Fig. 4: Memory capacity is enhanced by geometric deformation.
From: Explosive neural networks via higher-order interactions in curved statistical manifolds
Phase diagram of a curved associative memory with an extensive number of encoded patterns M = αN and J = 1 for (a) different T = 1/β at \({\gamma }^{{\prime} }=0\) (black dashed lines), 0.8, − 0.8 (solid lines), and for (b) different \({\gamma }^{{\prime} }\) at β = 2. F indicates the ferromagnetic (i.e., memory retrieval) phase, SG the spin-glass phase (where saturation makes memory retrieval inviable), M a mixed phase, and P the paramagnetic region. Both in F and M, ferromagnetic and spin-glass solutions coexist, but we differentiate these by calculating respectively whether memory-retrieval or spin-glass solutions are the global minimum of the normalising potential φγ. The dotted lines in (a) near T = 0 indicate the AT lines, below which the replica-symmetric solution is not valid. Increasing \({\gamma }^{{\prime} }\) to larger negative values extends the retrieval phase into larger values of α, indicating an increased memory capacity, while larger positive values reduce the extension of the mixed phase, increasing robustness of memory retrieval.
