Relationships among near set theory, shape maps and recent accounts of the Quantum Hall effect pave the way to neural networks computations performed in higher dimensions. We illustrate the operational procedure to build a real or artificial neural network able to detect, assess and quantify a fourth spatial dimension. We show how, starting from two-dimensional shapes embedded in a 2D topological charge pump, it is feasible to achieve the corresponding four-dimensional shapes, which encompass a larger amount of information. Synthesis of surface shape components, viewed topologically as shape descriptions in the form of feature vectors that vary over time, leads to a 4D view of cerebral activity. This novel, relatively straightforward architecture permits to increase the amount of available qbits in a fixed volume.

近集理论、形状图和最近对量子霍尔效应的解释之间的关系为在更高维度上执行的神经网络计算铺平了道路。我们说明了构建能够检测、评估和量化第四空间维度的真实或人工神经网络的操作过程。我们展示了如何从嵌入在二维拓扑电荷泵中的二维形状开始，实现相应的包含大量信息的四维形状是可行的。表面形状组件的合成，在拓扑上被视为随时间变化的特征向量形式的形状描述，导致大脑活动的 4D 视图。这种新颖、相对简单的架构允许在固定体积中增加可用 qbit 的数量。