A theoretical associative memory model with a practical implementation running in real-time on modern hardware was proposed, the Gripon-Berrou Neural Network or Cliques Neural Network,Larroque, S., Gooya, E. S., Gripon, V., & Pastor, D. (2015). Using Tags to Improve Diversity of Sparse Associative Memories. Proceedings of Cognitive, 1-7. an extension of the Hopfield network. This model suggest that the encoding of memories or information is done in constant O(1) time, by simply creating synapses between the neurons, creating a clique in a subgraph of the network, representing the memory. The decoding is then simple and fast, based on the biological neurons behavior of the all-or-none and winner-takes-all. This model demonstrates the usefulness of cliques, by allowing the reconstruction of a full memory from a partial or corrupted input, even with unreliable synapses and neurons, and providing an explanation for associative train of thoughts when pre-cueing subjects with a familiar sensory stimuli (e.g., Proust's madeleine).
