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From YouTube: Grid Cells (Episode 14)
Description
In this video, we explore the discovery of grid cells. We go over the discovery of these and other location cells in the brain, how they project onto space to represent locations, and how they can be interpreted as SDRs within HTM systems.
We also introduce the concept that grid cells might be used in the neocortex to represent all objects in the brain, not just locations relative to an agent's body.
2014 Nobel Prize Lecture: https://www.youtube.com/watch?v=P0tXhEbvjjg
Referenced papers:
- The representation of space in the brain (Roddy M. Grieves, Kate J. Jeffrey):
https://www.researchgate.net/publication/311915392_The_representation_of_space_in_the_brain
- Network Mechanisms of Grid Cells (Edvard Moser, May-Britt Moser, Yasser Roudi):
http://rstb.royalsocietypublishing.org/content/369/1635/20120511
- Computational Models of Grid Cells (Lisa M. Giocomo, May-Britt Moser, Edvard Moser):
http://www.cell.com/neuron/abstract/S0896-6273(11)00650-7
- Evidence for grid cells in a human memory network (Christian F. Doeller, Caswell Barry, Neil Burgess):
https://www.nature.com/articles/nature08704
- Mapping of a non-spatial dimension by the hippocampal-entorhinal circuit (Dmitriy Aronov, Rhino Nevers, David W. Tank):
https://www.nature.com/articles/nature21692
- Organizing conceptual knowledge in humans with a gridlike code (Alexandra O. Constantinescu, Jill X. O’Reilly, Timothy E. J. Behrens):
http://science.sciencemag.org/content/352/6292/1464
A
Hello
and
welcome
to
episode
14
of
HTM
school,
where
we'll
talk
about
one
of
the
most
exciting
and
intriguing
discoveries
in
modern
neuroscience
grid
cells.
In
2014,
the
Nobel
Prize
for
Physiology
or
medicine
was
awarded
to
doctors,
John
Okeefe
may
Britt,
Moser
and
edvard
moser
for
their
work.
Discovering
cells
that
deal
with
location
in
the
brain.
This
included
cells
called
grid
cells,
which
are
pyramidal
neurons
that
create
cognitive
maps
of
space.
In
this
experiment
by
dr.
A
Mae,
Britt
and
edvard
moser,
a
mouse
has
an
apparatus,
that's
monitoring
one
particular
neuron
in
its
internal
cortex,
suspected
to
be
involved
with
location.
Every
time
the
neuron
fires,
an
action
potential,
a
dot
is
rendered
to
the
screen
in
this
video.
At
first
look,
it
looks
like
the
neurons
just
firing
randomly,
but
as
the
mouse
explores
the
room,
you
can
see
a
grid
like
firing
field
appear
across
the
2d
space.
A
This
shows
that
that
one
neuron
called
a
grid
cell
responds
when
the
mouse
is
in
particular
places
in
the
room
and
those
places
are
spaced
out
in
a
hexagonal
lattice.
But
why
hexagons
I
asked
myself
the
same
question
and
that
answer
comes
from
circles.
If
you
pack
circles
as
close
together
as
possible,
their
centers
naturally
create
a
hexagonal
pattern.
I'm
not
saying
the
key
to
intelligence
in
the
brain
is
hexagons,
but
it's
hexagons.
A
Scientists
have
discovered
several
types
of
cells
in
the
brain
related
to
location
which
include
placed
cells
in
the
hippocampus
and
head
Direction
cells
in
the
dorsal
presa
bicular
grid
cells
have
been
found
in
the
intel,
Rhino,
cortex
and
rats,
but
there
is
also
ample
evidence
of
them
in
the
neocortex
of
humans.
For
a
great
summary
of
these
and
other
types
of
location
cells
in
the
brain
read
the
paper,
the
representation
of
space
in
the
brain.
A
Let's
take
a
closer
look
at
the
functionality
of
grid
cells
and
some
visualizations
that
show
how
grid
cells
can
project
onto
space.
Ok,
so,
let's
first
look
at
a
visualization
of
just
one
grid
cell.
So
in
this
visualization
I've
got
my
little
mouse
cursor
and
I'm
moving
through
a
2d
space
as
I
move
through
the
space
just
like
in
the
video
from
the
experiment
that
we
saw
sometimes
a
cell
fires.
