Hopfield attractor networks are robust distributed models of human memory, but lack a general mechanism for effecting state-dependent attractor transitions in response to input. We propose construction rules such that an attractor network may implement an arbitrary finite state machine (FSM), where states and stimuli are represented by high-dimensional random vectors, and all state transitions are enacted by the attractor network's dynamics. Numerical simulations show the capacity of the model, in terms of the maximum size of implementable FSM, to be linear in the size of the attractor network for dense bipolar state vectors, and approximately quadratic for sparse binary state vectors. We show that the model is robust to imprecise and noisy weights, and so a prime candidate for implementation with high-density but unreliable devices. By endowing attractor networks with the ability to emulate arbitrary FSMs, we propose a plausible path by which FSMs could exist as a distributed computational primitive in biological neural networks.

翻译：Hopfield吸引子网络是人类记忆的鲁棒分布式模型，但缺乏一种通用机制来实现输入驱动的状态依赖型吸引子转换。我们提出构造规则，使吸引子网络能够实现任意有限状态机（FSM），其中状态和刺激由高维随机向量表示，所有状态转换均由吸引子网络的动力学驱动。数值模拟表明，该模型在可实现FSM最大规模方面的容量与吸引子网络规模呈线性关系（针对稠密双极状态向量），而对稀疏二值状态向量则近似呈二次关系。我们证明该模型对不精确和含噪权重具有鲁棒性，因此成为采用高密度但不可靠器件实现的理想候选方案。通过赋予吸引子网络模拟任意FSM的能力，我们提出了一条合理路径，使FSM可作为生物神经网络中的分布式计算原语存在。