The latent structure of diversification from relatedness and network embeddings.

Economic diversification is commonly modeled using co-occurrence-based measures of relatedness that quantify pairwise overlap among activities in a capability network. Although such measures are derived from network structure, they operate at the level of first-order neighborhood relations and summarize proximity through local co-occurrence. They do not explicitly encode higher-order structural context, such as indirect connectivity patterns or global positional similarity, into a continuous representation of entities and activities. We develop an embedding-based framework that learns such representations from network topology, enabling the construction of interpretable geometric features, including capability alignment, displacement, and portfolio entropy, that extend standard measures used in economic complexity. We apply this framework to two systems: international trade (1998-2023) and public procurement firms (2009-2024). The resulting representations reveal different structural organization across scales: firms exhibit modular clustering patterns, whereas countries occupy broader, nested capability configurations. In predictive tasks for product and activity specialization, embedding-derived features provide additional explanatory power beyond relatedness in several settings, particularly when forecasting variation in the magnitude of comparative advantage. For country-level entry events, however, persistence remains the strongest predictor. Our results show that relatedness remains the dominant predictor of entry events. In contrast, embedding-derived features become more informative in specific settings, particularly for modeling variation in specialization magnitude and in low-relatedness regimes. More broadly, the findings indicate that diversification depends on structural signals that are both prediction-target-dependent and scale-dependent, with relatedness and embedding-derived features capturing different aspects of the capability space (local overlap vs. structural position).