So
this
is
just
one
grid
cell,
sometimes
it
fires
as
this
mouse
moves.
A
Through
this
space
see
it
looks
sort
of
random
in
the
bottom
left
corner
here,
I've
got
a
representation
of
that
grid.
Cell
I'm
gonna
show
you
all
the
places
in
the
space
that
this
cell
fires
as
I
hover
over
it.
Here's
this
grid
cells
firing
field.
It
will
fire
when
the
mouse
gets
close
to
any
one
of
these
locations.
In
this
two-dimensional
space,
and
as
you
can
see,
there
are
a
lot
of
locations
where
it
doesn't
fire
at
all.
The
mouse
just
runs
through
and
it
never
fires.
A
So
there's
a
couple
problems
with
just
having
this
one
grid
cell
one
is
that
it's
not
always
firing,
and
the
other
is
that
when
it
does
fire,
the
grid
cell
isn't
really
telling
you
exactly
where
the
mouse
is,
because
when
the
mouse
is
in
one
of
these
locations,
the
grid
cell
fires,
that
means
it
could
be
in
any
one
of
these
locations.
So
it's
an
ambiguous
representation
of
space,
so
we
don't
really
know
where
the
mouse
is.
A
We
just
know
it's
in
one
of
those
locations,
but
not
which
one
so
in
order
for
grid
cells
to
be
useful,
we
have
to
have
more
than
one
of
them
at
a
time,
so
I'm
going
to
show
you
what
we
refer
to
as
a
grid
cell
module,
which
is
a
group
of
grid
cells,
that
all
project
onto
a
space
in
the
same
way
so
take
a
look
at
this
I've
got
this
grid
cell
module
that
has
16
cells
in
it.
That
sort
of
have
this
parallelogram
shape
and
tile
across
this
whole
two-dimensional
shape.
A
So
the
grid
cells
themselves
are
not
arranged
in
any
way
in
the
brain.
They
are
tiled
across
a
two-dimensional
space
in
this
example.
So
it's
not
like
the
grid
cells
are
right
by
each
other
and
they're
retaining
this
shape.
This
is
just
how
they
represent
space.
This
tiling,
this
parallelogram,
so
as
I
walked
through
this
space
with
the
mouse.
Again,
you
can
see,
there's
always
a
grid
cell
in
this
module
firing,
so
we're
past
the
problem
of
not
being
able
to
represent
some
of
the
space.
A
But
again
it's
still
ambiguous
because
this
cell
12,
for
example,
still
has
a
firing
field
that
is,
could
represent
a
lot
of
different
places
in
the
space.
Let
me
turn
all
of
these
firing
fields
on
and
you
can
sort
of
see.
Here's
cell
six
firing
field
as
I
move
across
the
space
cell.
Three
is
now
firing
because
it's
being
stimulated,
but
we
still
don't
know
which
one
of
these
dots
in
the
space
is
the
mouse
in
it
could
be
any
one
of
these.
A
We
know
because
I
put
a
mouse
over
top
of
it,
but
this
grid
cell
module
doesn't
know
where
that
mouse
is
it
just
knows
it's
one
of
these
dots
moving
through
the
space.
So
before
we
move
on
to
tell
you
how
you
can
get
in
a
unique
representation,
let
me
show
you
a
couple
characteristics
of
grid
cell
modules.
For
example,
you
can
change
your
grid
cell
modules
orientation,
and
this
becomes
really
important
when
we
talk
about
using
multiple
grid
cell
modules
to
represent
space,
so
I
can
move
the
orientation.
A
However,
I
like
it
doesn't
change
the
functionality
of
what
the
grid
cells
are
doing
or
how
the
modules
are
interacting
with
each
other.
I
can
also
change
the
scale.
I
could
to
have
a
very
a
big
projection
or
a
small
projection.
It
still.
It
doesn't
change
the
functionality.
You
might
also
change
the
sensitivity
of
the
grid
cells.
So
here's
here's
a
an
example
where
two
good
cells,
the
closest
two
locations
to
that
the
mouse
right
now
are
going
to
be
firing,
but
what
I
really
want
to
show?
