text: In common real-world robotic operations, action and state spaces can be vast and sometimes unknown, and observations are often relatively sparse. How do we learn the full topology of action and state spaces when given only few and sparse observations? Inspired by the properties of grid cells in mammalian brains, we build a generative model that enforces a normalized pairwise distance constraint between the latent space and output space to achieve data-efficient discovery of output spaces. This method achieves substantially better results than prior generative models, such as Generative Adversarial Networks (GANs) and Variational Auto-Encoders (VAEs). Prior models have the common issue of mode collapse and thus fail to explore the full topology of output space. We demonstrate the effectiveness of our model on various datasets both qualitatively and quantitatively.
  @cite_49: Generating diverse yet specific data is the goal of the generative adversarial network (GAN), but it suffers from the problem of mode collapse. We introduce the concept of normalized diversity which force the model to preserve the normalized pairwise distance between the sparse samples from a latent parametric distribution and their corresponding high-dimensional outputs. The normalized diversification aims to unfold the manifold of unknown topology and non-uniform distribution, which leads to safe interpolation between valid latent variables. By alternating the maximization over the pairwise distance and updating the total distance (normalizer), we encourage the model to actively explore in the high-dimensional output space. We demonstrate that by combining the normalized diversity loss and the adversarial loss, we generate diverse data without suffering from mode collapsing. Experimental results show that our method achieves consistent improvement on unsupervised image generation, conditional image generation and hand pose estimation over strong baselines.
summary: Recent works have made substantial progress in imposing diversity constraint on the latent space of a generative model. In particular, Liu et. al. @cite_49 proposes the normalized diversification technique that effectively solves the problem of mode collapsing. Building on top of their prior work, we use a similar technique to learn an accurate encoding of action and state spaces in physical manipulation tasks. To our knowledge, our model is the first to use normalized diversification in these applications.