►
Description
Building upon his prior grid cell model, Marcus Lewis explores ways to transform an array of 1D grid cell oscillators to 2D grid cell modules. He evaluates and explains one possible deterministic mapping technique that could be used to achieve this.
In the second part, Jeff Hawkins attempts to explain the physical structure of minicolumns and how they might interact. He proposes a new mechanism that introduces the idea of a voltage controlled oscillator in dendrites for dimensional movement in grid cells. With this mechanism, the grid cell will represent much more complex interactions and could possibly explain how the cells make connections to each other.
Research meeting on Marcus's new grid cell model: https://youtu.be/7tF-ofr7VUo
Paper Jeff referenced on oscillatory interference: https://www.jneurosci.org/content/31/45/16157.short
Paper Subutai mentioned on gap junctions between pyramidal cells : https://www.sciencedirect.com/science/article/pii/B9780128034712000138
0:00 Marcus Lewis on deterministic mapping
20:06 Jeff Hawkins on voltage controlled oscillators in dendrites
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B
Okay,
I
have
a
brief
topic.
It's
a
it's,
a
it's
a
new
idea,
but
I
I
plan
on
probably
presenting
it
again
in
more
detail
in
the
future.
It's
in
some
detail
here
I
have
some
slides,
but
this
is
sort
of
a
preview
presentation
just
to
kind
of
give
you
a
snapshot
of
what
I'm,
what
I'm
doing
and
kind
of
a
a
possibly
cool
idea.
I'm
still
evaluating
how
much
I
like
it,
but
it's
it's
new
to
me.
B
C
B
I
can
do
it.
The
theory
really
does
stand
up.
I
can
use
the
same
ideas
from
here
and
just
substitute
a
good
cell
modules
and
it
would
work,
but
I'm
very
cautious
to
do
that
because
an
inconvenient
background,
so
it's
not
clear
that
the
brain
actually
performs
readouts
from
multiple
good
cell
scales.
If
you
look
at
it
anatomically
those
connections,
inconveniently
don't
seem
to
exist
and
if
that's
not
conclusive,
there's
those
studies
haven't
even
been
published
yet
like
they're
they're
looking
at
it.
B
B
Of
a
multi-module
grid
cell,
not
good
cell
readout,
with
when
2d
seems
biologically
implausible.
Usually
you
can't
just
assume
it's
there,
so
so
that
brings
up
a
second
idea
and
that
I'm
gonna
get
into
that
that
what,
if
both
exist,
we've
talked
about
this
as
well.
Maybe,
for
example,
the
mini
columns
and
cortex
are
1d
grid
cell
modules
and
2d
grid
cells
are
some
kind
of
readout
of
those
and
in
these
slides
I'm
going
to
do
some
version
of
that.
So
that's
that's.
B
An
appealing,
idea
and
and
other
models
have
other
models
exist
where
you
have
a
bunch
of
oscillators
and
2d
grid
cells
are
read
out
from
those
but
inconveniently
those
other
models
that
derive
2d
grid
cells
from
1d
oscillators,
don't
preserve
the
representational
capacity
of
the
1d
oscillators.
You
can't
just
represent
anything
here.
They
kind
of
collapse
on
to
a
small
set
of
combinations
that
are
allowed.
B
So
so
this
is,
this
is
the
kind
of
the
background
going
into
this,
and
so
in
an
appealing
vision
as
we've
drawn
versions
of
this
before,
but
I'm
just
trying.
This
is
the
one
I'm
drawing
today.
An
appealing
vision
is
that
the
cortical
sheet
consists
of
you
know
a
set
of
these
1d
grid
cell
analogs
or
oscillators
that
are
then
being
read
out
by
local
grid
cells.
B
This
picture
is
intended
to
look
like
a
data
tank
paper
and
and-
and
so
you
might
have
like
multiple
of
these-
these
readouts
occurring
within
one
module,
and
so
this
is
just
giving
you
a
mental
image
now,
a
more
a
more
like
theoretical
vision,
a
theoretical,
like
an
information
processing.
Explanation
of
this
would
be
at
it's
going
to
be
a
dimensionality
expansion
and
a
dimensionality
reduction
as
a
as
a
as
an
animal
moves
through
an
environment.
I
didn't
go
ahead
and
draw
this
updating.
B
Study
that'd
be
very
hard,
but
you.
