Soft Dynamic Time Warping for Multi-Pitch Estimation and Beyond

Many tasks in music information retrieval (MIR) involve weakly aligned data, where exact temporal correspondences are unknown. The connectionist temporal classification (CTC) loss is a standard technique to learn feature representations based on weakly aligned training data. However, CTC is limited to discrete-valued target sequences and can be difficult to extend to multi-label problems. In this article, we show how soft dynamic time warping (SoftDTW), a differentiable variant of classical DTW, can be used as an alternative to CTC. Using multi-pitch estimation as an example scenario, we show that SoftDTW yields results on par with a state-of-the-art multi-label extension of CTC. In addition to being more elegant in terms of its algorithmic formulation, SoftDTW naturally extends to real-valued target sequences.