# Translation-Equivariant Self-Supervised Learning for Pitch Estimation with Optimal Transport

arXiv: https://arxiv.org/abs/2508.01493 · HTML: https://mlsanity.com/paper/2508.01493/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 26 references that are in the map.
- First posted on arXiv 2 Aug 2025.

## Builds on (most cited first, 12 of 12)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [CREPE: A Convolutional Representation for Pitch Estimation](https://mlsanity.com/paper/1802.06182/) (2018)
- [SPICE: Self-supervised Pitch Estimation](https://mlsanity.com/paper/1910.11664/) (2019)
- [The Wasserstein-Fourier Distance for Stationary Time Series](https://mlsanity.com/paper/1912.05509/) (2019)
- [PESTO: Pitch Estimation with Self-supervised Transposition-equivariant Objective](https://mlsanity.com/paper/2309.02265/) (2023)
- [Cross-domain Neural Pitch and Periodicity Estimation](https://mlsanity.com/paper/2301.12258/) (2023)
- [Optimal spectral transportation with application to music transcription](https://mlsanity.com/paper/1609.09799/) (2016)
- [Equivariant Self-Supervision for Musical Tempo Estimation](https://mlsanity.com/paper/2209.01478/) (2022)
- [Unsupervised Harmonic Parameter Estimation Using Differentiable DSP and Spectral Optimal Transport](https://mlsanity.com/paper/2312.14507/) (2023)
- [STONE: Self-supervised Tonality Estimator](https://mlsanity.com/paper/2407.07408/) (2024)
- [Toward Fully Self-Supervised Multi-Pitch Estimation](https://mlsanity.com/paper/2402.15569/) (2024)
- [S-KEY: Self-supervised Learning of Major and Minor Keys from Audio](https://mlsanity.com/paper/2501.12907/) (2025)

## Abstract (arXiv)

In this paper, we propose an Optimal Transport objective for learning one-dimensional translation-equivariant systems and demonstrate its applicability to single pitch estimation. Our method provides a theoretically grounded, more numerically stable, and simpler alternative for training state-of-the-art self-supervised pitch estimators.