In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Ex Input:
For numerous domains, including for instance earth observation, medical imaging, astrophysics,..., available image and signal datasets often irregular space-time sampling patterns and large missing data rates. These sampling properties is a critical issue to apply state-of-the-art learning-based (e.g., auto-encoders, CNNs,...) to fully benefit from the available large-scale observations and reach breakthroughs in the reconstruction and identification of processes of interest. In this paper, we address the end-to-end learning of representations of signals, images and image sequences from irregularly-sampled data, {\em i.e.} when the training data involved missing data. From an analogy to Bayesian formulation, we consider energy-based representations. Two energy forms are investigated: one derived from auto-encoders and one relating to Gibbs energies. The learning stage of these energy-based representations (or priors) involve a joint interpolation issue, which resorts to solving an energy minimization problem under observation constraints. Using a neural-network-based implementation of the considered energy forms, we can state an end-to-end learning scheme from irregularly-sampled data. We demonstrate the relevance of the proposed representations for different case-studies: namely, multivariate time series, 2{\sc } images and image sequences.

Ex Output:
We address the end-to-end learning of energy-based representations for signal and image observation dataset with irregular sampling patterns.


Ex Input:
We consider reinforcement learning and bandit structured prediction problems with very sparse loss feedback: only at the end of an episode. We introduce a novel algorithm, RESIDUAL LOSS PREDICTION (RESLOPE), that solves such problems by automatically learning an internal representation of a denser reward function. RESLOPE operates as a reduction to contextual bandits, using its learned loss representation to solve the credit assignment problem, and a contextual bandit oracle to trade-off exploration and exploitation. RESLOPE enjoys a no-regret reduction-style theoretical guarantee and outperforms state of the art reinforcement learning algorithms in both MDP environments and bandit structured prediction settings.

Ex Output:
We present a novel algorithm for solving reinforcement learning and bandit structured prediction problems with very sparse loss feedback.


Ex Input:
In this paper, we study the representational power of deep neural networks (DNN) that belong to the family of piecewise-linear (PWL) functions, based on PWL activation units such as rectifier or maxout. We investigate the complexity of such networks by studying the number of linear regions of the PWL function. Typically, a PWL function from a DNN can be seen as a large family of linear functions acting on millions of such regions. We directly build upon the work of Mont´ufar et al. (2014), Mont´ufar (2017), and Raghu et al. (2017) by refining the upper and lower bounds on the number of linear regions for rectified and maxout networks. In addition to achieving tighter bounds, we also develop a novel method to perform exact numeration or counting of the number of linear regions with a mixed-integer linear formulation that maps the input space to output. We use this new capability to visualize how the number of linear regions change while training DNNs.  

Ex Output:

We empirically count the number of linear regions of rectifier networks and refine upper and lower bounds.