Grid cells and their potential application in AI

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GRID CELLS AND THEIR POTENTIAL APPLICATION IN AI

A PREPRINT

Jason Toy

somatic

jasontoy@gmail.com

October 24, 2022

ABSTRACT

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.

Keywords grid cells ·entorhinal cortex ·hippocampus ·artiﬁcial intelligence

1 Brief History

The Entorhinal cortex, also called the medial entorhinal cortex (MEC), is an area in the brain that sits between the

neocortex and hippocampus in an area called the medial temporal lobe. In Broadmann’s area, it is Broadmann area 28.

Ramon y Cajal described the area in 1902, but at the time thought it was part of the olfactory system used for processing

smell information.

In 2005, grid cells were discovered in the entorhinal cortex Hafting et al. [2005]. Grid cells are a type of neuron that

ﬁres at regular intervals as an animal navigates an area. Grid cells provide a multi-scale periodic representation that

functions as a metric for location encoding and is critical for recognizing places for navigation. When the scientists

plotted the points in 2D, they discovered that they formed a grid of tesselating triangles, hence the name grid cells.

The team that discovered grid cells consists of Edvard Moser, May-Britt Moser, and their students. The team ending up

winning a Nobel peace prize in Physiology or Medicine in 2014. Coincidently, they shared the prize with John O’Keefe

who discoverd place cells in the hippocampus. Together this Hippocampus and Entorhinal cortex (HEC) system are

believed to be the main system for building a cognitive map. The HEC system is also one of the most frequently studied

areas connecting neuroscience with artiﬁcial intelligence.

Neuroscienists have been optimistically studying the HEC system trying to unlock how exactly it works to accelerate

various ﬁelds of science. Place cells in the hippocampus are special in the brain in that their ﬁring rates act as bookmark

for landmarks or an indexing system. Tthey ﬁre only foor speciﬁc locations in an environment. For example a particular

place cell may only ﬁre when at the entrance to work, your favorite parking spot, or at your house. Place cells are

known to ﬁre on 1 to several locations. Contrast that with grid cells, they retain their basic ﬁring pattern regardless of

environment, making them generalized and context independent. The ﬁring rate forms a hexagonal like grid pattern that

tiles to the environment. Grid cells and Place cells feed into each other along with other inputs forming some kind of

recurrent network.

Grid cells have been found in mice, rats, bats, monkeys, and humans. It is believed that they exist in all mammals

similar to the neocortex. It is still unknown if grid cells appear in non-mammal animals.

arXiv:2210.12068v1 [q-bio.NC] 12 Oct 2022

Grid cells and AI A PREPRINT

2 Human Health

The EC seems to be a critical part of the mind and brain and its degradation seems to have severe effects on human

cognition and health. In Alzheimer’s disease (AD), the EC is one of the ﬁrst areas of the brain to be noticeably effected,

typically with a reduction in volume of the cortex Solstad et al. [2008]. AD common symptons are disorientation, easily

getting lost, problems with language, behavioral issues, among others. Early changes in the EC are used as a strong

predictor of AD and these EC changes are commonly used to test for AD Bottero et al. [2021]. Patient HM (1926-2008)

was the most studied patient in neuroscience history Squire [2009]. He had seizures since 10 years old from an accident

and at 27 years old had a surgery that removed his hippocampus, entorhinal cortex, and nearby areas. The procedure

stopped his seizures, but it created another problem in that he acquiried anterograde amnesia, he was unable to form new

memories. At the time of his death grid cells were only recently discovered and so there were not many experiments

done with him, but the fact that his EC was missing implicates it as being a key system for declaring new memories.

3 Grid Cell parameters

There are 3 parameters that determine a grid cell’s ﬁring pattern, the orientation of the grid, the spacing between ﬁring

ﬁelds (also called the wavelength), and the location (also called spatial phase) of the grid ﬁelds. Grid cells cluster

together into discrete modules sharing orientation and periodicity, but varying randomly in phase. Currently for all

possible conﬁgurations of parameters, it is believed that there are under 10 different modules. Grid cells will maintain

their ﬁring patterns even if speed or direction change. Grid cells are usually clustered together forming discrete modules

of computation.

4 Coordinates in the brain

To navigate and interact with our world, our brains must store this information in a way that we can retrieve it and use it

in new situations. One interpretation of the brain is that it is a coordinate translation machine: "a brain is a well-designed

machine for the frame conversion to internalize the external world" Arisaka [2022] and "the egocentric representations

of the primary sensory cortical areas must be transformed into an allocentric representation in the hippocampus, and

then transformed back to an egocentric motor representation for behavioral output" Byrne et al. [2007]. The brain

Grid cells and AI A PREPRINT

has been found to store multiple coordinate representations along with different orientations or points of view, mainly

allocentric and egocentric orientations.

Grid cells have an allocentric point of view (i.e. world-centered, external world, frame of reference). Their ﬁring does

not encode data from the point of view of the agent or ego. On the contrary, egocentric neurons ﬁre in relation to the

animals point of view such as visual neurons. For example BVCs are egocentric, they only ﬁre when the agent is near

certain borders and within certain angles. A 3D ﬁrst person shooter is played from the ego’s point of view where as

tic-tac-toe is played in an allocentric manner, you can the play game from just knowing the environment coordinates and

in any orientation. In the HEC, it is thought that most of the representations are allocentric, but there are new studies

showing that egocentric representations may also be stored. In one study Kunz et al. [2021] found abundant cells in

the parahippocampal cortex of human epilepsy patients that they dubbed "anchor cells". These anchor cells seem to

represent egocentric direction towards "anchor points" located in the environment. It is thought that these anchor cells

are used to transform perceptual signals into allocentric representations.

5 Other cells in the entorhinal cortex

The entorhinal cortex is made up primarily of grid cells, but there are other functional cell types as well: head direction

cells (HD cells), boundary vector cells (BVCs), and speed cells. There are also cells that form combinations of these

cells. Other cell types continue to be discovered.

5.1 Head direction cells

The cells ﬁre when the animal’s head points in a speciﬁc direction similar to a compass. They have a preferred ﬁring

direction that they will maintain regardless of the environment that they are in. HD cells are also found in other regions

of the brain such as the thalamus and retrosplenial cortex. One interesting note is that HD cells continue to ﬁre while an

animal is asleep, especially during REM sleep. In rats, HD cells appear before the animal has ever opened its eyes.

5.2 Boundary vector cells

Boundary vector cells (BVCs), also known as boundary cells or border cells ﬁre when an animal is at speciﬁc distances

and directions to environmental boundaries such as walls and dropoffs. They are thought to make up a little under

10The results of their experiments suggest that BVCs are tuned to geometric borders and not by content in the

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GRIDCELLSANDTHEIRPOTENTIALAPPLICATIONINAIAPREPRINTJasonToysomaticjasontoy@gmail.comOctober24,2022ABSTRACTSincetheirNobelPrizewinningdiscoveryin2005,gridcellshavebeenstudiedextensivelybyneuroscientists.Theirmulti-scaleperiodicringratestilingtheenvironmentastheanimalmovesaroundhasbeenshownascriticalf...

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