Topology of Neural Processes

Neural networks and stochastic processes are combined to produce Neural processes (NPs). This method breaks away from traditional Gaussian Processes that are limited by kernels. However, both NPs and their subsequent variants ignore the intrinsic relationship between context sample points. This problem causes the NPs family model to require the latent distribution for each context sample point. Topology can mine the intrinsic relationships between sample points. We use the Vietoris-Rips complex of topology to compute topological features as a representation of the intrinsic relationships between sample points. The different-dimensional topological features are expressed separately in terms of the latent distributions. Based on this idea, we propose a new model called the Topology of Neural Processes. The regression problem from the 1D dataset, Bayesian optimization, and the complete image of the 2D dataset obtained better results compared to the results of the NPs family.