Adaptive Sampling for Continuous Group Equivariant Neural Networks

Steerable networks, which process data with intrinsic symmetries, often use Fourier-based nonlinearities that require sampling from the entire group, leading to a need for discretization in continuous groups. As the number of samples increases, both performance and equivariance improve, yet this also leads to higher computational costs. To address this, we introduce an adaptive sampling approach that dynamically adjusts the sampling process to the symmetries in the data, reducing the number of required group samples and lowering the computational demands. We explore various implementations and their effects on model performance, equivariance, and computational efficiency. Our findings demonstrate improved model performance, and a marginal increase in memory efficiency.

DC3DO: Diffusion Classifier for 3D Objects

Inspired by Geoffrey Hinton emphasis on generative modeling, To recognize shapes, first learn to generate them, we explore the use of 3D diffusion models for object classification. Leveraging the density estimates from these models, our approach, the Diffusion Classifier for 3D Objects (DC3DO), enables zero-shot classification of 3D shapes without additional training. On average, our method achieves a 12.5 percent improvement compared to its multiview counterparts, demonstrating superior multimodal reasoning over discriminative approaches. DC3DO employs a class-conditional diffusion model trained on ShapeNet, and we run inferences on point clouds of chairs and cars. This work highlights the potential of generative models in 3D object classification.