LAPLEX: The FFT of Learnable Laplace Kernels
Researchers have introduced LAPLEX, a novel class of learnable Laplace-kernel operators designed to enable efficient, high-dimensional linear algebra in deep learning. LAPLEX layers act like full-rank dense matrices but are implicitly defined by a small set of learnable parameters, allowing for matrix-vector operations at scales up to $10^9$ dimensions on GPUs. This approach separates the expressivity of dense matrices from their storage cost, facilitating data-adaptive global interactions and enabling compact projections and interpretable soft routing models. AI
IMPACT Introduces a method to handle high-dimensional data and complex interactions efficiently in deep learning models.