What
would
happen
is
these
1d
rings
would
all
perform
a
bunch
of
their
own
updates
and
they're
actually
representing
something
like
that
is
representing.
What's
out
there,
it's
representing
you,
know
the
boundaries,
object,
vector
cells
and
so
on,
but
then
somehow
that
gets
reduced
onto
2d
grid
cells.
B
There
are
ways
to
do
this,
but
the
requirements
that
needs
to
meet
are
it
needs
to
be
an
unambiguous
mapping
such
that,
given
a
point
on
the
left,
given
the
combination
of
where
these
dots
are,
there's
a
single
correct
position
for
the
dot
on
the
right
and
the
second
requirement
for
it
to
behave
like
2d
grid
cells.
Is
you
can't
have
discontinuities
so
smooth
updating
on
the
left
should
cause
smooth
updating
on
the
right.
You
should
never
have
this
as
the
animal
moves.
This
shouldn't
just
hop
around.
It
should
move
smoothly.
A
You
know
those
are
on
the
left.
You
have,
you
know,
let's
say
mini
column
outputs,
and
so
you
have
pretty
sparse
high
dimensional
output
coming
in
and
then
you
have
a
just
a
random
spatial
cooler
with
topology,
maybe
not
random,
but
spatial
cooler
with
topology.
So
you
have
a
2d
grid
and
sort
of
local
inhibition
radii
and
some
you
know
sparsity,
so
that
you
get
very
small
activity.
I
wonder
if
you
would
get
something
like
that.
D
A
B
Yeah,
what
you're
saying
sounds
like
it
would
be
grid
like
I'm,
not
sure
if
it
would
be
metric,
so
that,
but
maybe
yeah,
that's
a
good
avenue
to
think
about
so
so
the
the
trick,
I'm
gonna,
show
to
help
think
about
it.
I'm
gonna
split
the
two
taurus
into
two
rings,
and
now
I'm
gonna
show
just
something
really
quite
simple
here
I
just
hadn't
thought
of
it
before
so
I'm
treating
these
rings.
B
I'm
drawing
this
almost
like
a
neural
network
where
these
rings
are
going
to
be
determined
by
in
some
sense
adding
these
up,
adding
up
some
combination
of
them
and
I'll
say
just
in
a
little
more
detail.
What
the
what
I
mean
so
the
rings
on
the
right
compute,
a
sum
of
rings
on
the
left.
It's
going
to
be
confusing
to
you
now.
I
need
to
get
say
more
precisely.
What
do
I
mean
by
sum
it
computes
the
sum
of
each
ring's
displacement
from
some
reference
point.
B
B
D
Is
it
because
what
maybe
maybe
it'll
help
explain
something
I
was
just
thinking
like
well,
if
the
dots
on
the
ring
on
the
end
taurus
is
on
the
left,
are
going
around
and
round,
and
you
think
about
a
number
line
and
you're
just
adding
it
up,
there
would
be
a
discontinuity
when
you
go
from
zero
to
ten
and
back
to
zero
again
or
something
like
that.
You
know
what
I'm
saying:
if
you
call
it
a
number
line,
then
how
does
it
you
know?
How
does
it
wrap
back
on
I
mean
I
can
imagine.
D
B
E
E
B
D
B
B
D
D
So
so,
well,
a
one-day
grid
zone
module
has
multiple
cells
in
it.
Right
right
has,
and
so
I
I
don't
know
what
it
means
to
add
up
different
cells,
but
if
I
call
it
a
voltage,
control
yeah,
you
know
what
I'm
saying:
it's
like:
okay,
there's,
actually
10
cells
there
you're
going
to
give
a
value
to
each
one,
they're
kind
of
equivalent,
just
10
different
cells.
B
This
is
this
is
my
last
slide.
This
is
me
showing
you
a
technique
that
will
that
will
work,
I'm
still
in
the
stages
of
following
all
of
its
following
ever
well
figuring
out
everything
that
follows
from
this
idea,
and
I
can
show
neural
mechanisms
for
it,
but
I'm
still
wrapping
my
head
around
it.
I
have
spent
time
sketching
it
optimized
it
works.
It
has
all
the
properties
you
want.
It
did.
D
B
This
certainly
loses
the
information.
However,
the
information
is
still
here.
