While neural networks are highly effective at learning task-relevant representations from data, they typically do not learn representations with the kind of symbolic structure that is hypothesized to support high-level cognitive processes, nor do they naturally model such structures within problem domains that are continuous in space and time. To fill these gaps, this work exploits a method for defining vector representations that bind discrete (symbol-like) entities to points in continuous topological spaces in order to simulate and predict the behavior of a range of dynamical systems. These vector representations are spatial semantic pointers (SSPs), and we demonstrate that they can (1) be used to model dynamical systems involving multiple objects represented in a symbol-like manner and (2) be integrated with deep neural networks to predict the future of physical trajectories. These results help unify what have traditionally appeared to be disparate approaches in machine learning.

中文翻译：

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使用空间语义指针模拟和预测动力系统。

虽然神经网络在从数据中学习与任务相关的表示方面非常有效，但它们通常不会学习具有假设支持高级认知过程的那种符号结构的表示，也不会自然地对问题域内的此类结构进行建模在空间和时间上连续。为了填补这些空白，这项工作利用了一种定义向量表示的方法，将离散（类似符号）实体绑定到连续拓扑空间中的点，以模拟和预测一系列动态系统的行为。这些向量表示是空间语义指针 (SSP)，并且我们证明了它们可以 (1) 用于对涉及以符号方式表示的多个对象的动态系统进行建模，以及 (2) 与深度神经网络集成以预测物理轨迹的未来。这些结果有助于统一机器学习中传统上看似不同的方法。