Identifiability of the generative hyperparameters

Determine the identifiability of the generative hyperparameter vector θ_t = (θ, β) that governs the latent-field-driven architecture and neuron biases in the stochastic graph neural network when learned from supervised input–output data via negative log-likelihood minimization.

Background

The training objective in the paper is to infer the generative hyperparameters that control the latent Gaussian random field, neuron placement via a Poisson process, sparse connectivity, and random weights. Despite preliminary analysis, the identifiability of this hyperparameter vector under the proposed likelihood-based approach is explicitly stated as unresolved.

This open problem focuses on whether and under what conditions θ_t can be uniquely recovered (up to equivalence) from observed input–output data in the proposed stochastic architecture, a key requirement for reliable inference and model interpretability.