Across systems, higher-order interactions between components govern emergent dynamics. Here we tested whether contextual threat memory retrieval in mice relies on higher-order interactions between dorsal CA1 hippocampal neurons requiring learning-induced dendritic spine plasticity. We compared population-level Ca2 ⁺ transients as wild-type mice (with intact learning-induced spine plasticity and memory) and amnestic mice (TgCRND8 mice with high levels of amyloid-β and deficits in learning-induced spine plasticity and memory) were tested for memory. Using machine-learning classifiers with different capacities to use input data with complex interactions, our findings indicate complex neuronal interactions in the memory representation of wild-type, but not amnestic, mice. Moreover, a peptide that partially restored learning-induced spine plasticity also restored the statistical complexity of the memory representation and memory behavior in Tg mice. These findings provide a previously missing bridge between levels of analysis in memory research, linking receptors, spines, higher-order neuronal dynamics and behavior.