On the storage capacity of the Hopfield model with biased patterns

We introduce a form of the Hopfield model that is able to store an increasing number of biased i.i.d. patterns (it is well known that the standard Hopfield model fails to work properly in this context). We show that this new form of the Hopfield model with N neurons can store (N)/(γ log N) or αN biased patterns (depending on which notion of storage is used). The quantity γ increases with an increasing bias of the patterns, while α decreases when the bias gets large