►
From YouTube: Numenta Research Meeting - Dec 16, 2019
Description
From Florian:
In response to Jeffs contemplation of MCs in 1-dimensional terms, I’m (re)reading a bunch of grid-cell papers with respect to their apparent dimensionality and what happens during projections into lower space (such as projections from 2D grid cells in navigation tasks on a linear track):
https://www.ncbi.nlm.nih.gov/pubmed/26898777
I also want to take a few minutes to talk about the non-hebbian behavioural timescale plasticity involved in spontaneous or targeted creation/remapping of place cells, described by Bitte and Milstein:
https://www.ncbi.nlm.nih.gov/pubmed/28883072
A
B
All
right
so
we're
gonna
talk,
since
we
are
talking
about
Eli
anyways
unit,
our
paper
with
Eli
and
tank
on
this
I
guess.
Half
of
the
data
also
came
from
from
that
I
think
about
somewhere
an
idea
of
explaining
the
response
properties
of
grid
cells
in
one
key
environments
and
sort
of
the
main
hypothesis
that
they're
testing
in
this
paper
is
the
idea
that
you
can
explain
the
1d
responses,
which
are
quite
different
from
the
2d
responses
and
that
they
have
their
in
key
amplitudes
and
they're.
C
B
D
Apartment
has
a
whole
bunch
of
1d
original
manga
that
are
aligned
with
me
because
he
comes
himself
one
day
and
I
went
through,
although
we
had
no
evidence
for
that
I,
eventually,
a
very
nice
explanation
for
how
I
wanted
things
work.
So
there
was
like
no.
There
was
a
lot
of
bias
and
then
you
said
yeah.
D
C
B
So,
to
be
clear,
this
comes
from
from
this
discussion
of
Jeff's
idea
and
I'm,
essentially
leg
revisiting
a
couple
of
different
place,
subjects
a
grid,
some
papers
now
to
sort
of
see
this
in
the
context.
We
can
find
ways
to
affirm
it
or
contradicted
passed
out
on
it
or
you
know,
find
interesting
new
perspectives.
D
D
D
So
the
idea
was
that
could
be
a
one-dimensional
original
model,
each
mini
call
and
therefore
you
have
several
hundreds
of
others
that
are
very
our
progress,
but,
on
the
other
hand,
would
be
there
Delilah
and,
and
then
I
want
to
from
that
idea.
Each
one
of
these
guys
intersecting
some
n-dimensional
space
on
the
paper
there
Mercola
marcus
work
done
and.
D
C
D
C
D
For
example,
when
you
have
an
orientation
I'm
sorry
to
do
this
directly,
but
if
you
have
an
orientation
by
Seaworth
in
the
3d
world,
you
have
different
3d
engines
like
which
way
you're
facing
and
somehow
you
have
to
take
that
3d
orientation
and
use
it
to
decide
which
way
to
update
the
3d
print
jobs
on
the
multiple,
its
own
module
based
on
your
movement
right,
it's
like
honey
to
do
that.
It's
really
hard
mathematically!
You
can
show
up
again,
though
here
is
all
you
have
to
do.
D
It
has
to
just
know
it's
orientation,
basically,
a
scalar
value,
which
is
how
much
of
that
may
become,
is
projecting
into
the
where
your
current
orientation
projection
for
that
one
day.
So
he's
mini-comic
an
update
on
its
own,
just
like
on
buy
one
scalar
value
and
then
I
showed
how
you
can
actually
get
a
value.
D
D
B
Okay,
so
first
things:
first,
you
start
with
a
bit
of
MA
for
like
just
very
broad
idea:
I
guess
you
have
familiar
with
the
2d
which
sells
wet.
So
this
is
how
it
looks
like
and
in
gray
the
the
outlined
track
of
the
of
these
rodents
in
a
2d
space
and
then
in
red
waiting
for
the
dot
in
this
map
whenever
they
spike-
and
you
very
nicely
see
that
from
doing
so.
These
are
two
different
petrodes
different
channels,
I
guess,
as
you
can
see
from
these
numbers
here,
you
get
the
aspiring
fields
right.
B
So
this
is
what
you
then
see
here
in
2d,
which
have
this
very
nice
very
nice
to
D
to
the
latter's
six
degrees,
and
you
can
obviously
record
from
the
exact
same
electrodes
right
then
on
a
linear
track,
and
typically
the
behavior
looks
a
little
bit
different
because
there,
it's
not,
you
know
clearly
periodic
in
that
sense,
and
the
amplitude
tends
to
varies.
If
you
do
find
rate
averaging
right
over
this
track,
looks
like
six
meters
long.
D
B
D
D
B
That
is
just
the
first
or
observation
which
makes
1d
behavior
interest
and
if
you
plot
the
firing
rate
so
of
these
instead
of
looking
at
the
raw
spikes
here
right.
So
if
you
get
some
of
the
it
is
the
average
over
multiple
apps,
then
you
see
these
nice.
You
know
piggy
behavior
here
actually
for
both
of
these
tetrax,
and
so
one
thing
that
one
can
do,
of
course,
is
take
a
look
at
how
do
these
sort
of
overlap
with
one
another?
You
see,
for
example,
that
defying
fields
first.
D
D
B
So
that's
just
it
to
be
for
analysis
very,
very,
very
nicely
get
those
three,
those
three
for
opening
angles
right
of
the
author
of
the
lattice,
so
that
these
60
degree
angles
you
see
in
the
no
that's
a
yeah.
