Deep Declarative Dynamic Time Warping for End-to-End Learning of Alignment Paths
This addresses the need for differentiable DTW in applications like music information retrieval and robotics, offering a novel approach for end-to-end learning with alignment paths, though it is incremental relative to existing differentiable DTW methods.
The paper tackled the problem of learning end-to-end models for time series data with temporal alignment via dynamic time warping by proposing DecDTW, a method based on bi-level optimization and deep declarative networks, which outputs optimal warping paths and achieved state-of-the-art results in audio-to-score alignment and visual place recognition tasks.
This paper addresses learning end-to-end models for time series data that include a temporal alignment step via dynamic time warping (DTW). Existing approaches to differentiable DTW either differentiate through a fixed warping path or apply a differentiable relaxation to the min operator found in the recursive steps used to solve the DTW problem. We instead propose a DTW layer based around bi-level optimisation and deep declarative networks, which we name DecDTW. By formulating DTW as a continuous, inequality constrained optimisation problem, we can compute gradients for the solution of the optimal alignment (with respect to the underlying time series) using implicit differentiation. An interesting byproduct of this formulation is that DecDTW outputs the optimal warping path between two time series as opposed to a soft approximation, recoverable from Soft-DTW. We show that this property is particularly useful for applications where downstream loss functions are defined on the optimal alignment path itself. This naturally occurs, for instance, when learning to improve the accuracy of predicted alignments against ground truth alignments. We evaluate DecDTW on two such applications, namely the audio-to-score alignment task in music information retrieval and the visual place recognition task in robotics, demonstrating state-of-the-art results in both.