►
From YouTube: Continual Lifelong Learning Paper Review / Jeff Hawkins on Grid Cell Modules - February 10, 2021
Description
Karan Grewal gives an overview of the paper “Continual Lifelong Learning with Neural Networks: A Review” by German Parisi, et al.. He first explains three main areas of current continual learning approaches. Then, he outlines four research areas that the authors advocate will be crucial to developing lifelong learning agents.
In the second part, Jeff Hawkins discusses new ideas and improvements from our previous "Frameworks" paper. He proposes a more refined grid cell module where each layer of minicolumns contains a 1D voltage-controlled oscillating module that represents movement in a particular direction. Jeff first explains the mechanisms within each column and how anchoring occurs in grid cell modules. He then gives an overview on displacement cells and deduces that if we have 1D grid cell modules, it is very likely that there are 1D displacement cell modules. Furthermore, he makes the case that the mechanisms for orientation cells are analogous to that of grid cells. He argues that each minicolumn is driven by various 1D modules that represent orientation and location and are the forces behind a classic grid cell / orientation cell module.
“Continual Lifelong Learning with Neural Networks: A Review” by German Parisi, et al.. : https://www.sciencedirect.com/science/article/pii/S0893608019300231
"A Framework for Intelligence and Cortical Function Based on Grid Cells in the Neocortex" paper: https://www.frontiersin.org/articles/10.3389/fncir.2018.00121/full
0:00 Continual Lifelong Learning Paper Review
40:55 Jeff Hawkins on Grid Cell Modules
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A
So
the
I'm
going
to
present
a
short
overview
of
this
review
paper
that
I've
been
going
through
over
the
last
couple
of
weeks.
I
there's
a
lot
of
this
paper
cites
a
lot
of
papers
and
they
go
into
a
lot
of
depth
here
and
there,
but
I
tried
to
keep
this
as
short
and
to
the
point
as
possible
so
that
we
can
extract
the
main
parts
from
here.
A
I
guess
solving
continual
learning,
and
I
think
this
part
is
interesting
because
it
ties
in
with
some
of
the
work
that
lucas
has
started
doing
on
embodied
ai,
okay,
so
I'll
jump
right
into
part,
one
which
is
the
three
types
of
three
main
types
of
approaches
towards
continual
learning.
First,
is
regulating
levels
of
plasticity,
and
this
so
so
here
what
we
have
is
the
amount
that
parameters
can
change
in
a
in
a
neural
network
as
it
trains
it
trains
over
time.
This
is
regulated
by
the
objective
function,
so
elastic
weight.
A
They
say
what
would
generally
happen
is
that
it
would
follow.
Perhaps
the
blue,
the
trajectory
to
the
next
point
in
weight
space
would
perhaps
follow
this
blue
arrow
here
to
get
somewhere
here.
But
what
they're
doing
is
they're
constraining
the
weights
so
that
it
ends
up
moving
somewhere
here,
where
you're
performing
well
on
cast
a
and
task
b
and
how
they're
doing
that
is
through
determining
which
weights
can
change
and
which
weights
can
change
and
that's
determined.
A
They
all
have
different
methods
here,
for
example,
in
elastic
weight
consolidation.
I
think
they
use
fissure
information
to
determine
which
weights
are
important
and
which
weights
aren't
so
important
towards
the
task.
So
you
can
so
one
way
to
think
about
it
here
is
that
you
know
some
weights
may
be
stronger
and
when
I
say
stronger,
I
mean
in
the
sense
that
it's
harder
to
change
them
as
the
network
tries
to
learn
subsequent
tasks.
A
But
one
shortcoming-
or
I
guess
two
shortcomings
with
this-
is
that
as
you
learn
more
and
more
tasks,
you're
starting
to
constrain
more
and
more
weights,
but
these
set
of
weights
are
going
to
be
more
important
for
cascade
and
another
set
of
weights
are
going
to
be
more
important
for
task
b
and
and
so
on.
Until
you
reach
a
point
where
not
many
weights
can
change
at
all,
so
it's
harder
to
learn.
A
A
The
next
method
is
allocating
additional
resources.
So
in
all
these
cases,
what
they're
doing
is
the
network
is
actually
expanding
its
architecture
so
the
first
type
of
case
they
have
progressive
neural
networks
where
all
they're
doing
is
they're,
adding
a
bunch
of
new
units
on
the
side
and
every
time
you
learn
a
new
task.
You
just
add
in
new
units
and
that
ends
up
learning
the
weights
for
the
new
tasks
and
you
don't
even
change
the
original
ones.
A
Now
the
problem-
or
I
guess,
okay
and
then
another
variant
of
that
is
instead
of
training,
everything
or
or
instead
of
always
adding
new
units.
You
can
add.
Sometimes
you
can
add
new
units
and
you
can
even
combine
them
with
older
units
that
have
already
been
trained,
and
that
is
beneficial
in
the
sense
that
you're
using
more
distributed
representations
here
and
not
and
you're,
not
always
and
you're,
probably
not
going
to
add
as
many
new
units
here
as
you
do
in
this
case.
