A general neural network memory formulation, $\mathrm{Mem} = \mathrm{Update}(S_{\mathrm{kv}}, \mathrm{Mem}_{\mathrm{pre}})$, can be configured to act as an RNN-like model. This occurs when the set of recent model states, $S_{\mathrm{kv}}$, is restricted to contain only the most recent key-value pair, $(\mathbf{k}_i, \mathbf{v}_i)$, and the $\mathrm{Update}(\cdot)$ mechanism is defined as a recurrent cell, denoted as $f$. This specific configuration can be expressed with the formula:

$\mathrm{Mem} = f((\mathbf{k}_i, \mathbf{v}_i), \mathrm{Mem}_{\mathrm{pre}})$