It's
a
2d
power,
spectral
density
of
the
Fourier
transform.
So
you
can
do
the
same
thing.
Obviously
in
the
1d
case.
D
B
D
B
D
C
F
E
D
B
Okay,
all
right,
so
this
slide
is
just
simply
putting
these.
You
know
like
2d
and
1d.
You
know
contrast
with
one
another
to
familiarize
you
with
the
idea
of
okay,
we
trans
bikes
into
flying
fields.
We
can
look
at
how
these
firing
fields
overlap,
don't
open
up,
and
we
can
do
a
Fourier
analysis
to
take
a
look
at
what
are
the?
B
What
are
the
the
periods
right
with
which
we
can
understand
these
firing
fields
to
repeat-
and
so
one
thing
that
is,
for
example,
rather
obvious
from
the
fact
that
you
have
multiple
spatial
Peaks
here
is
that
you
will
not
get
very
regular
oscillatory
periodic
spiking,
because
there
are
multiple
frequencies
in
here,
so
the
firing
fields
are
not
generated
by
one.
You
know
standing
sine
waves.
D
B
D
D
D
B
Yes,
okay,
all
right,
moving
on
from
the
first
figure,
let's
see
so
if
you
want
to
understand
so
this
is
completely
theoretical.
This
is
not
real
data
now
right.
This
is
theory
of
the
theoretical
idea.
If
you
had
a
perfect
2d
lattice
like
this,
and
you
decided
to
walk
through
it
at
different
angles,
so
you
have
this
data
and
you're
gonna
go
through
it.
What
would
be
the
firing
rate
that
you
would
expect?
A
B
Varying
the
angle
and
the
power
spectral
density,
you
see
these
Peaks
merging
right
from
2
into
3
into
2
into
1.
Again,
once
you
arrive
at
30
degrees,
you
again
get
a
regular
oscillation
at
a
higher
frequency,
though
right,
but
it
just
goes
to
show
that
you
can
do
this
kind
of
analysis
and
you
can
somehow,
if
this
was
ideal,
you'd
be
able
to
infer
the
angle
at
which
you
are
going
through
the
lattice
from
a
firing
rate
plot
like
this.
This
is
very
nice
and
clean,
because
it's
all
theoretical
could.
F
I
make
a
one
quick
point
that
sampling,
if
you're
doing
in
this
perfect
lattice,
also
corresponds
to
the
problem
in
computer
graphics
of
aliasing.
So
you
actually
get
some
of
these
components
wrapping
around
and
appearing
as
low
frequencies.
Because
of
that,
so
it's
even
more
complex
than
what
it
appears
there
because
of
that
wraparound
effect.
B
D
B
B
So
now.
The
interesting
idea
is
that
if
you
have,
if
you
do
parallel
slices
to
a
grid
and
which
is
going
to
be
important
for
understanding,
Co
modulated
cells,
I'll
talk
about
that
in
a
bit,
then
you
would
expect
that
while
they
have
a
different
face
depending
on
where
they
start,
they
have
the
same
power
spectral
density
because
they
traverse
it
at
the
same
lattice
angle
here
so.
D
B
E
G
E
C
E
B
B
B
B
So
now,
an
interesting
way
to
sort
of
look
at
the
data
in
a
slightly
different
way
is
to
instead
of
looking
at
the
frequencies,
which
are
hard
to
determine,
because
these
tracks
are
not
long
enough.
You
look
at
something
else,
a
lot
more
easy
to
measure,
which
is
the
gaps
right:
the
gaps
between
the
firing
fields
and,
of
course,
we
know
that
if
you
move
along
the
lattice
right
in
an
ideal
world
right,
you
have
this
spatial
factor
a,
and
that
is
the
distance
between
your
firing
fields.
B
B
B
So
this
is
sort
of
theoretical
idea
of
like
to
make
it
a
little
bit
more
tractable,
and
so
now
you
can
look
at
actual
recordings,
so
1d
spatial
tuning
cars.
So
these
are
just
recordings
right
from
rodents
and
one
d
1d
tracks
and,
as
you
know,
expected
you
do
see
sort
of
like
these
firing
fields,
so
they're
often
firing
at
the
same
position
in
the
multiple
different
labs
that
you
see
in
horizontal
lines.
Here,
there's
the
fact
two
different
databases
here
that
they're
passing
so
like
one
of
them
has
like
a
six
meter
track.
B
E
B
E
B
So
using
a
bit
of
math
that
I,
you
know
we
don't
need
to
go
into
much
depth.
I
hope
convinced
you
that
somehow,
from
this
analysis
of
the
firing
rate
and
then
looking
at
the
power
spectral
density,
we
can
infer
certain
parameters
like,
for
example,
the
angle
at
which
these
different
firing
fields
right
would
be
explained
by
the
idea
of
going
through
a
toonie
lattice.
D
B
So
too
does
briefly
step
back
a
little
bit.
One
of
the
things
since
this
lattice
gives
you
like
these
characteristic
lengths
of
a
square
root
of
3a
and
square
root
of
seven
a
what
you
are
expecting
in
terms
of
gap
ratios
are
one
over
square
root
of
3
1
over
square
root
of
7
and
square
root
of
3
over
7
as
gap
ratios.
B
This,
of
course,
does
not
tell
you
yet
whether
there
is
a
correspondence
between
the
2d
response
and
the
one
day
response.
This
just
goes
to
show
the
idea
that
you
can
somehow
fit
right.
