# LZMidi: Compression-Based Symbolic Music Generation

arXiv: https://arxiv.org/abs/2503.17654 · HTML: https://mlsanity.com/paper/2503.17654/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 9 of its 25 references that are in the map.
- First posted on arXiv 22 Mar 2025.

## Placed in

- Diffusion models / [Audio, speech and music](https://mlsanity.com/diffusion/audio-speech-and-music/)

## Builds on (most cited first, 9 of 9)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Language Modeling Is Compression](https://mlsanity.com/paper/2309.10668/) (2023)
- [Symbolic Music Generation with Diffusion Models](https://mlsanity.com/paper/2103.16091/) (2021)
- [A Hierarchical Latent Vector Model for Learning Long-Term Structure in Music](https://mlsanity.com/paper/1803.05428/) (2018)
- [Encoding Musical Style with Transformer Autoencoders](https://mlsanity.com/paper/1912.05537/) (2019)
- [Composer Style-specific Symbolic Music Generation Using Vector Quantized Discrete Diffusion Models](https://mlsanity.com/paper/2310.14044/) (2023)

## Built on by (most cited first, 1 of 1)

- [SAGE-Music: Low-Latency Symbolic Music Generation via Attribute-Specialized Key-Value Head Sharing](https://mlsanity.com/paper/2510.00395/) (2025)

## Abstract (arXiv)

Recent advances in symbolic music generation primarily rely on deep learning models such as Transformers, GANs, and diffusion models. While these approaches achieve high-quality results, they require substantial computational resources, limiting their scalability. We introduce LZMidi, a lightweight symbolic music generation framework based on a Lempel-Ziv (LZ78)-induced sequential probability assignment (SPA). By leveraging the discrete and sequential structure of MIDI data, our approach enables efficient music generation on standard CPUs with minimal training and inference costs. Theoretically, we establish universal convergence guarantees for our approach, underscoring its reliability and robustness. Compared to state-of-the-art diffusion models, LZMidi achieves competitive Frechet Audio Distance (FAD), Wasserstein Distance (WD), and Kullback-Leibler (KL) scores, while significantly reducing computational overhead - up to 30x faster training and 300x faster generation. Our results position LZMidi as a significant advancement in compression-based learning, highlighting how universal compression techniques can efficiently model and generate structured sequential data, such as symbolic music, with practical scalability and theoretical rigor.