A Mathematical Formalization of Hierarchical Temporal Memory's Spatial Pooler

IERARCHICAL temporal memory (HTM) is a machine learning algorithm that was inspired by the neocortex and designed to learn sequences and make predictions. In its idealized form, it should be able to produce generalized representations for similar inputs. Given time-series data, HTM should be able to use its learned representations to perform a type of time-dependent regression. Such a system would prove to be incredibly useful in many applications utilizing spatiotemporal data. One instance for using HTM with timeseries data was recently demonstrated by Cui et al. [1], where HTM was used to predict taxi passenger counts. The use of HTM in other applications remains unexplored, largely due to the evolving nature of HTM's algorithmic definition. Additionally, the lack of a formalized mathematical model hampers its prominence in the machine learning community. This work aims to bridge the gap between a neuroscience inspired algorithm and a math-based algorithm by constructing a purely mathematical framework around HTM's original algorithmic definition.