I
think
that's
the
the
Green
Line
is
the
fit,
and
the
black
is
the
real
data.
You
can
somehow
fit
the
firing
fields.
B
The
firing
rate
of
the
1d
responds
quite
nicely
with
an
idea
of
just
finding
a
slice
through
2d
grid
that
would
yield
similar
firing
fields
in
similar
positions
and
with
similar
amplitudes,
like
containing
the
same
frequency
components
and
also
somehow
fitting
the
gaps
between
the
fire
fields
and
so
that,
of
course,
you
have
to
control
whether
that
is
just
maybe
either.
Maybe
that's
just
a
very
powerful
thing
to
do
any
firing
rate
distribution
on
a
on
a
six
meter
track
can
be
fitted
by
a
slice.
B
If
you
are
free
to
choose
your
face
and
your
angle-
and
you
know
who
knows
so,
they
did
some
controls
by
creating
artificial
data
that
were
either
gap
randomized
or
like
completely
randomized.
So,
where
you
just
move
the
firing
fields
to
random
locations,
preserve
the
number
of
firing
fields
or
you
shuffle
the
the
gaps,
and
they
showed
in
mathematical
terms
that
the
fit
is
not
nearly
as
nearly
as
good
for
those.
In
fact,
it's
quite
a
bit
of
a
difference.
We
don't
need
to
go
into
this
exact
sheet,
a
quality
metric
that
they
have.
B
They
have
a
score
that
they
call
power,
string,
power,
spectral
density
creepiness.
This
p3
number
somehow
assesses
whether
there
are
three
strong
peaks,
as
predicted
by
such
theory,
but
the
the
worthwhile
thing
to
look
at
is,
for
example,
this
complete
aggregate
of
data
that
we
have
in
d
here
and
we
just
quickly
see
the
race.
So
that's
the
aggregate
black
aggregate
gap,
distribution
pulled
across
all
cells
in
the
data
set.
So
this
is
like
a
massive
average.
B
After
the
gaps
in
each
cells,
response
are
normalized
by
the
lattice
period
right,
so
you
take
out
the
lattice
period.
So
that
means
that
the
lattice
is
one
now,
and
so
what
you're
expecting
is
big
peaks
at
square
root
of
3
+
square
root
of
7?
It
turns
out
the
peaks.
Are
a
little
bit
earlier
than
that,
but
there
are
three
nice
Peaks,
so
it's
you
know
not
out
of
the
world
and,
judging
by
the
statistic
analysis
that
they
have,
this
explanation
is
way
more
likely
than
not
the
right
one.
B
Now
this
all
of
this
just
shows
that
we
can
fit
the
one
B
responses
with
this
method.
It
does
not
show
at
this.
There
is
a
strict
correspondence
between
the
2
D
and
the
1d
response.
One
way
to
assess
that
is
to
look
for
cone,
modulated
cells,
so
in
the
2d
grid,
and
see
whether
they
behave
accordingly
and
the
one
you
pick.
B
So
you
have
two
cells
that
are
part
of
the
same
module
and
that
have
the
same
firing
fields
so,
for
example,
you're
saying
yeah
exactly
so,
and
so
here
you
have
two
cells
first
in
the
2d
environment
up
here
and
then
no
that's
actually
not
it.
Let
me
see
whether
I
get
this
right
so
yeah.
So
the
idea
would
be
that
cells
that
are
Co
modular,
so
that,
like
fire
together
statistically
right
should
ideally
be
parallel
slices
with
a
similar
scale
factor.
B
So
because
the
angle
would
be
the
same,
so
that
would
have
the
same
power,
spectral
density
and
you
find
some
cells
for
this
holds
true,
and
then
you
would
infer
the
angle
from
it,
and
the
question
is
sort
of.
Is
it
true
that
all
all
Co
modulated
cells
then
have
the
same
slice
angle?
When,
when
you
sort
of
try
to
extract
the
slice
angle
that
they
did
here
right
from
a
1d
linear.
D
B
D
B
You
see
two
pairs
here,
one
up
here
and
a
and
B
and
one
in
C
and
D,
and
so
these
two
to
cell
pairs
have
very
similar
power.
Spectral
density
as
to
these
two
very
similar
power,
spectral
density,
and
so
the
model
will
suggest
that,
in
fact,
if
you
infer
what
that
means
as
a
2d
slice
that
these
are
parallel
slices,
so
they
have
a
different
face,
but
they
do
have
the
same
size
angle.
B
And
so,
if
you
now
look
at
at
the
distribution
in
the
in
the
recording,
what
are
the
slice
angles
that
you
get
out
and
what
are
the
scale
factors
that
you
get
out?
You
get
a
very
nice
distribution.
The
problem
is
that
in
this
uncured
data
you
don't
always
get
the
same
slice
angle,
so
you
have
to
comb
modulate
it
cells.
Don't
apparently,
don't
are
not
explained
by
the
same
size
angle.
C
B
Like
that,
so
they
find
an
experimental
procedure
to
pick
so
that
a
consistent
set
of
peaks
and
the
power
spectral
density
and
for
the
slice
angle
only
from
those
and
then
it
turns
out
the
fit,
is
quite
a
bit
better.
To
me
that
looks
a
little
bit
like
cheating.
I,
also
find
the
problematic
that
there's
sort
of
a
gap
here
at
0
to
10
degrees,
there's
very
few
cell
types
in
there,
but.
