Transformer Neural Processes -- Kernel Regression

Stochastic processes model various natural phenomena from disease transmission to stock prices, but simulating and quantifying their uncertainty can be computationally challenging. For example, modeling a Gaussian Process with standard statistical methods incurs an $\mathcal{O}(n^3)$ penalty, and even using state-of-the-art Neural Processes (NPs) incurs an $\mathcal{O}(n^2)$ penalty due to the attention mechanism. We introduce the Transformer Neural Process - Kernel Regression (TNP-KR), a new architecture that incorporates a novel transformer block we call a Kernel Regression Block (KRBlock), which reduces the computational complexity of attention in transformer-based Neural Processes (TNPs) from $\mathcal{O}((n_C+n_T)^2)$ to $O(n_C^2+n_Cn_T)$ by eliminating masked computations, where $n_C$ is the number of context, and $n_T$ is the number of test points, respectively, and a fast attention variant that further reduces all attention calculations to $\mathcal{O}(n_C)$ in space and time complexity. In benchmarks spanning such tasks as meta-regression, Bayesian optimization, and image completion, we demonstrate that the full variant matches the performance of state-of-the-art methods while training faster and scaling two orders of magnitude higher in number of test points, and the fast variant nearly matches that performance while scaling to millions of both test and context points on consumer hardware.