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.

翻译：序列记忆是自然智能和人工智能的基本属性，使智能体能够编码、存储和检索复杂的刺激与动作序列。已有研究提出了序列记忆的计算模型，其中递归的类Hopfield神经网络采用时间非对称的Hebbian规则进行训练。然而，由于记忆间的干扰，这些网络的序列容量（可存储序列的最大长度）有限。受近期密集联想记忆研究的启发，我们通过引入非线性相互作用项来增强模式间的分离度，从而扩展了这些模型的序列容量。我们推导了序列容量与网络规模之间的新型标度律，该标度律显著优于基于传统Hopfield网络的现有标度律，并通过数值模拟验证了这些理论结果。此外，我们引入了一种广义伪逆规则，用于回忆高度相关模式的序列。最后，我们将该模型扩展至存储状态间转换时间可变的序列，并描述了一种具有生物合理性的实现方案，该方案与运动神经科学相关。