/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 31 references that are in the map.
- First posted on arXiv 18 Mar 2024.

## Builds on (most cited first, 15 of 15)

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [DeepBach: a Steerable Model for Bach Chorales Generation](https://mlsanity.com/paper/1612.01010/) (2016)
- [This Time with Feeling: Learning Expressive Musical Performance](https://mlsanity.com/paper/1808.03715/) (2018)
- [PopMAG: Pop Music Accompaniment Generation](https://mlsanity.com/paper/2008.07703/) (2020)
- [A Comprehensive Survey on Deep Music Generation: Multi-level Representations, Algorithms, Evaluations, and Future Directions](https://mlsanity.com/paper/2011.06801/) (2020)
- [MMM : Exploring Conditional Multi-Track Music Generation with the Transformer](https://mlsanity.com/paper/2008.06048/) (2020)
- [GiantMIDI-Piano: A large-scale MIDI dataset for classical piano music](https://mlsanity.com/paper/2010.07061/) (2020)
- [Learning to Groove with Inverse Sequence Transformations](https://mlsanity.com/paper/1905.06118/) (2019)
- [MusIAC: An extensible generative framework for Music Infilling Applications with multi-level Control](https://mlsanity.com/paper/2202.05528/) (2022)
- [Learning a Latent Space of Multitrack Measures](https://mlsanity.com/paper/1806.00195/) (2018)
- [Performing Structured Improvisations with pre-trained Deep Learning Models](https://mlsanity.com/paper/1904.13285/) (2019)

## Abstract (arXiv)

Deep learning-based probabilistic models of musical data are producing increasingly realistic results and promise to enter creative workflows of many kinds. Yet they have been little-studied in a performance setting, where the results of user actions typically ought to feel instantaneous. To enable such study, we designed Notochord, a deep probabilistic model for sequences of structured events, and trained an instance of it on the Lakh MIDI dataset. Our probabilistic formulation allows interpretable interventions at a sub-event level, which enables one model to act as a backbone for diverse interactive musical functions including steerable generation, harmonization, machine improvisation, and likelihood-based interfaces. Notochord can generate polyphonic and multi-track MIDI, and respond to inputs with latency below ten milliseconds. Training code, model checkpoints and interactive examples are provided as open source software.