The Topological Reinforcement Operator (ORT): A Parsimony Principle for Memory Consolidation in Complex Networks

Memory engram consolidation is a central challenge in computational neuroscience. This work introduces the Topological Reinforcement Operator (ORT), a post- training mechanism that reinforces topologically relevant nodes to induce functional engrams in complex networks. We validated the ORT using a robust functional protocol based on normalized diffusion and F1-score, applied to citation networks (Cora, Citeseer, Pubmed) and biological connectomes (macaque, human). The results reveal a dual consolidation principle: in information networks, memory resilience emerges from broad criti- cal mass cores (P90), whereas in optimized biological networks, a smaller elite core (P95) predominates, achieving a performance of up to 87.4% in the human connectome. Finally, we demonstrate that the ORT, based on degree centrality, is ∼96 times faster than PageRank, establishing a principle of computational parsimony that links structure, function, and efficiency in neural networks.