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

2025-08-02

AI Summary

This work addresses numerical instability and insufficient theoretical grounding in self-supervised learning for monophonic pitch estimation. We propose the first translation-equivariant self-supervised learning framework grounded in optimal transport (OT). Our method formalizes pitch translation invariance as Wasserstein distance minimization between one-dimensional probability distributions, yielding a theoretically rigorous, differentiable, and numerically stable loss function. Coupled with a translation-equivariant neural architecture, the framework enables end-to-end optimization. Crucially, this is the first systematic integration of OT theory into one-dimensional translation-equivariant signal modeling—replacing heuristic contrastive or reconstruction objectives prevalent in prior work. Evaluated on standard monophonic pitch estimation benchmarks, our approach achieves state-of-the-art performance, with marked improvements in training stability and generalization accuracy. These results empirically validate the framework’s theoretical soundness, computational robustness, and practical efficacy.

Technology Category

• Machine Learning: Unsupervised & Self-Supervised Learning
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• Develop translation-equivariant pitch estimation using Optimal Transport
• Improve numerical stability in self-supervised pitch estimation
• Simplify training for state-of-the-art pitch estimators

Innovation

• Optimal Transport for translation-equivariant learning
• Self-supervised pitch estimation method
• Numerically stable and simpler training