B
B
So
anchoring
matters,
and
so
I,
don't
know
if
they
did
this
sort
of
like
or
where
the
reviewers
poked
them
at
it.
Exactly
this
question,
you
actually
have
a
plot
here
of
the
grid
orientation
versus
the
slice
angle
that
is
predicted
for
these
for
modulate
itself
again
the
cells
that
are
motivated
same
colonies.
You
would
expect
them
to
have
the
same
slice
angle
and
you
would
expect
them
to
predict
the
same
with
orientation,
and
so
this
is.
This
seems
to
work
quite
well.
D
B
D
E
G
D
B
D
F
E
B
F
B
As
well,
but
anyways
you've
seen
the
one
defining
way
how
it
evolves
right,
and
so
you
give
it
in
front
of
not
just
the
anger
based
on
the
power,
spectral
density
or
the
gamma
distribution
for
that
matter.
But
you
can
also
make
an
attempt
at
inferring
the
face
from
the
one
D
and
the
question
is:
does
the
one
D
predicted
face
actually
coincide
with
the
face
in
the
2d
response?
Sure
it.
D
E
B
So
because
of
what's
called
like
because
of
the
degeneracy
that
is
inherent
in
solving
this,
when
you
solve
these
equations,
you
actually
get
12
solutions
back
for
the
face,
and
so
you
kind
of
have
to
pick
one
so,
but
if
you
pick
the
one
that
fits
best,
then
you
get
this
very
nice
pairing
here
between.
Let's
see
what
is
it?
B
Well,
it's
a
face,
so
this
is
not
plotted
right
in
the
in
the
rhomboids,
so
the
face
to
0.5
0.5
to
you
know
you
put
pipes
and
predicted
in
color
triangles
and
then
the
actual
value
that
they
see
in
the
2d
data
is
the
circle.
So
you
would
hope
that
all
the
triangles
and
circles
of
the
same
colored
cells
are
always
very
close
by
right
and
of
course,
you
know
like
you
can
see
that
okay,
that
works
reasonably
well.
I
see
a
lot
of
pairings
here
right
if
I
go
through
this
diagram.
B
B
C
A
C
B
D
B
I
don't
know,
I
would
have
to
take
a
look
which
exact
data
set.
This
came
from,
but
they
had
like
a
virtual
track
ones
which
you
can
actually
be
set.
So
if
this
is
the
virtual
track
one
then
it's
very
easy.
I
mean
you
just
let
the
animal
run
to
six
meters
and
then
push
a
button,
and
you
said
it
like.
D
B
Not
always,
but
what
sometimes
happens,
which
you
cannot
analyze
with
the
students?
Is
these
drifting
firing
fields
where
they
seemed
to
drift
at
some
moderate
rate,
because
it
seems
it's
not
just
that
the
first
one
here,
sort
of
drifting
backward,
but
actually
the
second
one,
is
drifting
to
the
third
one.
The
fourth
one
gets
a
bit
messy
to
analyze
this
without
data
analysis,
but
you.
D
B
B
You
see
in
fact,
that
all
these
different
trials
predict
the
same
angle.
Just
you
know
a
little
bit
of
a
blip
here
up
and
down,
but
sort
of
all
the
data
suggests
that
this
is
going
at
the
20
degree
angle
through
the
grid
and
then
putting
you
know
pretty
much
a
constant
scale
factor
to
the
one
thing
that
seems
to
drift
slowly
but
steadily
I'm
interesting,
you're,
not
also
linearly
over
the
lap
numbers
is.
There
is
a
face
right
and
in
fact,
these
two
cells
drift
in
parallel.
D
B
So
if
you
now
do
the
analysis
right
on
lap
by
lap-
and
you
try
to
infer
the
2d
angle,
scale
factor
in
the
face,
then
in
fact
this
method
of
analysis
explains
this
data.
As
saying
look,
the
only
thing
that
was
happening
here
is
that
the
angle
of
a
scale
factor
stay
constant,
but
the
phase
shifting
so
the
right
way
to
view
this.
Is
this
behavior?
Where
essentially,
what
is
happening
is
that
this
is
the
power
spectral
density
here
right
and
then
gap
distribution
of
one
on
this
kind
of
mix.
D
B
Right
apparently,
one
also
sometimes
happens
particularly
on
tracks,
where
there
are
landmarks
that
these
things
can
change
rather,
roughly
because,
apparently
you
know
the
latest
we
anchoring
and
whatnot,
and
so
they
nicely
chose
datasets
where
there
are
no
landmarks
or
the
snow
remapping
happening
where
they
chose
the
cells.
That
are,
you
know
reasonably
consistent,
so
there's
all
kinds
of
pre-filtering
in
the
data
center
in
some
sense,
but
what
what
they
do
see
a
lot
is
abusive
parent
drift.
B
D
D
D
B
E
D
C
D
Modules,
Michael
taking
I've
got
a
little
1d
module
in
that,
and
so
there's
a
bunch
of
cells
in
that
1d
module
and
let's
say
that
I
three
of
those
modules
and
their
own.
It
at
60
degrees
monitor
right
now
that
module
is
only
thinking
in
1d,
but
I
think
it
would
think
which
still
exhibit
all
the
states.
G
F
Is
there
anything
where
they
tried
to
I
mean
if
the
rad
is
running
down
a
linear
track?
Is
there
what?
How
would
it
pick
the
the
base
angle,
you
know
I
mean,
wouldn't
there
be
a
only
small
deviations
from
whatever
that
base
angle
is
orientation
or
whatever
I'm
just
trying
to
figure
out
which
which
are
these
angles
in
a
linear,
environment
or
even
accessible
and.
