Interpretable Representation Learning from Videos using Nonlinear Priors

Learning interpretable representations of visual data is an important challenge, to make machines' decisions understandable to humans and to improve generalisation outside of the training distribution. To this end, we propose a deep learning framework where one can specify nonlinear priors for videos (e.g. of Newtonian physics) that allow the model to learn interpretable latent variables and use these to generate videos of hypothetical scenarios not observed at training time. We do this by extending the Variational Auto-Encoder (VAE) prior from a simple isotropic Gaussian to an arbitrary nonlinear temporal Additive Noise Model (ANM), which can describe a large number of processes (e.g. Newtonian physics). We propose a novel linearization method that constructs a Gaussian Mixture Model (GMM) approximating the prior, and derive a numerically stable Monte Carlo estimate of the KL divergence between the posterior and prior GMMs. We validate the method on different real-world physics videos including a pendulum, a mass on a spring, a falling object and a pulsar (rotating neutron star). We specify a physical prior for each experiment and show that the correct variables are learned. Once a model is trained, we intervene on it to change different physical variables (such as oscillation amplitude or adding air drag) to generate physically correct videos of hypothetical scenarios that were not observed previously.

Unsupervised Object Detection with Theoretical Guarantees

Unsupervised object detection using deep neural networks is typically a difficult problem with few to no guarantees about the learned representation. In this work we present the first unsupervised object detection method that is theoretically guaranteed to recover the true object positions up to quantifiable small shifts. We develop an unsupervised object detection architecture and prove that the learned variables correspond to the true object positions up to small shifts related to the encoder and decoder receptive field sizes, the object sizes, and the widths of the Gaussians used in the rendering process. We perform detailed analysis of how the error depends on each of these variables and perform synthetic experiments validating our theoretical predictions up to a precision of individual pixels. We also perform experiments on CLEVR-based data and show that, unlike current SOTA object detection methods (SAM, CutLER), our method's prediction errors always lie within our theoretical bounds. We hope that this work helps open up an avenue of research into object detection methods with theoretical guarantees.