The
difference
with
the
the
other
versions
is
that
it's
like
an
it's
almost
it
almost
like
the
other
versions
perform
an
error
correction
where
once
this
collapses
down
onto
the
two
taurus,
the
other
versions
are
going
right
back
to
this
and
lose
all
the
information.
That's
here,
this
isn't
gonna.
Do
that
it's
it's!
D
D
C
B
B
If
we
assume
I'm
right
about
this
middle
piece,
okay,
which
is
which
I'm
not
assuming
yet-
and
I
I
would
say
I
haven't
even
given
you
that
bit
of
a
pitch
for
it
yet
once
I
understand
it
more
fully
I'll
be
able
to
just
like
describe
it
in
the
right
way
where
it
clicks
and
feels
right
if
it's
right,
and
so
I'm
still.
This
is
the
snapshot
presentation,
the
new
grid
cell
trick
of
adding
angles,
causing
a
collapse
from
a
high
dimensional
torus
to
a
low
dimensional
torus.
D
D
Going
to
talk
about
it's
amazing,
how
much
overlap
is
between
what
you
present
here,
not
in
what
your
new
idea
is,
but
in
the
same
problem
I'm
trying
to
solve
in
some
ways
I
didn't
phrase
it
the
way,
but
this
can
be
somewhat
overlapped,
but
you
might
you
just
talked
about
what
I'm
going
to
talk
about,
but
I'm
coming
in
completely
different
direction.
So
so
it's
interesting
I'm
trying
to
get
my
head
around
it,
but
it'll
be
good
cross
fertilization.
Here.
B
That's
a
good
question.
I
I
guess
I'm
trying
to
figure
that
out.
I
mean
the
the
reason
we
need
it
is
because
grid
cells
exist
and
I'm
trying
to
explain
them
and
and
so
yeah
the
theoretical
reason
for
them.
It
seems
to
be
that
that
what
enter
rhino
core
test
texas,
passing
up
to
the
hippocampus
is
some
unique
memory,
footprint
or
fingerprint
footprint.
Some
unique
memory.
A
B
B
D
Yeah,
why
do
we
even
care
about
so
I
I
can
give
you
an
answer
why
they
exist.
It's
maybe
not
the
right
answer,
but
it's
an
answer.
One
of
the
things
is
that
we
also
know
from
biology.
Is
that
you
know
when
you're
moving
these
oscillators
go
and
their
voltage
control
means
their
speed
control.
The
oscillator
is
right,
so
it's
a
theta
frequency
and
it
increases
a
little
bit
based
on
how
fast
you're
moving
and
the,
but
as
soon
as
you
stop
moving
that
all
that
goes
away.
D
Theta
rhythm
stops
and
everything
stops.
You
need
something.
One
of
the
things
you
need
is
the
ability
to
latch
on
to
your
current
location
and
hold
it.
You
know
you
don't
forget
where
you
are
as
soon
as
you
stop
moving
and
we
also
need
it.
So
that's
one
of
the
things
you
might
get
from
having
a
2d,
taurus
or
the
2d
grid
cells
is
you
have
you?
E
D
D
You
know
center
surround
inhibition
and
maybe
the
center
on
the
ambition
is
just
there
to
to
lock
in
the
results
until
the
time
until
you
start
moving
again
at
least
that's
one
of
the
things
it
does
and
whether
that's
fun,
whether
it's
theoretically
essential
or
not,
is
a
question
right,
but
it
is
certain
as
marcus
says
it's
there.
We
see
these.
That's
what
grit
cells
look
like
right.
B
C
C
B
D
So
I've
been
working
on
the
same,
we're
all
working
on
the
same
problem.
You
know
this
is
working
on
this,
and
so
I've
been
trying
to
I've
been
trying
to
not
only
figure
out
how
the
quarter
of
a
column
implements
grid
cells,
but
I'm
trying
to
figure
out
how
it
implements
displacement
cells,
because
I'm
kind
of
working
through
a
theory
where
I
can
get
the
whole
I
mean
remember
in
the
end,
what
we
we
think
is
going
on
is
that
object.
D
Models
of
objects
are
objects
at
relative
locations
and
orientations
to
other
objects
which
are
relative
locations
and
orientations
other
objects,
and
we
have
this
concept
displacement
cells.
So
I'm
working
on
the
idea
of
how
good
cells
and
the
splicement
cells
can
be
all
implemented
in
a
cortical
column
and
and
the
displacement
cells
have
to
have
displacement
for
orientation
as
well
as
displacement
for
for
location
so
and
I'm
just
and
and
so
it's
really
a
lot
to
ask
a
quarter
column
to
do.
