Identifying an effective model of a dynamical system from sensory data and using it for future state prediction and control is challenging. Recent data-driven algorithms based on Koopman theory are a promising approach to this problem, but they typically never update the model once it has been identified from a relatively small set of observation, thus making long-term prediction and control difficult for realistic systems, in robotics or fluid mechanics for example. This paper introduces a novel method for learning an embedding of the state space with linear dynamics from sensory data. Unlike previous approaches, the dynamics model can be updated online and thus easily applied to systems with non-linear dynamics in the original configuration space. The proposed approach is evaluated empirically on several classical dynamical systems and sensory modalities, with good performance on long-term prediction and control.

Historical watermark recognition is a highly practical, yet unsolved challenge for archivists and historians. With a large number of well-defined classes, cluttered and noisy samples, different types of representations, both subtle differences between classes and high intra-class variation, historical watermarks are also challenging for pattern recognition. In this paper, overcoming the difficulty of data collection, we present a large public dataset with more than 6k new photographs, allowing for the first time to tackle at scale the scenarios of practical interest for scholars: one-shot instance recognition and cross-domain one-shot instance recognition amongst more than 16k fine-grained classes. We demonstrate that this new dataset is large enough to train modern deep learning approaches, and show that standard methods can be improved considerably by using mid-level deep features. More precisely, we design both a matching score and a feature fine-tuning strategy based on filtering local matches using spatial consistency. This consistency-based approach provides important performance boost compared to strong baselines. Our model achieves 55% top-1 accuracy on our very challenging 16,753-class one-shot cross-domain recognition task, each class described by a single drawing from the classic Briquet catalog. In addition to watermark classification, we show our approach provides promising results on fine-grained sketch-based image retrieval.