Hierarchical Linear Symbolized Tree-Structured Neural Processes

Traditional Neural Processes (NPs) and their variants aim to learn relationships between context sample points but do not consider multi-level information, resulting in a limited ability to learn complex distributions.This paper draws inspiration from features such as the hierarchical nature and interpretability of tree-like structures. This paper proposes a Hierarchical Linear Symbolized Tree-structured Neural Processes (HLNPs) architecture. This framework utilizes variables to build a top-down hierarchical linear symbolized tree-structured network architecture, enhancing positional representation information in a hierarchical manner along the deterministic path. In the latent distribution, the hierarchical linear symbolized tree-structured network approximates functions discretely through a layered approach. By decomposing the latent complex distribution into several simpler sub-problems using sum and product symbols, the upper bound of optimization is thereby increased. The tree structure discretizes variables to capture model uncertainty in the form of entropy. This approach also imparts a causal effect to the HLNPs model. Finally, we demonstrate the effectiveness of the HLNPs models for 1D data, Bayesian optimization, and 2D data.