D
There's
just
there's
a
lot
of
things
that
have
to
happen,
and
it
just
doesn't
seem
to
be
enough
cell
types
and
I'm
you
know
I've
been
really
trying
to
struggle
with.
So
I
went
back
to
an
idea.
I'll
tell
you
in
a
second,
which
is
the
idea
that
actually
the
the
grid
cells
come
about
because
there's
oscillations
in
the
individual
dendrites.
This
is
a
I'll
mention
that
again,
that
was
a
paper
that
merkel
reviewed
when
he
was
here.
So
let
me
just
go
through
this.
D
Is
this
is
overlapping
with
what
marcus
just
said,
but
here's
my
notes
on
my
notepad
here.
If
we're
going
to
make
a
grid
cell,
we
have
to
first
of
all
determine
the
velocity
of
movement
in
multiple
directions.
All
the
oscillatory
interference
models
require
this
so
and
they're
one
dimensional
directions,
and
so
that's
something
that
has
to
be
done.
D
Then
we
have
to
convert
that
velocity,
which
is
a
scalar
into
a
using
a
vco
into
an
oscillation
change.
So
we
now
we're
going
to
have
some
sort
of
oscillator
that's
running
around
theta,
but
when
we're
moving
in
a
particular
direction,
a
certain
amount,
the
faster
we
move
in
that
direction,
the
faster
that
rhythm
goes
above
the
base
theta.
D
D
Here
I
say
for
each
vco:
we
need
a
set
of
vcos,
it's
actually
a
set
of
sub
vcos
if
you
will
right
or
that
that
they
have
the
same
incremented
frequency,
but
have
different
phases,
because
the
way
we're
going
to
get
one
grid
cell
module,
the
fire
one
location
another
which
will
follow
next
to
is
that
they
have
to
be
looking
at
the
same
voltage:
control.
Oscillators,
but
at
different
phases
of
the
voltage-controlled
oscillator,
so
there's
been
proposals
on
how
that
happens,
and
we
also
with
something
we
haven't
really
discussed
much.
D
We
need
a
way
of
of
anchoring
grid
cells.
I
don't
I
don't
have
this
written
here,
that's
down
here.
I
guess
I
can
I'll
get
to,
but
but
basically
we
need
a
way
of
anchoring
grid
cells
on
different
environmental
conditions.
So
we
go
into
an
environment.
We
immediately
anchor
our
grid
cells
and
that's
another
requirement.
D
D
I
don't
remember
the
authors
or
the
title
of
the
paper,
but
if
someone
has
it
and
could
send
it
on
slack
that'd
be
great,
because
I
want
to
read
it
again,
but
in
this
paper
that
merkel
reviewed
the
idea
was
that
individual
dendrites
have
their
own
oscillations
and
in
that
the
individual
dendrites
oscillated
differentially
in
in
different
directions
of
movement.
So
let's
say
this
dense
right
here
would
go
from
one
direction
and
this
would
go
another
direction.
D
Just
go
another
direction
that
they
would
summit
the
cell
body
and
you
get
the
oscillatory
inference
happening
here.
So
I
show
six
here
because
one
of
the
complications
of
of
this
whole
system
is.
We
know
that
these
these
voltage
control
assets
only
work
in
one
direction.
So
when
I
measure
movement
in
north
and
then
I
head
south-
it's
it's
not
like
the
one
oscillator
goes
faster.
Then
it
goes
slower.
It
doesn't
appear
to
be
that
way.
It
appears
to
be
like.
D
D
So
this
idea
was:
when
merkel
read
this
paper.
I
was
kind
of
like
incredulous
about
us,
like
I
never
heard
of
these
voltage,
these
oscillations
and
dendrites.
It
seemed
kind
of
like
a
complicated
system
how's
this
going
to
work,
but
maybe
for
those
who've
been
around
a
while.
You
remember
that
paper.
Hopefully
that
merkel
presented
it
was.
It
was
an
alternate.
It
was
basically
saying
that
these
oscillators
are
not
cells.
D
So
now
recall
and
marcus
just
mentioned
this-
and
I've
been
proposing
that
the
many
columns
themselves
because
of
the
complex
cells
in
them
look
like
they
would
represent
a
movement
vector
in
a
particular
1d
dimension.
