Efficient graph field integrators meet point clouds
We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion(RFD), uses popular epsilon-nearest-neighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.
We propose Dual PatchNorm: two Layer Normalization layers (LayerNorms), before and after the patch embedding layer in Vision Transformers. We demonstrate that Dual PatchNorm outperforms the result of exhaustive search for alternative LayerNorm placement strategies in the Transformer block itself. In our experiments, incorporating this trivial modification, often leads to improved accuracy over well-tuned Vision […]
Recent vision transformer based video models mostly follow the “image pre-training then finetuning” paradigm and have achieved great success on multiple video benchmarks. However, full finetuning such a video model could be computationally expensive and unnecessary, given the pre-trained image transformer models have demonstrated exceptional transferability. In this work, we propose a novel method to […]
Large pretrained language models have shown surprising In-Context Learning (ICL) ability. With a few demonstration input-label pairs, they can predict the label for an unseen input without additional parameter updates. Despite the great success in performance, the working mechanism of ICL still remains an open problem. In order to better understand how ICL works, this […]
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