Many machine learning techniques rely on minimizing the covariance between output feature dimensions to extract minimally redundant representations from data. However, these methods do not eliminate all dependencies/redundancies, as linearly uncorrelated variables can still exhibit nonlinear relationships. This work provides a differentiable and scalable algorithm for dependence minimization that goes beyond linear pairwise decorrelation. Our method employs an adversarial game where small networks identify dependencies among feature dimensions, while the encoder exploits this information to reduce dependencies. We provide empirical evidence of the algorithm's convergence and demonstrate its utility in three applications: extending PCA to nonlinear decorrelation, improving the generalization of image classification methods, and preventing dimensional collapse in self-supervised representation learning.

During training, supervised object detection tries to correctly match the predicted bounding boxes and associated classification scores to the ground truth. This is essential to determine which predictions are to be pushed towards which solutions, or to be discarded. Popular matching strategies include matching to the closest ground truth box (mostly used in combination with anchors), or matching via the Hungarian algorithm (mostly used in anchor-free methods). Each of these strategies comes with its own properties, underlying losses, and heuristics. We show how Unbalanced Optimal Transport unifies these different approaches and opens a whole continuum of methods in between. This allows for a finer selection of the desired properties. Experimentally, we show that training an object detection model with Unbalanced Optimal Transport is able to reach the state-of-the-art both in terms of Average Precision and Average Recall as well as to provide a faster initial convergence. The approach is well suited for GPU implementation, which proves to be an advantage for large-scale models.

Monocular 3D object detection has recently shown promising results, however there remain challenging problems. One of those is the lack of invariance to different camera intrinsic parameters, which can be observed across different 3D object datasets. Little effort has been made to exploit the combination of heterogeneous 3D object datasets. In contrast to general intuition, we show that more data does not automatically guarantee a better performance, but rather, methods need to have a degree of 'camera independence' in order to benefit from large and heterogeneous training data. In this paper we propose a category-level pose estimation method based on instance segmentation, using camera independent geometric reasoning to cope with the varying camera viewpoints and intrinsics of different datasets. Every pixel of an instance predicts the object dimensions, the 3D object reference points projected in 2D image space and, optionally, the local viewing angle. Camera intrinsics are only used outside of the learned network to lift the predicted 2D reference points to 3D. We surpass camera independent methods on the challenging KITTI3D benchmark and show the key benefits compared to camera dependent methods.