A
You
is
many
grid
cell
modules
working
together
to
represent
a
space,
so
here's
an
example
again
of
just
one
grid
cell
module
and
I've
made
it
pretty
small.
So
you
can
see
this
example
as
the
mouse
moves.
We
don't
know
exactly
where
it
is.
We
just
know
it's
in
one
of
these
dots
and
it's
moving
through
space.
Now,
if
I
add
a
No
grid
cell
module
to
the
mix,
we're
gonna
get
and
I'm
gonna
change
its
orientation,
so
it's
vastly
different
okay,
so
that
makes
it
makes
a
difference.
I'm
gonna
turn
off
the
lines
too.
A
So
now
I've
got
to
grid
cell
modules
that
are
kind
of
interplaying
together
here.
So
let's
take
this
example
where
the
mouse
is
like
right
around
here:
I'm
gonna,
freeze
the
screen
and
we're
gonna
draw
a
little
bit
over
here.
So
here's
where
the
mouse
is,
and
these
two
grid
cell
modules
both
have-
are
both
responding
to
this
location
right
here
very,
very
well,
because
it's
almost
a
complete
overlap
right
there,
but
back
where
we
there
might
have
been
a
big
Uwe
T
before
there's
no
confusion
where
there
is
confusion
is
say.
A
This
is
where
the
mouse
is
there's
another
area
right
here
where
there's
overlap,
there's
a
little
overlap
here,
a
little
overlap
here,
so
these
firing
fields
are
overlapping.
There's
a
lot
of
overlap
right
there.
The
firing
fields
are
overlapping
and,
while
there's
not
like
a
complete
ambiguity,
it's
not
like
every
dot
in
the
hexagonal
lattice
could
be
where
the
mouse
is.
A
Now
we
have
many
fewer
places
where
the
mouse
might
be,
because
we're
coordinating
one
grid
cell
modules,
representation
of
the
space,
with
another's
representation
of
the
space
and
they're
both
projecting
on
to
the
space
in
slightly
different
ways.
One
has
a
different
orientation.
It
looks
like
it's
a
little
bit
larger
and
you
can
see
as
we
move
and
add
another
grid
cell
module.
That
ambiguity
gets
less
and
less
because,
as
you
add
more
modules,
let's
go
ahead
and
add
all
five
grid
cell
modules.
A
Here
and
now
you
can
see
so
I'm
gonna
freeze
this
again
right
here
where
the
mouse
is
and
and
show
you.
Okay,
here's
all
of
those
grid
cell
modules
have
a
firing
field.
That's
that's
overlapping
with
every
other
grid
cell
module
right
here,
so
they
all
think
that's
the
mouse
could
be
here.
This
is
the
only
place
in
the
whole
two-dimensional
space
that
they
all
think
the
mouse
might
be.
A
Now
there
may
be
some
spots
where
there's
some
random
collisions,
like
you
know
over
over
here,
they're
getting
kind
of
close,
and
maybe
over
here
you
know,
there's
three
out
of
five
or
overlapped,
but
it
doesn't
look
like
there's
any
other
location
in
this.
This
particular
2d
space
where
there's
any
ambiguity.
This
is
the
only
place
right
here
in
the
middle,
where
the
mouse
actually
was
where
all
of
the
modules
agreed
and
had
overlap.
A
So,
if
we
add
more
modules,
we'll
get
better
resolution
on
our
locations
and
we
can
represent
more
unique
spaces
in
this
way
now,
I
also
want
to
talk
about
another
projection
onto
one
dimensional
space.
So
I
just
showed
you
two
dimensions,
but
I
want
to
show
one
dimension
so
that
we
can
talk
about
three
dimensions
in
a
moment.
I'm
doing
the
exact
same
thing
here
that
I
was
doing
in
two
dimensions,
but
with
just
one
dimension
here,
as
you
can
see,
I've
got
several
grid
cell
modules
with
a
little
bit
different
scalings.
A
We
don't
have
to
worry
about
orientation
in
this
case,
so
they're
just
a
little
bit
different
scalings.
They
all
have
five
grid
cells.
In
them,
and
in
this
case
they're
only
projecting
across
one
dimension-
let's
add
a
one
dimensional
line,
but
it
works
the
same
way
using
them
all
together.
