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.

We present Value Propagation (VProp), a set of parameter-efficient differentiable planning modules built on Value Iteration which can successfully be trained using reinforcement learning to solve unseen tasks, has the capability to generalize to larger map sizes, and can learn to navigate in dynamic environments. We show that the modules enable learning to plan when the environment also includes stochastic elements, providing a cost-efficient learning system to build low-level size-invariant planners for a variety of interactive navigation problems. We evaluate on static and dynamic configurations of MazeBase grid-worlds, with randomly generated environments of several different sizes, and on a StarCraft navigation scenario, with more complex dynamics, and pixels as input.
We present planners based on convnets that are sample-efficient and that generalize to larger instances of navigation and pathfinding problems.

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 extbf{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.
Manifold-structured latent space for generative models

Posterior collapse in Variational Autoencoders (VAEs) arises when the variational distribution closely matches the uninformative prior for a subset of latent variables. This paper presents a simple and intuitive explanation for posterior collapse through the analysis of linear VAEs and their direct correspondence with Probabilistic PCA (pPCA). We identify how local maxima can emerge from the marginal log-likelihood of pPCA, which yields similar local maxima for the evidence lower bound (ELBO). We show that training a linear VAE with variational inference recovers a uniquely identifiable global maximum corresponding to the principal component directions. We provide empirical evidence that the presence of local maxima causes posterior collapse in deep non-linear VAEs. Our findings help to explain a wide range of heuristic approaches in the literature that attempt to diminish the effect of the KL term in the ELBO to reduce posterior collapse.
We show that posterior collapse in linear VAEs is caused entirely by marginal log-likelihood (not ELBO). Experiments on deep VAEs suggest a similar phenomenon is at play.