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

ABSTRACT 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. 1. INTRODUCTION Pitch estimation is a core task in audio analysis, long studied in the speech and Music Information Retrieval (MIR) communities [1]. It involves estimating the fundamental frequency of harmonic or quasi-harmonic signals, with traditional methods relying on signal processing techniques to extract harmonicity cues [2-4], or by matching the input spectrum to that of a synthetic waveform [5]. Recently, supervised deep learning approaches leveraging large annotated datasets (such as CREPE [6]) have achieved impressive accuracy, but come with notable challenges. In particular, labeling audio with the temporal precision needed for training (typically within a few milliseconds) is labor-intensive and prone to errors.