Each
each
mini
column
looks
like
that.
That's
what
the
complex
cells
look
like,
they're
doing,
they're,
saying
I'm
going
to
be
active
when
I'm
moving
in
one
direction
and
if
I'm
moving
it
better
off
a
little
bit
less
active
and
I'm
moving
orthogonal,
I'm
not
active
at
all.
D
Dendrite,
remember:
minicoms
are
pretty
small,
they
get
anywhere
from
30,
microns
or
80
microns,
or
something
like
that,
so
dendritic
arbors
are
typically
much
larger
than
that,
and
so
the
dendritic
arbor
of
this
cell
here
would
be
would
be
coursing
through
all
a
bunch
of
minicoms
nearby.
In
fact
most
of
them
it
doesn't
mean
it's
connecting
to
them,
but
it's
coursing
through
them.
D
Now
imagine
if
each
of
these
mini
columns
was
a
essentially
a
voltage,
controlled
oscillator
and
imagine
that
for
various
possible
mechanisms
that
they
are,
they
are
essentially
creating
each
dendritic
branch
to
be
a
voltage-controlled
oscillator
or
or
you
know.
Yes,
that's
basically
what
it
is
as
opposed
to
the
the
picture
down
here
or
I
showed
six
of
them
or
in
that
paper
they
showed
three
of
them.
D
Imagine
now
that
all
these
dendritic
branches
are
essentially
picking
up
the
oscillation
of
the
local,
the
mini
column,
that's
that
they're
coursing
through,
and
so
now
you
have
a
cell.
It
essentially
has
the
ability
to
to
aggregate
lots
of
different
movement
commands
that
would
that
that
it
would
use
now
at
any
particular
point
in
time.
Most
of
these
minicoms
would
be
inactive.
D
You
could
get
this
oscillatory
interference
happening
at
every
in
some
sense
or
any
junction
along
the
any
section
of
these
dendrites
or
any
junction
of
these
dendrites.
You
could
be
having
the
same
kind
of
effect
that
you
have
down
here
and,
and
so
this
is
a
way
of
merging
you're
sort
of
bringing
the
oscillatory
interference,
idea
the
mini
column
or,
excuse
me,
the
voltage,
control
oscillator
for
dimensional
movement,
the
minicom
uniting
with
this
idea,
but
just
making
it
a
lot
more
complicated,
but
it'd
also
be
a
very
physical
thing.
D
It
just
it
just
would
naturally
occur
as
these
dendrites
course
through,
whether
it
whether
there's
a
like
a
you
know
it
could
be.
For
example,
it
could
be
like
a
bipolar
cell,
which
is
very
constrained
for
a
mini
column.
That's
a
cell!
That's
very
constrained.
Tremendous
could
be
forming
synapses
on
these
dendrites
saying
you
should
be.
You
should
be
locked
in
synchronization
with
me.
I'm
a
mini
column.
This
blue
circle,
I'm
oscillating,
I'm
going
to
I'm
going
to
make
you
oscillate
with
me.
A
D
But
here,
but
I'm
not
even
I'm,
not
I'm
not,
this
doesn't
doesn't
require
that
there
actually
has
to
be
synapses
here,
I'm
going
to
get
the
synapses
in
a
moment.
The
most
important
thing
right
now
is
that
the
dendritic
segment
is
oscillating
in
its
along
with
the
mini
column,
and
it
could
be
because
our
synapses
on
here
that
are
that
are
firing
that
are
coming
from
the
main
column
or
it
could
be.
D
D
Yes,
it's
a
good
analogy.
It
just
makes
me
laugh
yes
like
little
antennas,
so
it
could
be
because
their
synapses
are
forming
and
those
synapses.
If
they
were,
then
those
those
synapses
would
have
to
come
in
cells
that
are
only
in
this
mini
column,
which
is
why
I
suggested
it
might
be
the
bipolar
cells,
because
they
were
constrained.
Those
little
very
fine
constrained,
axons
that
are
within
the
minicom
or
it
could
be
just
a
local
field
potential
antenna
as
kevin
says,
but
that's
the
basic
idea
and
I'm
working
through
it.
D
But
here's
what
here's?
What
you
get
with
this
you
get
a
whole
nother
level
of
abstraction
a
whole
another
level
of
what's
driving
this
grid
cell
under
many
many
different
contexts.
