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.
Few-shot learning involves learning an effective model from only a few labeled datapoints. The use of a small training set makes it difficult to avoid overfitting but also makes few-shot learning applicable to many important real-world settings. In this work, we focus on Few-shot Learning with Auxiliary Data (FLAD), a training paradigm that assumes access […]
It is well established that increasing scale in deep transformer networks leads to improved quality and performance. This increase in scale often comes with an increase in compute cost and inference latency. Consequently, research into methods which help realize the benefits of increased scale without leading to an increase in the compute cost becomes important. […]
Continuous normalizing flows (CNFs) are an attractive generative modeling technique, but they have thus far been held back by limitations in their simulation-based maximum likelihood training. In this paper, we introduce a new technique called conditional flow matching (CFM), a simulation-free training objective for CNFs. CFM features a stable regression objective like that used to […]
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