Define capacity for mixed auto- and hetero-associative CDAM

Determine an appropriate formal notion of storage capacity for Correlated Dense Associative Memory (CDAM) that accommodates mixtures of auto-association and hetero-association and arbitrary memory graphs, and specify precisely what this capacity measure quantifies for such mixed dynamics.

Background

Classical associative memory models quantify capacity by asking whether network dynamics recover a stored pattern from a noisy cue in the pure auto-associative regime. Sequence capacity has been analyzed for linear, purely hetero-associative cases.

CDAM generalizes to continuous-valued patterns with simultaneous auto- and hetero-association over arbitrary memory graphs, so standard capacity notions do not directly apply. The authors explicitly note that it is unclear how to define capacity and what it should measure in this mixed setting.