  Hierarchical Associative Memory models have recently been proposed as a
versatile extension of continuous Hopfield networks. In order to facilitate
future research on such models, especially at scale, we focus on increasing
their simulation efficiency on digital hardware. In particular, we propose two
strategies to speed up memory retrieval in these models, which corresponds to
their use at inference, but is equally important during training. First, we
show how they can be cast as Deep Equilibrium Models, which allows using faster
and more stable solvers. Second, inspired by earlier work, we show that
alternating optimization of the even and odd layers accelerates memory
retrieval by a factor close to two. Combined, these two techniques allow for a
much faster energy minimization, as shown in our proof-of-concept experimental
results. The code is available at https://github.com/cgoemaere/hamdeq
