text: [Summary] The paper is overall well written  and the literature review fairly up to date. The main issue is the lack of novelty. The proposed method is just a straightforward dimensionality reduction based on convolutional and max pooling layers. Using CNNs to handle variable length time series is hardly novel. In addition, as always with metric learning, why learning the metric if you can just learn the classifier? If the metric is not used in some compelling application, I am not convinced. [Detailed comments and suggestions] * Since "assumptions" is the only subsection in Section 2,  I would use \texbf{Assumptions.} rather than \subsection{Assumptions}. * Same remark for Section 4.1 "Complexity analysis". * Some missing relevant citations: Learning the Metric for Aligning Temporal Sequences. Damien Garreau, Rémi Lajugie, Sylvain Arlot, Francis Bach. In Proc. of NIPS 2014. Deep Convolutional Neural Networks On Multichannel Time Series For Human Activity Recognition. Jian Bo Yang, Minh Nhut Nguyen, Phyo Phyo San, Xiao Li Li, Shonali Krishnaswamy. In Proc.  of IJCAI 2015. Time Series Classification Using Multi-Channels Deep Convolutional Neural Networks Yi ZhengQi LiuEnhong ChenYong GeJ. Leon Zhao. In Proc. of International Conference on Web-Age Information Management. Soft-DTW: a Differentiable Loss Function for Time-Series. Marco Cuturi, Mathieu Blondel. In Proc. of ICML 2017.