Critical alpha scaling in Erdős–Rényi memory graphs

Establish whether, for CDAM with the memory graph M drawn from the Erdős–Rényi model with edge probability gamma, the critical value of the auto-association parameter alpha that marks the transition from neutral quiescence to wide hetero-association is proportional to gamma in the asymptotically connected regime.

Background

In the directed memory graph case, the energy function introduces complexities due to directionality, making general analysis harder. The authors discuss regime transitions between neutral quiescence and wide hetero-association.

To guide future analysis, the authors propose a specific conjecture linking the transition’s critical alpha to the connectivity parameter of an Erdős–Rényi random graph, focusing on the asymptotically connected regime.