If
I
have
a
mouse
running
across
this
line.
These
grid
cell
modules
can
all
work
together.
To
give
me
a
very
obvious
representation
that
the
mouse
is
here.
A
You
can
there's
really
no
other
place
in
here
that
the
mouse
might
be,
which
is
great,
so
this
works
in
two
dimensions
as
well
as
one
dimension,
and
you
could
potentially
imagine
building
a
three
dimensional
representation
by
simply
taking
the
grid
cell
modules
that
project
onto
a
2d
space
and
adding
another
set
of
grid
cell
modules
that
are
projecting
onto
a
1d
space
so
that
you
can
capture
all
three
dimensions
and
have
a
representation
of
that.
So
another
thing
I
like
to
show,
and
so
you're
gonna
see
some.
A
This
is
kind
of
a
fun
little
wallpaper
here.
If
you
will
so,
what
I've
done
here
is
I've
taken
a
bunch
of
different
grid
cell
modules,
I
think
there's
ten
of
them
here
and
I've
scaled
them
all
differently
and
oriented
them
differently
and
I've
turned
on
more
than
one
cell
in
each
grid.
Cell
module
and-
and
the
thing
I
like
to
show
here-
is
look
at
this
SDR
in
the
top
left.
A
This
is
just
the
concatenation
of
every
one
of
those
grid
cell
modules,
all
other
on
bits
and
off
bits,
and
it
gives
us
a
unique
representation
of
this
2d
space
as
we
move
the
mouse
around
and
that's
in
essence,
what
grid
cell
modules
are
is
their
little
SDR,
so
you
combine
them
all
together
and
you
have
a
big
SDR
that
represents
unique
locations
in
space
that
can
map
high
dimensional
space
just
using
these
grid
cell
modules.
If
we
move
this
mouse
to
another
room,
its
grid
cell
modules
would
project
onto
that
space.
A
Another
interesting
thing
is
that
when
you
turn
off
the
lights
on
the
mouse
in
the
room,
its
grid
cells
continue
to
fire
normally
as
it
moves
around
in
complete
darkness.
This
suggests
that
grid
cells
may
be
involved
in
computations
related
to
path
integration.
Every
grid
cell
plays
a
role
in
SD
ours
that
represent
different
spaces.
Grid
cell
modules
are
combined
into
larger
populations
of
cells
that
represent
many
unique
spaces.
A
We
believe
grid
cells
are
not
only
used
to
create
cognitive
maps
of
physical
space,
but
are
also
used
to
create
conceptual
maps
of
ideas
in
your
brain.
There
is
actually
experimental
evidence
of
this
in
some
current
neuroscience
papers
in
the
video
description
below,
but
think
about
what
it
takes
for
you
to
learn
a
new
concept,
especially
one
that
is
said
to
have
a
lot
of
moving
parts.
You
are
said
to
explore
the
ideas
and
visualise
how
they
work
together.
Even
the
words
I've
just
used
like
moving
parts,
have
a
spatial
component.
A
Some
concepts
feel
similar
to
other
concepts,
even
though
they
describe
different
phenomena.
Think
about
what
you're
going
to
be
doing
later
today,
it's
right
around
the
corner.
Isn't
it
what
about
tomorrow?
That's
further
away
from
you
next
week
next
month?
What
do
you
see
yourself
doing
next
year?
Is
it
too
distant
to
visualize
too
fuzzy
to
nail
down?
You
see
my
point
here
think
about
sound
for
a
moment
and
the
terms
you
use
to
describe
it
low
versus
high
pitches,
smooth
or
rough
tones
distortion,
etc.
A
A
We
humans
have
a
tendency
to
try
and
describe
non
spatial
things
in
spatial
terms,
because
that's
how
we
experience
reality,
it
makes
sense
that
grid
cells
might
play
an
extremely
important
role
in
representing
everything
in
your
brain,
not
just
places
that
you've
been
I'll,
expand
on
these
ideas
in
future
episodes.
I
hope
this
leaves
you
with
a
lot
to
think
about
and
a
fascination
for
how
things
are
really
working
in
your
brain,
be
sure
to
check
out
the
show
notes
below
for
links
to
all
the
papers
and
talks.
I
mentioned
thanks
for
watching
HTM.