Adaptive Sampling for Continuous Group Equivariant Neural Networks
This work addresses computational bottlenecks in machine learning for symmetric data, but it is incremental as it builds on existing steerable network methods.
The paper tackled the problem of high computational costs in steerable networks for continuous groups by introducing an adaptive sampling approach that dynamically adjusts to data symmetries, resulting in improved model performance and a marginal increase in memory efficiency.
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.