A
But,
of
course,
the
disadvantage
here
is
that
your
model
complexity
grows
with
the
number
of
tasks,
and
and
actually
they
make
a
case
for
being
able
to
train
sub
networks,
and
I
guess
this
is
something
we're
really
looking
into
right
now,
too,
training
subnetworks
to
learn
each
new
task
in
sequence,
but
but
there's
no
mention
of
sparsity
or
anything
here.
So
I
guess
this
is
why
it
ends
up.
It
ends
up
hitting
hitting
hitting
a
wall
eventually.
A
Somehow
I'm
gonna
highlight
just
two
methods
here
that
sort
of
build
on
this
idea,
so
the
first
one
was
developed
by
jeff
hinton
back
in
the
80s,
and
so
in
his
in
his
model
he
had
between
every
I
guess:
every
every
weight
actually
was
with
two
different
weights.
One
was
a
fast
weight
and
one
was
a
slow
weight
which
changed
a
lot
slower,
and
so
the
fast
way
to
you
can
think
of
it
as
having
a
higher
learning
rate.
A
It's
learning
the
task,
that's
at
hand
and
not
worrying
about
what
it
learned
before
at
all,
and
then
slow
weight
is
sort
of
aggregating.
All
that
was
learned
over
a
whole
learning
trajectory
and
through
and
then
it's
it
and
then
the
knowledge.
I
guess
what
the
fast
way
is
learning
over
time.
It
gets
consolidated
into
the
slow
weight.
Now,
I'm
not
sure
about
the
details
on
exactly
how
this
is
done,
but
they
have
but
yeah
and
then
another
one
that
I
thought
was
a
bit
interesting
was
this
idea
of.
A
So
I
guess
this
other
method
here
actually
took
basically
created
a
neural
network
out
of
both
the
hippocampal
parts
and
the
cortex
part,
so
they
have
a
pfc
network
and
a
hippocampal
network,
and
what
they're
doing
here
is
every
time
they
have.
They
want
their
model
to
make
a
prediction:
they're
they're,
sending
the
outputs
they're
they're
using
both
to
predict.
But
then
then
the
output
goes
to
this
to
this
other
network
bla
network,
which
is
basolateral
amygdala
network,
and
that
is
deciding
which
which
network
should
be
used
for
the
output.
A
B
C
B
A
D
A
And
the
and
the
reason
why
they
have
these
encoder
and
decoder
parts,
which
just
like
kevin
mentioned,
is
because
ultimately,
this
this
this
approach
boils
down
to
replay
or
they
refer
to
it
as
a
rehearsal,
a
lot
in
the
the
actual
review
paper
so
replay.
The
idea
is
that,
as
as
you're
as
you're
learning,
you
store
previous
examples
in
memory,
and
then
you
replay
those
so
that
you
retrain
on
those
so
that
you're
not
entirely
forgetting
them,
and
there
is
additional
memory
cost
to
storing
during
those
examples
from
the
past.
A
So
in
this
case,
what
they're
doing
is
sudo
replay,
which
is,
I
guess,
a
bit
different
in
that
in
that
you're,
not
exactly
storing
examples
in
memory.
But
you
do
have
this
sorry,
this
this
decoder
network,
which
is
able
to
sort
of
generate
synthetic
examples
for
your
replay
purposes
so,
and
I
think
this
is
used.
This
is
part
of
this-
is
used,
especially
in
their
sleep
phase,
as
they
call
it
to
consolidate
knowledge
between
the
hippocampal
network
and
pfc
network.
E
E
A
So
the
three
I
just
mentioned
are
so,
if
you
take
all
the
research,
that's
been
done
today
on
continual
learning
in
the
especially
in
the
neural
network
community,
how
you
can
sort
of
categorize
those
into
three
different
types
of
approaches?
Okay,
I
guess
that
was.
That
was
the
main
point
of
their
paper
to
review.
I
got
that.
A
E
A
E
F
A
So
the
first
one
is
developmental
and
curriculum
learning.
The
reason
why
they
think
this
is
important
is
because
humans
don't
learn
from
examples
of
data
in
isolation
in
random
order,
which
is
mostly
how
neural
networks
now
right
now
are
trained,
and
so
you
know
taking
inspiration,
so
they
make
a
case
for
taking
inspiration
from
how
kids
learn
and
also
through
having
some
sort
of
curriculum
which,
which
has
been
shown
in
the
past
in
in
neural
networks,
to
improve
the
speed
at
which
a
model
learns.
A
So
the
key
idea
here
is
that
in
infants
there's
a
critical
learning
period
where
the
brain
is
highly
plastic
and
you
can
learn
really
fast
and
then
over
time
it
sort
of
slows
down.
I
guess
the
neural
network.
Analog
of
this
would
be
like
a
decaying
learning
rate
that
would
that
would
be
like
the
simplest
way
of
looking
at
it
and
in
terms
of
curriculum
learning.