For
example,
going
back
to
the
issue
that
grid
cells
have
to
anchor
right.
Remember
when
you
go
in
an
environment,
they
have
to
somehow
know
I'm
supposed
to
be
active
and-
and
we've
never
really
talked
about.
You
know,
given
some
environmental
input,
you
know
how
that
occurs.
D
D
That's
the
pattern,
I'm
seeing
in
the
world
and
under
a
different
you
know,
and
even
that
segment
could
be
shared
with
other
different
patterns.
It
basically
allows
that
the
allows
me
to
lock
in
a
set
of
dendritic
activations
and
which
essentially,
it
locks
in
this
cell's
activity
under
many
many
many
different
contexts.
D
I'm
not
saying
what
those
contacts
are
in
a
moment.
I
I
want
them
to
be
objects
at
some
pose,
or
you
know,
orientation
and
distance
from
from
the
observer
observer.
But
but
for
the
moment
it
just
allows
me
to
give
me
a
mechanism
like
we
have
it's.
We
preserved
another
level
of
indirection
where,
where
the
grid
cell
is
actually
the
sum
it's
it's
a
representing
it's
the
same
thing
that
marcus
is
doing.
D
I
want
this
grid
cell
to
represent
a
much
more
complex
set
of
interactions
that
are
going
out
there,
that
all
kind
of
go
on
to
the
cell
being
active,
and
so
that's
what
this
does
it,
and-
and
so
that's
pretty
much
the
idea
as
I'm
working
on
right
now
and
what
I
like
about
it
too,
is
it
it.
It
just
naturally
incorporates
the
local
it's
a
physical
mechanism,
where
the
physical
proximity
of
the
dendrite
to
the
mini
columns
is
passing
by
causes
the
oscillations
on
these
dendrites.
D
A
About
that
I
was
just
kind
of
looking
up
thinking
about
mechanisms
again
and
one
other
possible
mechanism
is
to
look
at
gap
junctions
that
are
in
pyramidal
neurons
and
they
may
be
perhaps
they're
formed
by
these
bipolar
cells.
I'm
not
sure,
but
I
was
just
doing
a
little
bit
of
searching
and
there's
a
whole
there's
a
review
paper
on
gap,
junctions
and
pyramidal
neurons
and
how
they
lead
to
oscillations
of
different
types
in
the
membrane
potential.
A
D
D
D
So
it
just
makes
this
really
beautiful
result.
It
also
is
interesting.
I
thought
I
thought
it's
an
interesting
thought
too,
that
there's
a
couple
other
complications
here.
First
of
all,
adjacent
many
adjacent
grid
cells
have
to
have
you
know
they
have
they're,
not
identical,
and
so
you
need
them
to
you
know.
Essentially
what
happens
is
the
the
oscillation
on
this?
Let's
say
the
oscillation
on
in
here
oscillation
on
this
dendrite
here
is
going
to
be.
I
have
to
have
another
oscillation
on
the
next
cells.
D
The
next
grid
cell
over
has
to
be
able
to
get
a
similar
oscillation,
but
from
the
same,
maybe
mini
column,
but
a
different
phase
right.
It
has
to
be
a
different
phase,
I
mean
so.
A
voltage
controlled
oscillator
has
to
have
cells
in
multiple
phases
to
get
multiple
grid
cells
in
a
grid
cell
module.
That
was
that's
part
of
the
theory.
So
what
that
tells
me
there
is
like
okay.
D
That
means,
if
I'm
looking
at
a
mini
column
like
this
mini
column
and
mini
columns
oscillating
at
this
theta
plus
frequency,
because
we're
moving
in
its
direction,
I
have
to
have
multiple
cells
within
the
mini
column
that
are
that
are
cycling
through
their
phase
or
I
shaft,
or
at
least
I
have
to
have
different.
I
have
to
have
somehow
in
that
minicom.
I
have
to
represent
the
different
phases
of
that
oscillation,
whether
it's
a
cell
firing
or
if
it's
traveling
oscillation
that
goes
down
the
mini
column.
D
I
don't
know
what
it
is,
but
there
has
to
be
multiple
phases
represented
so
that
the
next
cell
over
might
also
pick
it
up,
but
would
pick
up
at
a
different
phase
and
I've
been.
I
just
started
to
work
through
the
learning
mechanisms
for
this,
but
I
think
this
whole
thing
could
be
learned.
