Global Perception Based Autoregressive Neural Processes

Abstract

Increasingly, autoregressive approaches are being used to serialize observed variables based on specific criteria. The Neural Processes (NPs) model variable distribution as a continuous function and provide quick solutions for different tasks using a meta-learning framework. This paper proposes an autoregressive-based framework for NPs, based on their autoregressive properties. This framework leverages the autoregressive stacking effects of various variables to enhance the representation of the latent distribution, concurrently refining local and global relationships within the positional representation through the use of a sliding window mechanism. Autoregression improves function approximations in a stacked fashion, thereby raising the upper bound of the optimization. We have designated this framework as Autoregressive Neural Processes (AENPs) or Conditional Autoregressive Neural Processes (CAENPs). Traditional NP models and their variants aim to capture relationships between the context sample points, without addressing either local or global considerations. Specifically, we capture contextual relationships in the deterministic path and introduce sliding window attention and global attention to reconcile local and global relationships in the context sample points. Autoregressive constraints exist between multiple latent variables in the latent paths, thus building a complex global structure that allows our model to learn complex distributions. Finally, we demonstrate the effectiveness of the NPs or CFANPs models for 1D data, Bayesian optimization, and 2D data.