Latent persistence in fMRI dynamics during human memory consolidation

Human memory consolidation involves the gradual stabilization and reorganization of memory traces over time. Despite numerous empirical and computational accounts emphasizing different aspects of this process, an integrated framework for evaluating consolidation theories against brain data remains limited. We propose a biologically informed, data-driven framework based on Koopman operator analysis to examine latent dynamical structure in fMRI signals associated with memory consolidation. The Koopman framework lifts nonlinear brain dynamics into a linear function space, enabling spectral characterization of persistence and stability. In practice, we employ Dynamic Mode Decomposition (DMD) together with an observability-aware extension tailored to consolidation-related neural dynamics. We organize existing theories into three functional clusters: standard consolidation, episodic replay during rest, and distributed long-term storage, and then align open-access fMRI datasets with each cluster to assess their dynamical plausibility. Across datasets, delayed or repeated retrieval conditions generally tend to show greater spectral persistence than early encoding-related conditions. Among the three analyses, Cluster 3 yielded the clearest statistically reliable subject-level contrast, with semantically abstracted autobiographical content exhibiting higher mean eigenvalue magnitude and more near-unit modes than event-specific episodic content. This finding is compatible with transformation-oriented and distributed-storage accounts but does not constitute a direct temporal test of consolidation. Replay-related conditions show strong spectral differentiation across task states, although part of this separation likely reflects task structure in addition to consolidation-related dynamics. For the standard consolidation cluster, effects are directionally consistent with theory but remain small and not statistically significant at the subject level. Overall, the proposed framework provides an interpretable operator-theoretic approach for linking memory consolidation theory to latent brain dynamics and for comparing competing accounts in a common spectral language.