A
So-
and
this
brings
us
to
the
third
point
which
we're
going
to
talk
about
soon
curiosity
and
motivation,
because
if
it's
not
necessarily
that
there's
only
one
dimension,
that
you
can
look
at
a
a
a
on
which
you
can
order
a
set
of
tasks
and
saying
okay,
this
is
clearly
the
hardest.
This
is
clearly
the
easiest,
so
we
should
do
it
this
way,
but
rather
this
these
curriculums
can
change
based
on
how
learning
has
progressed
so
far.
D
D
The
other
thing
is
that
in
a
baby,
there's
accessibility,
there
are
certain
things
that
can
only
that
can
be
learned
at
a
certain
age,
but
nothing
more
complex
and
then
once
those
are
kind
of
mastered,
you
go
on
to
the
next
one,
so
both
of
them
imply
kind
of
a
structured
approach
to
curriculum,
and
I'm
just
wondering
how
the
neural
net
community
would
try
to
organize
things
so
that
it
it
actually
the
curriculum
actually
is
structured.
I
mean
you
can
talk
about
simple
to
complex
but
they're.
A
So
I'm
not,
they
didn't
make
any
mention
of
how
exactly
they
would
do
it
in
a
continual
learning
setup,
but
I
would
guess
that
it
would
be
you
have.
I
guess
this
would
sort
of
carry
over
into
transfer
learning
where
you
have.
If
you
have
one
set
of
tasks,
if
learning
one
task
is
believed
to
help
in
learning
the
next
task,
then
maybe
you'd
learn
the
first
task.
First
and
in
the
neural
network
community,
it's
they.
They
see
curriculum
learning
as
a
sort
of
pre-training.
A
Yeah
so
by
pre-training
I
mean
like
if
you
learn,
if
you
learn
something,
that's
I
guess
a
little
more
general
and
then,
if
you're,
something
that's
more
general
and
something
that's
somewhat
more
specific,
then
learning
the
first
thing
will
speed
up
in
learning.
The
second
thing,
I'm
not
sure
if
I
answered
your
question.
D
H
So
kevin,
I
think
it's
a
very
interesting
question
and
usually
curriculum
learning
in
machine
learning
is
seen
as
simple
to
complex
just
because
these
networks,
they
don't
have
this
notion
of
hierarchy
right
you're,
just
you
have
like
one
single
output
layer
and
you
just
softmax
across
the
whole
thing,
so
there's
no
notion
of
general
versus
specialized
test.
So
it's
more
of
a
showing
the
easier
examples
first
and
then
showing
the
more
complex
examples
later.
H
D
Okay,
I
was,
I
was
kind
of
hoping
that
you
could.
You
could
show
a
progressive
that
that
the
the
hierarchy
becomes
kind
of
embedded
in
the
network
hierarchy
where
certain
the
the
precursors
of
certain
tasks
reside
in
some
lower
levels,
and
then
they
get
combined
in
upper
levels
and
whether
you're
trying
to
drive
that
kind
of
structure
onto
the.
H
D
I
mean
in
in
in
to
to
what
quran
say:
that's
kind
of
like
putting
formalism
to
transfer
learning
where
the
the
lower
levels
get
reinforced,
because
they're
continually
useful
for
the
upper
levels
and
at
some
point
you
decide
that's
good
enough
for
you.
I
don't
need
to
learn.
My
learning
rate
doesn't
need
to
be
as
high
on
those
lower
levels
and
I
can
start
concentrating
on
the
upper
levels
and
you
know
so.
A
I
also
want
to
point
out
that
there
was
one
work
that
I
think
was
done
by
pierre
you've
audrey,
who
is
a
who
is
a
rl
who
focuses
mostly
on
reinforcement,
learning
and
he
he
had
some
work
where
the
curriculum
actually
was
determined
through
they
had
they
had
some
sort
of
a
policy
where
they
were
determining
at
each
time.
What
next
learning,
which
next
task
would
improve?
A
I
guess
the
overall
overall
learning
and-
and
so
that's
like
you
know-
that's
combining,
I
guess,
curiosity
and
some
sort
of
motivation
with
curriculum
learning
and
I
I
don't
recall
exactly
how
they
defined
it,
but
how
they
defined
what
their?
What
would
be
the
best
next
one
to
learn,
but
there
are
probably
many
ways
to
do
it:
okay,
yeah.
A
The
next
one
is
curiosity
and
intrinsic
motivation,
which
we're
already
somewhat
talking
about.
So
the
reason
why
this
is
they
picked
this
as
one
of
the
one
of
the
pillars
is
because
right
now,
as
as
weak
as
the
neural
networks,
continually
learn,
they
are.
They
are
being
shown
one
task
after
another,
whereas
the
goal
of
a
lifelong
learning
agent
is
to
actually
go
out
and
you
know
be
able
to
decide
what
they
want
to
learn
when
and
so
this
idea
of
having
some
some
sort
of
some
heuristic
for
curiosity
or
motivation.
A
This
would
be
able
to
allow
an
agent
to
decide
what
it
is
that
they
would
want
to
learn
next
or
what
would
it
make
sense
to
learn
next
and
this,
and
that
could
be
like
to
for
to
minimize
some
sort
of
forgetting
or
or
whatever,
and
let's
see
so.
