Lei Li

Yang Jing, Lei Li

Deep generative models aim to learn the underlying distribution of data and generate new ones. Despite the diversity of generative models and their high-quality generation performance in practice, most of them lack rigorous theoretical convergence proofs. In this work, we aim to establish some convergence results for OT-Flow, one of the deep generative models. First, by reformulating the framework of OT-Flow model, we establish the $Γ$-convergence of the formulation of OT-flow to the corresponding optimal transport (OT) problem as the regularization term parameter $α$ goes to infinity. Second, since the loss function will be approximated by Monte Carlo method in training, we established the convergence between the discrete loss function and the continuous one when the sample number $N$ goes to infinity as well. Meanwhile, the approximation capability of the neural network provides an upper bound for the discrete loss function of the minimizers. The proofs in both aspects provide convincing assurances for OT-Flow.

Souhail Hadgi, Lei Li, Maks Ovsjanikov

Transfer learning has long been a key factor in the advancement of many fields including 2D image analysis. Unfortunately, its applicability in 3D data processing has been relatively limited. While several approaches for point cloud transfer learning have been proposed in recent literature, with contrastive learning gaining particular prominence, most existing methods in this domain have only been studied and evaluated in limited scenarios. Most importantly, there is currently a lack of principled understanding of both when and why point cloud transfer learning methods are applicable. Remarkably, even the applicability of standard supervised pre-training is poorly understood. In this work, we conduct the first in-depth quantitative and qualitative investigation of supervised and contrastive pre-training strategies and their utility in downstream 3D tasks. We demonstrate that layer-wise analysis of learned features provides significant insight into the downstream utility of trained networks. Informed by this analysis, we propose a simple geometric regularization strategy, which improves the transferability of supervised pre-training. Our work thus sheds light onto both the specific challenges of point cloud transfer learning, as well as strategies to overcome them.