B
B
F
D
D
D
B
One
thing,
of
course,
that
I
was
thinking
about.
Like
you
mentioned
this
idea,
you
know,
is
there
any
way
that
you
would
get
the
appearance
of
2d
lattice?
Even
if
the
mentally
you
know
like
units
close
by
are
actually
Lundy?
Is
that
possible
and
I
think
the
answer
to
that
is
to
look
at
to
look
at
patch-clamp
recordings
of
grid
cells,
because
that
way
you
would
get.
You
would
know
that
this
is
not
like.
You
know,
coincident
by
the
electrode,
but
it's
it's
actually
D
cell
itself.
B
D
B
D
D
D
D
D
D
D
D
D
They
really
are
annuity
and
there's
a
complex
mechanism
there,
and
maybe
the
exact
same
things
going
on
the
cortex
so
they're
both
like
that.
You
just
don't
understand,
because
we
don't
really
insane
how
it
works.
The
other
possibility
is
that
do
a
lot
of
cortex,
it's
not
the
same
cortex.
It
may
be
cortex,
which
is
really.
D
Evidence
wanna
cortex
is
traded
with
sort
of
the
miniconjou
geneticists.
Maybe
it
is,
but
we
know
that
the
cortex
is
built
and
therefore
maybe
the
cortex
works
on
a
slightly
different
structure
with
it's
not
the
same
as
enter
outer
cortex.
But
then
now,
we've
seen
like
fMRI
data
that
suggests
that
there
is
a
60
degree
orientation
in
some
parts
of
prefrontal
cortex,
although
it's
weaker
than
the
internal
cortex
and
that's
good
thing
and
or
the
other
possibility
is
that
maybe
both
of
these
systems
are
really
one
dimension.
D
B
No,
no
none
of
this
makes
a
functional
argument.
How
will
this
works
right?
This
is
all
descriptive,
and
then
you
know
in
this
case
putting
a
very
nice
mathematical
model
on
it,
which
turns
out
to
work
well
right,
which
I
found
very
nice
I
mean
this
paper
was
a
blast
to
read
just
because
it's
so
nicely
graphical
use.
You
know
it's
like
plot
these
lines
through
the
2d
lattice
system,
try
to
understand
from
Sapodilla,
so
it
is
a
amount
of
topological
in
understanding.
D
B
Well,
it's
to
quickly
point
out
how
this
would
look
like
in
1d
right
this
cell,
but
the
grid
one
would
be
the
prediction
from
the
2d
slice
and
it
turns
out
there's
no
bump
here,
even
though
the
prediction
says
there
should
be
one
and
this
bomb
is
half
the
amplitude.
That
would
be
expected
yeah
right.
So
maybe
this
is
what
we're
talking
about.
I.
D
Think
the
one
paper
I'm
familiar
with
it
was
consistent.
It
wasn't
yes,
it
was
like
that.
Yes,
it
was
very.
It
was
varying
levels
than
this
ones.
If
I
would
call
making
Homer
Marcus
what
I
call
it
was
not.
It
was
a
graded
in
this
sometimes
they're,
completely
missing.
So
I
thought
it
was
half
as
much,
but
it
was
consistent,
and
that
was
like.
D
D
On
top
of
it,
we
just
markets
were
saying
when
I
was
saying:
that's
an
additional
coding
scheme,
artisan
that
do
babies
papers
that
that
can
tell
you
more
about
were
the
animal
is
so
I
I
thought
that
was
I'd
like
to
read
that,
because
I
think
is
the
tank
people
I
read,
there
was
no
speculation
about
where
you
can
talk
about.
What
would
you
call
it
just
again?
I
missed,
but
you
know
that's
was
interesting
observation,
but
they
didn't
do
any
analysis
of
it.
Oh
they
didn't
someone
else,
but
not
back.
G
D
D
We
have
to
say
we're
in
when
we're
in
a
reference
frame
with
some
object
and
we
have
some
location
in
that
object,
but
we
also
have
to
do
for
the
state
of
that
object
like
the
cell
phone
state
or
so
I
was
excited
about
that,
and
that's
another
sort
of
complication
going
on
after
this,
but
I'd
like
I
would,
if
you
could
just
send
me
one
of
those
early
papers
that
he's
not
look
better
I'd
like
to
look
at
that
who'd.
You
say.
G
Was
again
I
don't
remember
first
off
there,
but
I
appreciate
that
and
so
okay,
a
couple
dollars
came
up.
You
one
is
you're
talking
like
certain
problems
just
vanish
once
you
use
1d
modules,
problems
involving
orientation
and
I.
Think
oh
I,
don't
think
any
problems
vanish,
except
for
the
number
of
cells
needed
well.
D
So,
for
example,
just
how
I
would
here's
here's
where
I
don't
know
if
you
hurry,
but
it
did
nicely
put
a
little
bit
okay.
So
if
you
have
a
3d,
let's
have
a
3d
orientation
in
a
3d
space
right,
I,
don't
know
if
that
3d
space
is
represented
by
a
bunch
of
two
events
online.
You
know
like
how
we
represent
that
maybe
but
different
slices
of
2d
that
we're
representing
that
space
by,
but
then
I
anyway.
D
I
have
some
sort
of
3d
orientation
and
push
that
through
the
orientation
dictates
when
I
move
with
how
each
of
the
grid
cells
mind
will
update
a
very
precisely
they
took.
