TASK DEFINITION: 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.
PROBLEM:  Auto-encoding and generative models have made tremendous successes in image and signal representation learning and generation. These models, however, generally employ the full Euclidean space or a bounded subset (such as $[0,1]^l$) as the latent space, whose trivial geometry is often too simplistic to meaningfully reflect the structure of the data. This paper aims at exploring a nontrivial geometric structure of the latent space for better data representation. Inspired by differential geometry, we propose \textbf{Chart Auto-Encoder (CAE)}, which captures the manifold structure of the data with multiple charts and transition functions among them. CAE translates the mathematical definition of manifold through parameterizing the entire data set as a collection of overlapping charts, creating local latent representations. These representations are an enhancement of the single-charted latent space commonly employed in auto-encoding models, as they reflect the intrinsic structure of the manifold.   Therefore, CAE achieves a more accurate approximation of data and generates realistic new ones. We conduct experiments with synthetic and real-life data to demonstrate the effectiveness of the proposed CAE.

SOLUTION: Manifold-structured latent space for generative models

PROBLEM: Most recent gains in visual recognition have originated from the inclusion of attention mechanisms in deep convolutional networks (DCNs). Because these networks are optimized for object recognition, they learn where to attend using only a weak form of supervision derived from image class labels. Here, we demonstrate the benefit of using stronger supervisory signals by teaching DCNs to attend to image regions that humans deem important for object recognition. We first describe a large-scale online experiment (ClickMe) used to supplement ImageNet with nearly half a million human-derived "top-down" attention maps. Using human psychophysics, we confirm that the identified top-down features from ClickMe are more diagnostic than "bottom-up" saliency features for rapid image categorization. As a proof of concept, we extend a state-of-the-art attention network and demonstrate that adding ClickMe supervision significantly improves its accuracy and yields visual features that are more interpretable and more similar to those used by human observers.

SOLUTION: A large-scale dataset for training attention models for object recognition leads to more accurate, interpretable, and human-like object recognition.

PROBLEM: Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo with simple mechanisms for proposing new states, which hinders exploration efficiency and often requires long runs to deliver accurate posterior estimates. In this paper we present an alternative approach: a variational framework for Bayesian phylogenetic analysis. We approximate the true posterior using an expressive graphical model for tree distributions, called a subsplit Bayesian network, together with appropriate branch length distributions. We train the variational approximation via stochastic gradient ascent and adopt multi-sample based gradient estimators for different latent variables separately to handle the composite latent space of phylogenetic models. We show that our structured variational approximations are flexible enough to provide comparable posterior estimation to MCMC, while requiring less computation due to a more efficient tree exploration mechanism enabled by variational inference. Moreover, the variational approximations can be readily used for further statistical analysis such as marginal likelihood estimation for model comparison via importance sampling. Experiments on both synthetic data and real data Bayesian phylogenetic inference problems demonstrate the effectiveness and efficiency of our methods.

SOLUTION:
The first variational Bayes formulation of phylogenetic inference, a challenging inference problem over structures with intertwined discrete and continuous components