Sequence memory is an essential attribute of natural and artificial
intelligence that enables agents to encode, store, and retrieve complex
sequences of stimuli and actions. Computational models of sequence memory have
been proposed where recurrent Hopfield-like neural networks are trained with
temporally asymmetric Hebbian rules. However, these networks suffer from
limited sequence capacity (maximal length of the stored sequence) due to
interference between the memories. Inspired by recent work on Dense Associative
Memories, we expand the sequence capacity of these models by introducing a
nonlinear interaction term, enhancing separation between the patterns. We
derive novel scaling laws for sequence capacity with respect to network size,
significantly outperforming existing scaling laws for models based on
traditional Hopfield networks, and verify these theoretical results with
numerical simulation. Moreover, we introduce a generalized pseudoinverse rule
to recall sequences of highly correlated patterns. Finally, we extend this
model to store sequences with variable timing between states' transitions and
describe a biologically-plausible implementation, with connections to motor
neuroscience.

通过引入非线性相互作用项扩增了模型的序列容量，提出了一种基于连续关联记忆的计算模型，验证了序列容量随网络规模的新的比例规律，并通过数值模拟验证了这些理论结果。此外，还引入了广义伪逆序列回忆规则，并将模型扩展到可以存储具有状态转换间隔变化的序列，提出了一种生物可信实现，与运动神经科学相关。