I
think
a
lot
of
work
in
in
this
area,
especially
has
been
probably
done,
mostly
in
reinforcement
learning
where,
in
the
cases
where
rewards
are
very
sparse
and
in
environments
in
general,
that
can
be
potentially
sparse
or
noisy
that
you
can
add.
A
Some
sort
of
you
can
add
a
heuristic
for
curos
curiosity
and
that
will
help
the
agent
go
and
find
find
or
that'll
be
some
sort
of
additional
signal
for
the
agent.
I
think
lucas.
You
you
mentioned
to
me
once
that
there
was
this
work
where
they
they
define.
Curiosity
as
like
neg
as
like
amount
of
error
or
something,
and
so
the
agent
goes
towards
whatever
they're
really
bad
at
to
to
learn
to
get
better
at
it.
H
Yeah,
I
mean
that's,
that's
the
basic
basic
idea
behind
the
epoch's
work
and
curious
based
learning.
So
you
have
two
networks.
One
is
learning
about
of
the
word:
the
transition
function,
the
other
is
learning
the
police
which
action
to
take
and
and
the
reward
for
the
police
is
the
negative
of
the
loss
in
the
model
function.
H
I
If
that
makes
sense
like,
for
example,
if
there's
like
random
noise
in
the
environment,
that
leads
to
a
lot
of
error.
But
you
have
no
control
over
that
as
an
agent
whereas
like
if
you
can
predict
what
action
would
actually
result
in
that
and
use
that
as
a
training
signal,
then
you
actually
go
to
things
where
there's
a
lot
of
error,
but
there's
also
a
potential
for
your
actions
to
influence
the
environment.
A
D
Sort
of
looked
to
me
as
if
the
kind
of
a
middle
ground
is
that
if
the
agent
looked
for
things
that
were
seemingly
accessible
to
it,
in
other
words,
you
know
it
kind
of
gets
a
somewhat
good
result,
but
not
too
bad.
Maybe
he'll
work
work
on
that,
whereas
something
that
he
basically
bounces
off
entirely
just
gets
no
results
whatsoever.
Might
avoid
that
and
try
to
get
better
at
the
things
that
it
seemingly
you
know,
has
some
handle
on
and
then
return
back
to
the
other
tasks
later
on.
D
So
you
can
kind
of
think
of
you
know:
you're
you're,
sitting
there
and
and
learning
how
to
plunk
out
a
tune
on
on
on
some
some
musical
instrument
and
you're.
Not
gonna.
Do
you're
not
gonna
jump
from
there
and
try
to
concerto,
but
you
might,
you
know,
pick
similar
tunes
and
then,
after
you
know,
you
know,
I
I
think,
there's
the
reward
aspect
of
the
curiosity.
Is
you
know?
Don't
you
know,
don't
beat
your
head
against
a
wall
on
something
that
is.
D
I
A
Right
oops
and
the
the
final
pillar
that
we'll
talk
about
is
multi-sensory
learning
and
the
reason
for
what
the
claim
and
why
this
is
important
is
because
agents
generally
operate
in
a
really
noisy
world,
and
this
and
cross
and
multicentury
learning
will
allow
them
to
generally
be
more
robust
to
all
the
different
sorts
of
inputs.
They're
receiving,
which
are
usually
will
probably
contain
lots
of
noise,
and
it's
useful
for
three
reasons
that
they
highlighted
here.
E
E
You
can
say
it
is
different,
sensory
inputs.
I
know
it
technically,
it's
not,
but
you
can
just
think
of
it.
Like
you
know,
brain
tissue
is
brain
tissue
and
it
doesn't
any
particular
column,
doesn't
know
what
its
input
actually
represents,
and
so,
at
one
level
you
can
say
yeah
the
the
different
fingers
are
different,
different
sensory
organs
and
whether
they
have
the
exact
same
sensor.
E
The
devices
on
their
tips
doesn't
matter
that
much.
You
know
it's
not
it's
not
that
important.
It's
more
important
that
they're
all
moving
and
sensing
something.
So
I
think
you
can
actually
argue
that.
That's
how
often
I
thought
about
that.
Is
that
that
really
it's
this
it's
a
certain
arbitrary
distinction,
sometimes
between
the
different
sensory
modulus.
J
E
G
E
E
Our
voting
mechanism
to
me
right,
you
know
you've,
got
different
columns.
Different
parts
of
the
court
check
so
they're
voting
and
if
one
part
of
the
cortex
is
I'm
sensing,
some
object
at
this
position,
then
the
other
the
voting
basically
tells
the
other
guys.
You
know
you
should
be
sensing
it
too.
Even
it's
a
different
modality.
E
What
you
don't
need,
though,
is
the
the
voting
mechanism.
Does
you
don't
need
to
do
the
integration?
The
voting
sort
of
voting
in
the
thousand
brain
theory
says
you
don't
need
to
bring
them
all
together.
