Finite-dimensional latent representations for neighbor-triplet aggregation

Determine whether the angle-feature dimension in the HGNN can be bounded or substantially reduced relative to the number of neighbor triplets while retaining the universal approximation and completeness guarantees.

Background

The DeepSets-based proofs use the angle-feature dimension as the latent dimension of the aggregation. According to the paper, the required dimension grows at least with the number of neighbor triplets, whereas practical architectures commonly use much smaller dimensions, such as 64. Closing this theoretical-practical dimensionality gap is explicitly identified as unresolved.