Since their Nobel Prize winning discovery in 2005, grid cells have been
studied extensively by neuroscientists. Their multi-scale periodic firing rates
tiling the environment as the animal moves around has been shown as critical
for path integration. Multiple experiments have shown that grid cells also fire
for other representations such as olfactory, attention mechanisms, imagined
movement, and concept organization potentially acting as a form of neural
recycling and showing the possible brain mechanism for cognitive maps that
Tolman envisioned in 1948. Grid cell integration into artificial neural
networks may enable more robust, generalized, and smarter computers. In this
paper we give an overview of grid cell research since their discovery, their
role in neuroscience and cognitive science, and possible future directions of
artificial intelligence research.

本文综述了自 2005 年以来神经科学家对于网格细胞的研究，概括了它们在神经科学和认知科学中的作用，并探讨了将网格细胞整合到人工神经网络中的可能未来方向。

网格细胞及其在人工智能中的潜在应用

Grid cells and their potential application in AI

Knowing how the effects of directed actions generalise to new situations
(e.g. moving North, South, East and West, or turning left, right, etc.) is key
to rapid generalisation across new situations. Markovian tasks can be
characterised by a state space and a transition matrix and recent work has
proposed that neural grid codes provide an efficient representation of the
state space, as eigenvectors of a transition matrix reflecting diffusion across
states, that allows efficient prediction of future state distributions. Here we
extend the eigenbasis prediction model, utilising tools from Fourier analysis,
to prediction over arbitrary translation-invariant directed transition
structures (i.e. displacement and diffusion), showing that a single set of
eigenvectors can support predictions over arbitrary directed actions via
action-specific eigenvalues. We show how to define a "sense of direction" to
combine actions to reach a target state (ignoring task-specific deviations from
translation-invariance), and demonstrate that adding the Fourier
representations to a deep Q network aids policy learning in continuous control
tasks. We show the equivalence between the generalised prediction framework and
traditional models of grid cell firing driven by self-motion to perform path
integration, either using oscillatory interference (via Fourier components as
velocity-controlled oscillators) or continuous attractor networks (via analysis
of the update dynamics). We thus provide a unifying framework for the role of
the grid system in predictive planning, sense of direction and path
integration: supporting generalisable inference over directed actions across
different tasks.

利用傅里叶分析工具拓展了通过特定状态转移之间的网络格代码的特征向量泛化推广到任意平移不变有向转移结构的模型，并证明了其在路径整合、预测规划和方向感知等任务中的适用性.