You
can,
but
you
don't
need
to
anyway,
so
the
vote
that,
with
our
labeled
enhancement,
can
really
be
more
than
just
enhancement
it
can.
It
could
be
just
voting
and
then
everybody's
agreeing
on
the
same.
A
A
Okay,
so
that
does
it
for
the
few
pillars
that
they
advocate
for
and
then
this
is
my
last
slide,
and
this
is
something
I
guess
to
that.
That
has
made
me
think
quite
a
bit,
which
is
when,
when
should
forgetting,
really
occur
so
there's
this
case
study
that
the
repaper
talks
about
where
they
take
a
bunch
of
kids
that
were
born
in
korea
and
up
until
sometime
between
the
ages
of
about
three
to
eight.
They
were
fully
immersed
in
up
until
the
age
of
roughly
five
years
old.
A
A
This
studies
were
done
where
they
they
tried
to
measure
how
responsive
these,
how
well
these
kids
were
able
to
identify
korean,
which
they
really
didn't,
have
any
exposure
to
after
first
few
years
of
their
life,
and
they
found
that
there
was
no
difference
in
their
exp
and
their
response
to
korean,
as
opposed
to
the
just
regular
other
other
kids
who
grew
up
in
france,
their
whole
life.
So
this
shows
that
clearly
there
there's
they
forgot
how
to
speak
korean
altogether.
A
Now
you
know,
whereas
you
know,
if
you
have,
I
guess
a
lot
of
modern
neural
networks.
You'll
see
if
we
forget
task
a
after.
We
learn
task
b,
we'll
we'll
say,
okay.
Well,
this
is
the
problem.
We
shouldn't
forget
how
to
do
task
a,
but
are
there
I've
been
thinking
about?
Are
there
cases
where
we
actually
it's
okay
to
forget,
or
we
would
expect
it
to
forget
in
this
case,
so.
E
That's
an
interesting
question
because
it
might
be
might
be
essential
that
we
forget
to
do
continuous
learning.
So
you
know
I
mean
what
there
was
earlier
talked
about:
adding
additional
resources
but-
and
there
are
some
parts
of
the
brain
where
that's
happening
where
well,
I
wouldn't
say
additional
resources
where
resources
are
turning
over
like
you
get
new
cells,
but
presumably
the
other
ones
are
disappearing,
and
but
if.
E
The
brain
as
sort
of
a
fixed
resource
like
I
can,
I
can't
double
the
number
of
double
the
number
of
neurons
in
my
brain
throughout
my
lifetime.
It's
not
going
to
happen
right.
You
can
think
it's.
You
know
a
bunch
of
adulthood.
The
number
is
pretty
well
fixed
again
they
can
be
changing
in
some
dying.
Some
new
ones
come
in,
but
so,
if
you
have
fixed
resources
in
some
sense,
you
have
to
forget
at
some
point
you
know,
and
so
it's
how
you
forget
and
what
not
just
what
you
forget.
E
B
This
way,
like
also
just
tons
of
stuff
just
in
everyday
life,
that
we
just
don't
remember
even
a
few
days
later,
yeah
that
may
be
actually
required.
Like
you
know,
when
I
was
going
into
work
driving
into
work,
I
wouldn't
remember
where
I
parked
the
car
three
days
earlier.
It's
just
not
relevant
and
yeah.
I'm
sure
my
brain
does
not
have
the
capacity
to
remember
yeah,
but.
E
Even
things
yeah,
so
there's
stuff
like
that
every
day
today,
like,
as
you
said
like
what
did
I
have
for
breakfast
two
days
ago,
you
know,
I
can't
tell
you
but
but
there's
other
things
like
you
know,
you
know
the
roads
around
the
house
where
I
grew
up
well,
I
knew
those
intimately
when
I
was
a
child
teenager
and
young
adult,
but
I
would
struggle
with
them
now.
I'd
have
some
few
of
the
basic
things
that
most
of
the
details
would
be
forgotten
and
so
that
occurred
slowly.
It
didn't
crawl
at
once.
E
D
E
Well,
yeah
no
savants
aren't
always
impaired,
they
tend
to
not
generalize
well
so,
but
they
do
human.
They
can
remember
huge
amounts
of
data.
I
I
think
I
think,
there's
other
explanations
for
that.
I
think
it's
basically
saying
they're
taking
the.
What
that
tells
me
is
that
a
human
brain
has
this
very,
very
large
capacity,
because
there
are
savants,
who
can
remember
every
word
in
every
book.
They've
ever
you
know
every
page,
whatever
they've
read
it's
incredible.
E
I
E
I'm
saying
the
capacity
in
terms
of
neural
the
number
of
neurons
and
potential
synapses
is,
is
going
to
be
roughly
equivalent
to
these
people
right,
whether
you're,
savant
or
not.
So
savants
have
something
different
and
arguably
not
as
good,
but
maybe
we
could
just
don't
get
into
that
argument.
But
there's
something
different
about
the
structure
of
the
brain,
to
allow
them
to
remember
the
details
that,
whereas
we
would
remember,
we
would
somehow
be
able
to
generalize
some
details.