You
know,
different
orientations,
the
multiples
in
different
directions
and
I
have
to
make
the
differentiation
between
the
different
quit
so
Martha's
house.
So
I
have
this
sort
of
mathematically.
It
might
be
easy
to
explain.
No
I
have
a
3d
orientation.
I
have
a
3d
space.
D
How
should
my
bub
move
in
3d
space
based
on
the
orientation
I'd
be
easy,
but
the
target
I've
never
been
up
to
see
a
neural
mechanism
for
that
that
was
easy,
whereas
in
the
1-day
sense
it
was
pretty
easy.
I
only
had
them
to
have
as
a
scalar
value
per
1d
mini
column
and
that
scalar
value
would
be
basically
sort
of
represent
the
how
orthogonal
the
1d
dimension
is
relative
to
the
orientation
of
sort
of
like
you
know
bits.
What
is
you
know?
How
much
is
it
if
I'm
moving
forward,
how
much?
D
Even
less
than
that,
because
I
was
bargaining
that
that
could
be
actually
I,
also
I
figured
out
a
way
of
using
sensory,
and
please
determine
that
and
and
therefore
what
I
was
thinking
was,
if
you,
if
you
had
this
a
bunch
of
bipolar
cells
that
were
not
that
were
representing
orientation
and
those
bipolar
cells,
receive
input
from
centers
that
were
where
flow
information.
It
wasn't
a
spatial
pattern.
D
What
I
get
out
of
it
when
I
get
a
bunch
of
scalar
values
that
represent
the
orient,
the
projection
of
orientation
onto
that
dimension,
and
so
I
could
using
a
simple
spaceship.
Ulla
process
using
sensory
I
know
exists.
I
can
now
have
a
scalar
value
and
a
bunch
of
mini
columns
and
that
skill
evaluate
just
say
if
I'm
moving
how
much
this
problem?
How
quickly
should
this
problem,
but.
D
D
Let's
take
that
first
sorry
I,
really,
maybe
the
rat
can
do
them.
You
know
I
can
do
that,
but
let's
just
start
for
the
idea
that
maybe,
if
I'm
stepping
sideways,
maybe
what
I'm
really
doing
is
changing
my
orientation
and
I'm
not
changing
the
direction
of
my
head.
So
if
I,
if,
if
you
think
of
the
orientation,
is
the
direction
you're
going
to
move,
not
the
which
way
your
head
is
facing,
it
might
work,
but
but
yes,
we
are
making
a
bunch
of
simplifications.
My.
D
Yes,
I
do
that
and
there
two
of
those
going
there
nothing
I
can
buy
nice
about.
This
is
if
I
think
about
this
I
think
it's.
The
theta
is
between
the
theta
minus
theta
between
the
cortex
and
thalamus
and
I've
already
won
the
psi.
That
might
be
a
scalar
that
represents
the
speed
of
movement
and
so
that
all
you
need
to
have
an
orientation
and
a
speed
of
movement
and
they're.
All
all
the
individual,
one-dimensional
cells
would
update
automatically
so
Lisa
I
am,
but
I
can
work
through
a
scenario.
D
D
But
anyway,
that's
your
point.
Every
question
Marcus
I
felt
like
for
the
first
time,
I
had
a
workable
system
where
I
could
say
sensory
input
can
determine.
My
orientation
can
can
tell
me
what
my
number
of
dimensions
I
have
in
the
world.
You
tell
me
an
updated
cell
modules.
I.
Can
you
know
I
have
enough
good
cell
modules
that
I
could
sample
for
him
to
get
the
right
answer
and
even
I
don't
know
if
its
own
modules
that
I
could
so
I
could
use
a
higher
level
of
coding,
which
is
making
some
look
miss.
D
You
know
basically
like
let's
say:
I
have
200
bits
of
Michael's
and
they
all
they
were
divided
into
three
dimensions
or
360-degree
dimensions,
or
something
like
that
then
I
could
jump.
I
could
activate
some
subset
over
to
represent
they'd
all
be
updated
with
some
subset
to
represent
the
state
of
this
display
get
a
mandatory
complexity.
D
So
I
don't
know
it
was.
It
was
I
made
it
very
clear
that
it
wasn't
a
full.
It
didn't
fit
everything,
but
it
was
an
interesting
thing
to
think
about.
It
was
like
there
was
something
about
and
I
really
liked
the
idea
that
I
could
use
this
sort
of
flow
or
sensory
data
like
the
directional
sensitivity
to
know
how
to
update
my
orientation
and
my
position.
Yes,.
G
D
Else,
don't
we
are
what
you
see
when
we
give
you
know,
but
we
generally
don't
talk
about,
but
remember
we
will
be
talking
about
playing
and
you're
sitting
in
front
of
a
screen
and
you're
plenty
of
indicating
you're
moving
your
character
around,
and
we
know
that.
That's
one
of
the
scenarios
that
the
contents
and
a
few
people
did
to
test
their
theory
right
and
what.
F
D
D
Well,
what
I'm
saying
is
the
Delta
its
imagine
the
following
men,
not
in
your
centre
native
divided
in
two
parts?
One
is
a
spatial
pattern
like
the
depressions
on
my
finger
and
when
I'm,
detecting,
enhance
or
not,
and
the
other
is
sensors
that
detect
motion
across
independent
of
the
pattern.
Those
exist
under
the
envision
and
in
touch.
You
have
these
two
separate
things.
