Autoencoders exhibit impressive abilities to embed the data manifold into a low-dimensional latent space, making them a staple of representation learning methods. However, without explicit supervision, which is often unavailable, the representation is usually uninterpretable, making analysis and principled progress challenging. We propose a framework, called latent responses, which exploits the locally contractive behavior exhibited by variational autoencoders to explore the learned manifold. More specifically, we develop tools to probe the representation using interventions in the latent space to quantify the relationships between latent variables. We extend the notion of disentanglement to take the learned generative process into account and consequently avoid the limitations of existing metrics that may rely on spurious correlations. Our analyses underscore the importance of studying the causal structure of the representation to improve performance on downstream tasks such as generation, interpolation, and inference of the factors of variation.

In this work, we present an approach to deep visuomotor control using structured deep dynamics models. Our model, a variant of SE3-Nets, learns a low-dimensional pose embedding for visuomotor control via an encoder-decoder structure. Unlike prior work, our model is structured: given an input scene, our network explicitly learns to segment salient parts and predict their pose embedding and motion, modeled as a change in the pose due to the applied actions. We train our model using a pair of point clouds separated by an action and show that given supervision only through point-wise data associations between the frames our network is able to learn a meaningful segmentation of the scene along with consistent poses. We further show that our model can be used for closed-loop control directly in the learned low-dimensional pose space, where the actions are computed by minimizing pose error using gradient-based methods, similar to traditional model-based control. We present results on controlling a Baxter robot from raw depth data in simulation and RGBD data in the real world and compare against two baseline deep networks. We also test the robustness and generalization performance of our controller under changes in camera pose, lighting, occlusion, and motion. Our method is robust, runs in real-time, achieves good prediction of scene dynamics, and outperforms baselines on multiple control runs. Video results can be found at: https://rse-lab.cs.washington.edu/se3-structured-deep-ctrl/.