So
I
don't
know.
G
And
so,
instead
of
forgetting,
you
know
how
to
draw
their
or
write
their
own
name
or
how
to
paint
or
something
they
forgot,
the
the
means
to
communicate
in
a
different
language.
So
it's
kind
of
like
an
intelligent
way
of
like
swapping
out
specific
task
learning
but
yeah.
So
those
are
just
a
couple
of
points
there.
A
Yeah,
I
think
that
probably
that
probably
is
likely
what
happened
here.
In
fact
in
this
paper,
where
they
did
this
study,
they
they
hypothesized
that
it
was
the
same
brain
region.
It
was
the
same
brain
regions
that
they
would
have
been
using
for
korean.
That
now
became
active
for
french,
so
it
so.
It's
like
french,
totally
overrode
korean
here.
C
Yeah,
I'm
sorry
that
was
really
interesting.
Apologies
for
missed,
but
did
they
specifically
address
kind
of
the
importance
of
abstraction
and
kind
of
disentanglement,
because
that
seems
to
be
kind
of
like
a
really
important
one
for
continuing
learning,
and
I
was
just
wondering
if
they
kind
of
discussed,
why
maybe
they
didn't
include
that
as
one
of
their
sort
of
pillars?
C
This
idea
kind
of
like
say
on
a
reinforcement,
learning
task,
if
you,
rather
than
learning
kind
of
a
one-to-one
mapping
between
pixels
and
an
image
which
you
could
get
a
perfect
score.
If
you
instead
have
a
kind
of
disentangled
notion
of
a
hazard
and
the
notions
of
xy
location,
then
you
could
much
more
rapidly
or
you're
kind
of
likely
to
be
able
to
use
that
same
kind
of
representation
without
overwriting
it
to
then
learn
on
a
new
task.
A
No,
they
didn't
really
talk
about
representations
or
any
of
that
at
all.
No,
but
I
guess
you
mentioned
you
mentioned
something
about
going
from
pixels
to
these
representations
right.
I
guess
that
there's
an
implicit
assumption
there
that
the
input
will
always
be
pixelated
or
something
like
that.
Yeah.
C
So
that
say,
for
example,
a
kind
of
hazard
like
an
object
that,
if
you
jump
on
you
die
in
the
top
left,
will
look
nothing
like
one
in
the
lower
right
and
a
typical
reinforcement.
Learning
agent
will
learn
this
whole
problem,
just
as
well
as
if
you
use
the
original
pixel
input
that
the
the
human
learns
on.
But
of
course
a
human
learns
much
better
on
the
the
original
one,
because
you
understand
that
these
two
things
are
related
and
you
don't
kind
of
essentially
relearn
for
every
pixel
in
the
image.
C
E
In
my
next
talk,
if
we
get
to
it
it's
an
interesting,
I
think,
relates
to
what
you're
just
saying
niels.
It's
some.
You
know
we
have
the
ability,
sometimes
you
remember
specific
things,
but
we
also
generalize
we
do
both
of
those
and
and
one
of
the
ones.
That's
always
puzzled.
Me
is
like
with
music,
because
I
can
I
learn
a
song.
E
I
can
generalize
it
very
rapidly
because
I
can
hear
it
in
any
key
and
I
recognize
immediately
it's
the
same
song.
I
can
sing
it
back
in
any
key.
I
never
heard
it
before
so
I've
determined
sort
of
an
invariant
property
of
the
song,
yet
I
also
tend
to
people
tend
to
know
the
actual
key
that
it
was
that
they
learned
it
in
or
the
key
that
is
it's
popularized
by
a
particular
group
or
singer,
and
so
we
had
a
specific
memory
and
a
generalized
memory.
E
At
the
same
time,
it
always
always
struck
me,
as
I
think
I
have
an
explanation
for
that
right
now,
so
I'm
going
to
get
to
that.
I
don't
let
relate.
I
think
that
relates
what
you
were
just
talking
about,
but
there's
a
sort
of
generalized
learning
that
has
to
occur.
I'm
going
to
talk
about
the
displacement
cells.
E
All
right,
if
we're
up
for
it,
we'll
do
a
neuroscience
talk,
I'm
a
little
nervous
about
this,
because
it's
it's
really
deep
down
dirty
stuff
and
I'm
not
sure
everyone
is
up
on
all
these
things.
I'm
gonna
talk
about.
I
know
a
few
of
us.
I've
been
thinking
about
these
things
for
years
so
and
I'm
also
don't
have
anywhere
near
as
nice
presentation
as
quran.
E
Let
me
just
get
going.
I'm
gonna
share
my
screen
and,
unlike
last
week
I
hit
all
my
windows
that
show
personal
stuff,
like
my
email,
so
hopefully
it'll
work
different
this
time.
Does
everyone
see
this
word
document
yeah?
So
this
is
the
the
topics
I'm
gonna
talk
about.
I
I
just
thought
I'd
clarify
some
terminology.
Just
I
was
afraid
people
might
get
confused
by
this.
