Entropy Injection in Fused Market Networks: HSBM–MDL Quantification of News-Driven Structural Reconfiguration

Understanding how semantic information flow reorganizes market topology remains an open challenge in financial network analysis. Prior work typically emphasizes price correlations or sentiment polarity, but rarely quantifies the structural response of the market network to information inflow within a unified coding framework. We propose a fusion-based approach to measure topology-aware information impact. Specifically, we construct a Price Network <inline-formula> <tex-math notation="LaTeX">$G_{P}$ </tex-math></inline-formula> from return co-movements and a Semantic Network <inline-formula> <tex-math notation="LaTeX">$G_{N}$ </tex-math></inline-formula> from LLM-based text embeddings, and integrate them into a Fused Network <inline-formula> <tex-math notation="LaTeX">$G_{F}$ </tex-math></inline-formula>. Using the Hierarchical Stochastic Block Model (HSBM) under the minimum description length principle, we estimate structural entropies for <inline-formula> <tex-math notation="LaTeX">$G_{F}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$G_{P}$ </tex-math></inline-formula> (<inline-formula> <tex-math notation="LaTeX">$H_{F}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$H_{P}$ </tex-math></inline-formula>), and define the marginal structural cost of information injection as <inline-formula> <tex-math notation="LaTeX">$\Delta H = H_{F} - H_{P}$ </tex-math></inline-formula>. Empirically, using S&#x0026;P 100 constituents over 2023&#x2013;2025, we find that <inline-formula> <tex-math notation="LaTeX">$\Delta H$ </tex-math></inline-formula> is consistently positive, indicating that semantic information inflow acts as an entropy injector relative to the price backbone. High-risk regimes (periods of elevated volatility) exhibit markedly larger <inline-formula> <tex-math notation="LaTeX">$\Delta H$ </tex-math></inline-formula> together with a reorganization of the inferred hierarchy, characterized by deeper partitions and increased fine-grained communities, consistent with micro-fragmentation of market structure. At the macro level, normalized modularity <inline-formula> <tex-math notation="LaTeX">$Z_{Q}$ </tex-math></inline-formula> declines on high-volatility days, suggesting weaker sectoral separability and intensified cross-community coupling. Finally, permutation-based counterfactual tests that disrupt semantic alignment show that the observed regime separation in <inline-formula> <tex-math notation="LaTeX">$\Delta H$ </tex-math></inline-formula> is not attributable to arbitrary mixing, supporting the interpretation that information shocks induce organized structural reconfiguration rather than random disorder. Overall, our framework provides a principled, topology-aware link between semantic information flow and market-wide risk states.