D
Two
separate
paths:
Lee
now
imagine
that
may
take
the
pathway
that
representing
flow
I
can't
I
can't
determine
what
the
actual
fingers
what's
the
pattern,
I
think
I
could
just
tell
the
trade
flowing
if
I
take
that
information
now
I
have
the
ability,
like
imagine,
I'm,
just
looking
at
the
game
and
I'm
like
you
know
how
do
I
not
turn
left
or
turn
right
or
going
forward,
and
going
that
only
information
I
have
by
leading
that
stream
is
a
relative
flows.
That's
it
there's
nothing
else,
matters
it
doesn't
matter
what
objects
are
there?
D
We
told
my
cells
being
updated
by
motor
behavior,
but
and
she
has
to
learn
using
the
sensory
day
that
we
concluded
this
ones
that
have
to
learn
to
use
sensory
data
to
determine
first
determine
your
movement,
and
then
you
could
associate
that
with
motor
that
up
front.
You
don't
want
motor,
be
he
was
making
room,
so
it
really
had
been
century
German
experience
and
the
video
game
is
proof
of
that.
D
D
D
D
D
D
F
D
F
D
D
F
D
You
have
a
model
if
you
blur
in
this
environment,
you
have
a
model
of
the
world,
you
have
to
now
you're
open
your
eyes.
You
have
to
infer
both
your
location
in
their
orientation
and
you
can
only
do
that.
If
you
recognize
something
in
front
of
you,
you
know
so
it's,
but
it's
the
interaction
between
the
sensory
input,
spatial
right.
F
D
D
That
exactly
no
that's
a
purely
a
sensory
component
I'm
not
doing
any
motor
output
right
I'm.
Just
looking
at
the
screen
and
the
first-person
perspective,
what
my
character
is
moving
through
the
screen:
there's
no
motor
output,
a
light
part
I'm,
just
inferring
that
movement
through
visual
input.
That
was
that
was
that
was
the
key
insight.
I
was
thinking
about
video
games.
What
about
perception.
B
D
D
That's
detecting
movement
or
flow
could
be
put
through
a
spaceship
full
of
process,
creating
a
bunch
of
many
columns
that
then
represent
one
of
these
dimensions
of
space
and
and
could
update
appropriately
based
on
that
and
then,
whenever
we're
going
to
go
back
and
blue
and
Brian
I
have
to
refer
to
that
right.
Yes,
I
have
to
I,
have
to
reenter.
D
D
Know
for
a
long
time,
I'm
sort
of
stuck
on
the
whole
grid
cell
thing,
there's
so
many
things
that
just
don't
have
up
you
don't
have
enough
modules
is
not
clear
down
to
the
white
oak
tree
turbine
or
n
dimensional
space.
You
don't
know
how
to
learn
that
we
anchor.
We
don't
know
how
to
learn
what
the
dimensionality
of
space
is
to
even
the
knowledgebase.
B
D
G
D
D
D
If
there
was
a
separate
input
coming
in
layer,
five,
which
we
know
there's
a
separate,
confining
layer,
five,
which
represent
the
flow
sensor,
data
and
those
from
those
mini
columns
there
on
down
that
they
wrote,
was
they're
all
representing
his
face,
and
so
I
have
the
space
analysis
and
reading
counting
space
in
the
bottom
and
the
mini
columns
representing
object,
features
in
the
top
areas
and
how
those
because
I,
basically
a
place,
no
result.
I
put
a
1-1,
testable
hypotheses.
We
know
that
there's
these
two
sensory
inputs
come
from
the
thalamus
foot.
D
F
D
That
are
related
to
movement
in
the
century
extreme
and
that's
known
to
exist
that
they're
there
a
lot
of
more
than
project
that
would
support
this
hypothesis.
So,
basically,
you
have
two
different
sensors
on
your
eyes.
Ones
that
are
spatial
patterns
want
to
detecting
movement,
that
the
rumor
detectors
have
going
to
the
lower
there's
a
pattern
to
the
upper
layers
that
would
kind
of
fit
with
this
model
too,
and.
D
F
D
Simple
cell
is
across
all
different
layers,
if
maybe
the
wrong,
and
maybe
in
the
situation,
we
have
been
anesthetized
animal
and
you're
just
giving
it
well
think
about
how
you
know
what
happens
with
Whoville
and
bezel.
They
didn't.
They
couldn't
get
any
cell
to
respond
to
anything
until
they
actually
accidentally
slid
the
slide,
and
so
the
edge
of
the
slide
moved
across
the
visual
field
of
the
cat,
and
that
was
the
first
time
they
ever
recorded
a
cell
fire
based
on
the
input
you're
trying
to
show
the
cat
on
the
input.
D
So
now,
what
do
we
do
now?
When
we
show
we
want
to
characterize
what
a
cell
responds
to.
We
show
it
sinusoidal
gratings,
which
is
almost
all
movement.
It's
not
really
problems
at
all.
It's
just
a
movement
vector
in
that.
So
that's
the
idea
again
and
that
may
be
the
activity
of
a
column
is
really
representing
by
the
way
that
movement
is.
It
is
literally,
my
hair
shines
from
the
grating,
and
so
we
talk
about
different
orientations.
Well,
they
may
respond
great.
D
A
graded
response
based
on
the
orientation
that
literally,
would
represent
the
projection
of
the
orientation
to
to
the
in
some
sense
of
flow
would
be
defining.