E
We've
been,
and
I
with
the
most
guilty
party,
perhaps
of
all
have
been
talking
about
when
we
talk
about
grid
cells
and
head
direction,
cells
and
place
cells.
Those
are
all
cells
that
are
in
the
hippocampus
or
the
anterinal
cortex
other.
You
know
non-cortical
areas,
but
we're
talking
about
things
in
the
cortex
and
we
think
there's
equivalent
cells
in
the
cortex,
so
I
often
will
use
instead
of
grid
cell
I'll
call
it
like
a
location
instead
of
a
head
direction.
E
Cell
I'll
call
it
orientation
and
we've
used
these
terms
a
lot
and,
unfortunately,
in
my
personal
writing
I
go
back
and
forth
between
these
all
the
time.
So
when
I,
if
I
say
location,
I'm
like
a
location
cell,
I
mean
a
grid
self,
I
say
a
location
module.
I
mean
it's
the
same
as
a
grid
cell
module,
but
I'm
talking
about
in
the
cortex,
if
I
say
an
orientation
cell
or
mutation
module,
that's
going
to
be
the
same
as
a
head
direction
cell.
E
E
So
I
want
to
go
over
those
I'm
going
to
start
with
a
review
of
this
idea
of
1d
location
cells
versus
2d
location
cell
modules.
We've
been
talking
about
that
on
and
off.
I
just
want
to
review
some
things
about
that.
Then
I'm
going
to
talk
about
displacement,
cells
and
displacement
cell
modules,
and
I
have
a
much
better
understanding.
E
I
think
how
they
work
right
now,
which
is
great
and
then
I'll
have
some
thoughts
about
you
know,
orientation
and
location
are
determining
orientation,
determine
location,
head
direct
themselves
and
grid
cells
are
actually
really
just
two
flavors
of
the
same
thing
and
and
then
sort
of
map
out
all
the
possibilities
so
I'll,
just
I'm
just
going
to
keep
going.
But
if
anyone
has
questions
you
should
stop
me.
E
E
I
hope
you
can
see
the
framework
paper
here
and
in
this
paper
this
came
out
two
years
ago
we
talked
about
representing
space
in
the
cortex
or
in
the
in
the
up
and
around
cortex,
either
one,
and
we
had
this
idea
that
oh
you've
got
these
grid
cell
modules,
where
your
cell
responds
multiple
places
in
an
environment,
so
you
don't
really
know
where
you
are,
and
then
you
have
another
grid
cell
module
that
responds
at
a
different
scale
orientation
in
there.
You
can
combine
the
two
and
you
can
say
well
now.
E
I
know
more
specifically
where
I
am
by
the
intersection.
So
there's
something
I
think
we
got
fundamentally
wrong
about
this
and
something
we
got
fundamentally
right.
The
thing
I
think
we
got
fundamentally
wrong
is,
I
think
the
brain
never
wants
to
operate
in
this
mode.
Where
you
have
a
cell
responding
in
multiple
places
within
a
particular
environment.
E
E
So
that's,
I
think
what
we
got
wrong.
What
we
got
right
is
the
idea
that
multiple
modules
have
this
really
magical
property.
Where
you
can,
if
you
combine
them,
you
can
create
very,
very
large
spaces,
but
the
modules
that
we're
going
to
combine
are
not
grid
cells.
These
2d
grid
cell
motions,
the
modules
we're
going
to
combine,
are
the
1d
modules
that
are
used
to
generate
these.
So
we've
been
talking
about
that
too.
So
I'll
go
back
and
review
that
right
now.
E
So
let's
go
back
to
my
word
file
here,
so
so
the
basic
idea
here
is
you-
and
these
are
just
like
cartoon
drawings-
they're,
not
really
they're
from
my
benefits.
So
please
excuse
that.
There's
lots
of
little
quirks
of
how
I
drew
these
things.
So
here's
a
2d
grid
cell
module-
you
can
think
about.
You
know,
there's
a
bunch
of
cells,
each
one
responds
to
some
location
environment,
another
one
responds
to
different
location
environments
so
on,
and
it
doesn't
matter
how
the
animal
gets.
E
Some
location
you
get
to
a
location
environment
that
sells
behind
you,
go
to
another
location,
another
cell
response,
but
we
think
that
now
we
have
we've
learned
a
lot
about
how
these,
how
grid
cells
come
about
and
the
basic
ideas
they
come
about
from
1d
motion,
sensitive
velocity,
controlled
obsolete.
So
what
I've
been
proposing
for
quite
a
while
now
is
that
in
the
cortex
you
have
many
columns.
These
representing
these
pictures
represent
a
layer
of
cells
in
one
mini,
different
mini
columns
and
each
mini
column
in
each
situation.
E
Here
represents
movement
in
a
particular
direction,
and-
and
these
can
be
I
mean
they-
don't
have
to
be
a
diagonal
just
as
long
as
they
cover
the
basis
of
the
of
the
space,
and
these
can
be
observed.
As
I
talked
about
you'll.