That
is,
if
we
force
two
grid
cells
next
to
each
other.
D
If
we
force
a
bunch
of
grid
cells
into
a
2d
center
surround
type
of
inhibitory
network,
so
that
we're
forcing
this
pattern
we
see
of
grid
cells
in
a
module
where
multiple
cells
are
spaced
out,
and
so
on
that
you
could.
I
think
I
haven't
worked
it
through
yet,
but
I
think
you
could
get
it
to
force
the
next
cell
over
to
form
synapses
with
the
form
synapses
or
or
connect
to
a
different
part
of
the
minicom
for
different
phase,
because
that's
what's
required
to
go
from
one
grid
cell
to
the
next.
D
So
somehow
the
thalamus
is
projecting
a
base
theta
across.
Let's
say
all
the
apical
dendrites
for
these
cells,
so
the
cell
is
looking
at
the
soma
of
the
cell
is
getting
a
base
theta
from
its
apical
dendrite,
and
it's
getting
the
it's
getting
the
sum
of
the
or
no,
I
guess
yeah.
I
you
know
I
haven't
worked
through,
that.
Does
the
base
data
have
to
be
presented
at
each
dendritic
junction.
C
B
D
I
thought
I
thought
that
wasn't
the
case.
I
thought
for
the
I
thought
for
the
the
the
voltage
control
oscillators
that
they
only.
I
can't
even
remember
what
the
evidence
for
this
was,
but
I
the
impression
they
only
only
become
active
when
you're
moving
and
when
you
stop
moving
they
just
they
just
either
silent.
They
don't
have
to
keep
moving
they're
not,
and
it
doesn't
matter.
D
I
guess
it
doesn't
really
matter
for
me
if
it's,
if
the
oscillator,
if
the,
if
the
base,
also
if,
if,
if
say
I'm
not
moving
in
this
dimension,
if
I'm
not
moving
in
a
dimension,
is
if
the
oscillation
of
the
vc
of
the
vco
was
exactly
theta,
then
it
wouldn't
have
any
wouldn't
make
any
contributory
effect.
It
would
just
be
theta,
and
so
as
if
it
was
nothing
it's
only.
It's
only
the
only
important
thing
about
it
is
when
it
speeds
up
relative
to
theta.
B
C
D
C
D
D
D
You
know,
for
example,
if
you
remember
layer,
6
cells,
they
they
send
their
dendrites
up
into
layer,
four,
not
only
the
projector
layer
for
but
there's
under
dendrites
up
in
the
layer
four,
so
so
you
might
be,
and
so
you
might
be
getting
on
a
dendritic
branch
or
a
genetic
tree
of
a
particular
grid
cell.
If
you
will,
you
might
be
getting
some
of
it
is
going
to
be
getting
input.
That
represents
one
thing
and
someone's
going
to
represent
inputs
in
another
thing.
So
what
what?
E
D
A
A
E
D
Well,
I
do
know,
I
do
know
that
in
some
neurons-
and
I
don't
know
all
neurons,
but
some
neurons-
the
tips
of
the
dendrites,
just
like
the
tips
of
the
axons,
can
grow
all
the
time,
they're
constantly
reaching
out
trying
to
find
new
connections,
and
that
will
be
tracked
if
they
don't
find
anything
useful.
They
retract
and
they'll
try
going
in
a
different
direction.
C
D
You
can
I
can
see
what
subita
is
saying
you
can
easily
imagine
there
might
be
some
really
stupid
algorithm.
That
just
says
you
know.
If
I've
gone
certain
distance,
I
should
fork
because
that's
going
to
be
an
efficient
way
of
getting
finding
more
things.
You
know
it's
like
trees
right.
You
know.
When
does
the
tree
decide
to
branch?
It's
it's
yeah.
A
D
E
D
Well,
there's
there's
definitely
there's
there's
a
couple
things
here.
First
of
all,
when
the
brain
is
developing,
you
know
in
utero
or
even
after
europe,
there
are
gradients
that
say:
oh
I'm
supposed
to
send
this
neuron
is
supposed
to
move
over
to
here,
and
this
neuron
is
going
to
send
its
axon
up
to
here.
So
there's
this
basic
new
wiring
that
occurs,
but
as
far
as
we
know,
all
the
end
result
wiring
all
the
individual
synapses.