LIFT-GS: Cross-Scene Render-Supervised Distillation for 3D Language Grounding

Our approach to training 3D vision-language understanding models is to train a feedforward model that makes predictions in 3D, but never requires 3D labels and is supervised only in 2D, using 2D losses and differentiable rendering. The approach is new for vision-language understanding. By treating the reconstruction as a ``latent variable'', we can render the outputs without placing unnecessary constraints on the network architecture (e.g. can be used with decoder-only models). For training, only need images and camera pose, and 2D labels. We show that we can even remove the need for 2D labels by using pseudo-labels from pretrained 2D models. We demonstrate this to pretrain a network, and we finetune it for 3D vision-language understanding tasks. We show this approach outperforms baselines/sota for 3D vision-language grounding, and also outperforms other 3D pretraining techniques. Project page: https://liftgs.github.io.

On Linear Separability under Linear Compression with Applications to Hard Support Vector Machine

This paper investigates the theoretical problem of maintaining linear separability of the data-generating distribution under linear compression. While it has been long known that linear separability may be maintained by linear transformations that approximately preserve the inner products between the domain points, the limit to which the inner products are preserved in order to maintain linear separability was unknown. In this paper, we show that linear separability is maintained as long as the distortion of the inner products is smaller than the squared margin of the original data-generating distribution. The proof is mainly based on the geometry of hard support vector machines (SVM) extended from the finite set of training examples to the (possibly) infinite domain of the data-generating distribution. As applications, we derive bounds on the (i) compression length of random sub-Gaussian matrices; and (ii) generalization error for compressive learning with hard-SVM.