Various pose estimation and tracking problems in robotics can be decomposed into a correspondence estimation problem (often computed using a deep network) fol-lowed by a weighted least squares optimization problem to solve for the poses. Recent work has shown that coupling the two problems by iteratively refining one conditioned on the other's output yields SOTA results across domains. However, training these models has proved challenging, re-quiring a litany of tricks to stabilize and speed up training. In this work, we take the visual odometry problem as an example and identify three plausible causes: (1) flow loss interference, (2) linearization errors in the bundle adjust-ment (BA) layer, and (3) dependence of weight gradients on the BA residual. We show how these issues result in noisy and higher variance gradients, potentially leading to a slow down in training and instabilities. We then propose a sim-ple, yet effective solution to reduce the gradient variance by using the weights predicted by the network in the inner opti-mization loop to weight the correspondence objective in the training problem. This helps the training objective 'focus' on the more important points, thereby reducing the variance and mitigating the influence of outliers. We show that the resulting method leads to faster training and can be more flexibly trained in varying training setups without sacrificing performance. In particular we show 2-2.5x training speedups over a baseline visual odometry model we modify.

We present ReLU-QP, a GPU-accelerated solver for quadratic programs (QPs) that is capable of solving high-dimensional control problems at real-time rates. ReLU-QP is derived by exactly reformulating the Alternating Direction Method of Multipliers (ADMM) algorithm for solving QPs as a deep, weight-tied neural network with rectified linear unit (ReLU) activations. This reformulation enables the deployment of ReLU-QP on GPUs using standard machine-learning toolboxes. We evaluate the performance of ReLU-QP across three model-predictive control (MPC) benchmarks: stabilizing random linear dynamical systems with control limits, balancing an Atlas humanoid robot on a single foot, and performing a whole-body pick-up motion on a quadruped equipped with a six-degree-of-freedom arm. These benchmarks indicate that ReLU-QP is competitive with state-of-the-art CPU-based solvers for small-to-medium-scale problems and offers order-of-magnitude speed improvements for larger-scale problems.

Rapid growth in the number of nanosatellite deployments has heightened the need for rapid, cost-effective, and accurate orbit determination (OD). This paper introduces a solution to this "lost-in-space" problem that we call Visual-Inertial Navigation for Satellites (VINSat). VINSat performs OD using data from an inertial measurement unit (IMU) and a low-cost RGB camera. Machine learning techniques are used to identify known landmarks in images captured by the spacecraft. These landmark locations are then combined with IMU data and a dynamics model in a batch nonlinear least-squares state estimator to determine the full state of the spacecraft. We validate VINSat in simulation using real nadir-pointing imagery and find that 85% of simulated satellites are localized to under 5 km within 6 hours (4 orbits). This performance substantially surpasses that of ground radar, demonstrating significantly faster and more precise localization without any reliance on ground infrastructure.

Many tasks in deep learning involve optimizing over the inputs to a network to minimize or maximize some objective; examples include optimization over latent spaces in a generative model to match a target image, or adversarially perturbing an input to worsen classifier performance. Performing such optimization, however, is traditionally quite costly, as it involves a complete forward and backward pass through the network for each gradient step. In a separate line of work, a recent thread of research has developed the deep equilibrium (DEQ) model, a class of models that foregoes traditional network depth and instead computes the output of a network by finding the fixed point of a single nonlinear layer. In this paper, we show that there is a natural synergy between these two settings. Although, naively using DEQs for these optimization problems is expensive (owing to the time needed to compute a fixed point for each gradient step), we can leverage the fact that gradient-based optimization can itself be cast as a fixed point iteration to substantially improve the overall speed. That is, we simultaneously both solve for the DEQ fixed point and optimize over network inputs, all within a single "augmented" DEQ model that jointly encodes both the original network and the optimization process. Indeed, the procedure is fast enough that it allows us to efficiently train DEQ models for tasks traditionally relying on an "inner" optimization loop. We demonstrate this strategy on various tasks such as training generative models while optimizing over latent codes, training models for inverse problems like denoising and inpainting, adversarial training and gradient based meta-learning.

Semantic shape completion is a challenging problem in 3D computer vision where the task is to generate a complete 3D shape using a partial 3D shape as input. We propose a learning-based approach to complete incomplete 3D shapes through generative modeling and latent manifold optimization. Our algorithm works directly on point clouds. We use an autoencoder and a GAN to learn a distribution of embeddings for point clouds of object classes. An input point cloud with missing regions is first encoded to a feature vector. The representations learnt by the GAN are then used to find the best latent vector on the manifold using a combined optimization that finds a vector in the manifold of plausible vectors that is close to the original input (both in the feature space and the output space of the decoder). Experiments show that our algorithm is capable of successfully reconstructing point clouds with large missing regions with very high fidelity without having to rely on exemplar based database retrieval.

Poaching continues to be a significant threat to the conservation of wildlife and the associated ecosystem. Estimating and predicting where the poachers have committed or would commit crimes is essential to more effective allocation of patrolling resources. The real-world data in this domain is often sparse, noisy and incomplete, consisting of a small number of positive data (poaching signs), a large number of negative data with label uncertainty, and an even larger number of unlabeled data. Fortunately, domain experts such as rangers can provide complementary information about poaching activity patterns. However, this kind of human knowledge has rarely been used in previous approaches.

A class of recent approaches for generating images, called Generative Adversarial Networks (GAN), have been used to generate impressively realistic images of objects, bedrooms, handwritten digits and a variety of other image modalities. However, typical GAN-based approaches require large amounts of training data to capture the diversity across the image modality. In this paper, we propose DeLiGAN - a novel GAN-based architecture for diverse and limited training data scenarios. In our approach, we reparameterize the latent generative space as a mixture model and learn the mixture models parameters along with those of GAN. This seemingly simple modification to the GAN framework is surprisingly effective and results in models which enable diversity in generated samples although trained with limited data. In our work, we show that DeLiGAN can generate images of handwritten digits, objects and hand-drawn sketches, all using limited amounts of data. To quantitatively characterize intra-class diversity of generated samples, we also introduce a modified version of inception-score, a measure which has been found to correlate well with human assessment of generated samples.