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Highlights d The geometry of abstraction supports generalization d Hippocampal and PFC representations are simultaneously abstract and high dimensional d Multiple task-relevant variables are represented in an abstract format d Representations in simulated neural networks are similar to recorded ones

Memories are stored and retained through complex, coupled processes operating on multiple timescales. To understand the computational principles behind these intricate networks of interactions, we construct a broad class of synaptic models that efficiently harness biological complexity to preserve numerous memories by protecting them against the adverse effects of overwriting. The memory capacity scales almost linearly with the number of synapses, which is a substantial improvement over the square root scaling of previous models. This was achieved by combining multiple dynamical processes that initially store memories in fast variables and then progressively transfer them to slower variables. Notably, the interactions between fast and slow variables are bidirectional. The proposed models are robust to parameter perturbations and can explain several properties of biological memory, including delayed expression of synaptic modifications, metaplasticity, and spacing effects.

In two remarkable recent papers the planar perturbative expansion was proposed for the universal function of the coupling appearing in the dimensions of high-spin operators of the N=4 super Yang-Mills theory. We study numerically the integral equation derived by Beisert, Eden, and Staudacher, which resumes the perturbative series. In a confirmation of the anti-de Sitter-space/conformal-field-theory (AdS/CFT) correspondence, we find a smooth function whose two leading terms at strong coupling match the results obtained for the semiclassical folded string spinning in AdS5. We also make a numerical prediction for the third term in the strong coupling series.