What
is
it
pride,
which
is
the
primary
1b
dimension
and
other
other
columns
would
respond
graded
ly
or
not
at
all,
depending
on
there,
so
that
whole
idea
of
what
a
mini
column
is
representing
8a
orientation
column?
That's
almost
always
determined
by
movement
like
flow
through
time,
Rizzoli
ratings,
which
that
really,
what
is
detecting
is
the
is
the
response
from
any
column
then
becomes
less
than
the
pattern.
D
It
becomes
more
of
the
tagging
ality
of
the
projection
of
the
orientation
to
them
to
the
movement.
It
says
how:
how
much
is
this
mini
column
represent
movement
in
that
direction,
see
what
it
represents.
That
became
the
signal
that
we
could
use,
update
the
location
cells,
I.
Think
there's
something
to
that
idea.
It
just
it
just.
D
F
D
F
E
F
I'm,
just
looking
at
you
know,
if
you
have
a
composite
thing
with
it's
made
of,
you
know
a
huge
number
of
spatial
frequencies,
whether
there's
some
place.
Where
that
all
correlates
and
saying
yeah
I
still
got
motion,
irrespective
of
you
know,
I'm
going
to
do
all
the
grading
patterns
light
up.
You
know
when
you
drag
random
dots
across.
D
F
My
point
is:
is
the
you
had
mentioned
that
until
they
drag
an
edge
across
and
again
any
response?
What
I'm
wondering
is:
is
that
do
you
if
anyone's
tried
it
where
it's
it's,
it's
moving
of
the
textures
rather
than
a
specific
spatial
frequency
grid
moving
across
and
whether
that
correlates
in
is
that
creates
the
same
firing
pattern
if
you
wish
in
and
where
you're.
D
F
D
Remember
they
want
to
characterize
these
cells,
usually
there's
some
experiment.
They
want
to
like
figure
out
what
the
quote
classic
receptor
field
for
the
sellers,
and
so
they
quickly
came
out,
decide
that
the
best
way
for
figuring
that
out
the
best
responses
they
got
word
from
sinusoidal
gratings.
They
didn't
start
there.
So
I,
don't
know
what
else
they
try
and.
F
Well,
given
that
you
have
you
know,
if
you
wish
feature
detectors
in
the
obstacles,
cortex
for
actually
finding
edges
that
make
sense,
I
was
just
looking
at.
You
know
where
you're,
what
the
Gestalt
sense
of
motion,
where
that
would
locate
whether
it's
just
an
integration
of
all
the
the
spatial
cells
or
whether.
D
F
F
D
There
are
motion
sensitive
cells
in
the
auditory,
cortex
and
cochlea
because
they
detect
you
know
moving
frequencies
and
the
back.
These
are
that
it's
almost
so
much
of
people
look
at
when
they
characterize
these
cells.
In
many
common,
like
he
was
almost
all
the
vast
majority
of
not
all,
but
many
many
of
them
are
voting
sensitive.
They
want
to
respond
when
they
spawn
trash
like
the
one.
The
stimulus
was
in
one
direction
or
the
other
direction.
D
D
G
D
D
A
A
A
So
if
you're
watching
this,
you
might
be
interested
and
now
that
I
feel
totally
like
I'm
not
prepared
Kurtis
over
to
this
on
December
23rd,
that's
when
Gary
Marcus
and
yoshua
bengio
are
debating,
and
so
I
thought
we
would
do
a
live
stream.
People
do
this
on
Twitch.
Sometimes
you
watch
something
live
with
your
audience,
so
I'm,
inviting
all
of
you
guys
out
there
to
come.
Join
me:
December
23rd,
that's
a
week
from
today
at
4
p.m.
Pacific
7
p.m.
A
Eastern
on
my
twitch
channel,
and
so
that
my
twitch
channel
for
those
of
you
not
familiar
with
trich
it
sort
of
can
be
sort
of
confusing.
This
is
my
twitch
channel.
Somebody
else
is
on
it
right
now.
That's
fine!
That
happens.
But
if
you
go
to
this
twitch
channel
I,
don't
know
what
any
of
this
stuff
is.
This
is
an
ad
or
something,
but
if
you
go
to
my
twitch
channel
and
one
week
at
4
p.m.
A
on
Monday
you'll
get
to
watch
me
watch
Gary
Marcus,
you
know,
she's
been
show,
debate
live
for
as
long
as
they
go
and
then
we'll
chat
I'll
go
up
to
chat,
room
open
and
we
will
also
have
like
I'm
thinking
some
type
of
polling
or
voting
mechanisms,
so
that
you
guys
can
interact,
give
give
people
points
when
they
deserve
them.
I,
don't
know
we'll
do
something
fun
like
that:
I'll
have
to
figure
it
out
by
then
and
I'll
be
prepping
for
it
on
my
twitch
stream.
A
If
you
want
to
check
out
my
Twitter
stream,
please,
like
this
video
and
subscribe
to
the
YouTube
channel.
It's
very
helpful.
I
know
it
seems
silly.
Everybody
asked
for
it.
That's
because
everybody
wants
it,
and
also
the
very
last
thing
I
could
mention
is
I
got
a
new
HTML
video
in
case
you
missed
it
HTM
school
16,
it's
about
hierarchy,
where's
there
we
go
thousand
brains,
theory
and
higher.
So
I
really
explain
hierarchy.
Just
google,
it
I
explain
why
a
hierarchy
in
the
brain
is
different
than
the
way
we
think
hierarchy
in
the
brain.