Remember
that
you
could
you
could
from
like
from
the
retina.
You
can
flow
bits
will
tell
you
what
are
the
movements
have
been
experienced,
so
these
are
observed,
but
what
you've
got
here
is
a
set
of
cells
that
represent
movement
in
one
direction.
E
So,
if
I'm
moving,
if
I'm
moving
north
and
then
this
guy
might
have
some
at
some
speed,
my
delta
or
something
this
represent
moving
east,
then
it
would
be
not
there'd,
be
no
delta,
it
wouldn't
be
moving
at
all
and
so
that
the
progression
of
changes
here
which
cell
is
active,
depends
on
how
fast
it's
moving
and
these
different
cells
are
represent
different
phases
of
the
theta
cycle.
So
you
can
imagine
a
wave
of
activity.
E
That's
that's
traveling
within
one
theta
cycle,
where
this
guy
is,
is
at
its
peak,
its
peak
depolarization.
This
one's
follows
and
this
one
follows
and
this
and
follows
the
listen
pulse
and
the
active
cell
represents
where
the
which
of
the
cells
it's
at
its
peak
at
the
same
time
as
the
base
theta
right.
So
this
is
not
something
we've
made
up.
We've
just
we've.
Just
I've
just
pushed
this.
This
idea
is
pretty
clear.
This
has
to
happen.
E
E
You
could
say
that
it
represents
a
location
in
the
room
when
the
animal
is
moving
in
a
particular
direction,
so
this
cell
will
become
active
when
the
animal
is
moving
in
a
particular
direction
out
of
the
location
in
the
room.
If
it's,
it
won't
become
active
if
the
animal
is
moving
in
a
methadone
direction.
So
it's
it's
sort
of
a
combination
of
a
bit
of
a
it's,
an
oriented
and
location.
It's
partly
gritty
and
partly
orientation.
E
No,
it
doesn't
move
backwards
so,
and
I
base
that
on
the
idea
that
if
you
look
at
the
cortex,
you
look
at
the
responses
of
the
mini
columns.
There's
you
know
one
that
moves.
You
know
you
could
say
they
say.
Moving
left,
there's
a
different
one
that
moves
right
and
and
when
the
one
that's
active,
moving
left,
the
other
one
moving
right
doesn't
become
less
active,
it
doesn't
become
negative,
active
it
just
is
inactive,
so
we're
working
on
that
assumption.
E
I've
been
I've
been
assuming
that
all
along
that
that
these
are
these
are
truly
one
directional
vectors,
and
if
I
wanted
to
cover
two
direct
two
dim,
you
know
moving
forward
and
backwards.
I'd
have
to
have
two
of
them
and
I
think
everything
else
here
before
I
get
off
this
page.
One
of
the
things
we
know
has
to
happen
with
grid
cells
or
location
cells
is
they
have
to
anchor
meaning
they
have
to.
E
When
you
enter
an
environment,
you
recognize
that
you
say:
oh,
I
have
to
anchor
which
cells
are
active,
we've
talked
about
anchoring
the
grid
cells
and
then
even
just
last
week
I
talked
about.
Perhaps
I
thought
I
showed
a
mechanism
about
how
that
might
happen.
I
don't
think
that's
likely.
I
think
the
angling
is
going
to
occur
here
that
and
what
it
means
is
that
somehow
there's
a
sensory
input
and
I'm
not
going
to
go.
E
I
have
some
ideas
about
I'm
not
going
to
go
into
it
today,
but
there's
a
sensory
input
that
comes
in
which
says.
Oh,
I
know
I
recognize
the
sensory
input.
Well,
I'm
going
to
decide
which
cell
is
at
its
peak
right
at
the
same
time
as
with
cell,
which
is
the
base
theta.
So
basically,
what
anchoring
means
is
just
picking
which
of
these
cells
is,
is
currently
at
its
its
peak
frequency
to
match
the
theta
and
and
that's
sort
of
like
saying
that's
my
location
and
I'll
start
moving
from
there.
E
F
The
way
you've
written
this
I'd-
maybe
you
have
an
answer
coming
up
to
this,
but
if
you
only
have,
if
say
this
is
tracking
the
location
of
my
finger,
I
lift
my
finger
up.
One
of
my
one
of
my
rings
updates
in
response
to
that.
Maybe
multiple,
I
move
my
finger
back
to
a
starting
position,
a
different
set
of
rings
update,
so
I've
lost
the
path,
integration
property
because
it's
a
I've.
E
Well,
you've
lost
the
path,
integration
property
here.
These
1d
modules,
I'm
not
sure,
you've
lost
it
down
here
at
the
2d
module
stage.
Okay,
so
it's
an
interesting
question
why
you
have
2d
modules
in
1d
modules
and
I
I
have
partial
I
partial
the
answer
to
that,
but
I
haven't
spent
a
lot
of
time
on
it.
So
again
you
wouldn't
have
lost
it
here
and
I
don't
know
the
interaction
between
you.
I
guess.
Last
week
I
presented
how
these
mini
columns
could
could
drive
the
3d
cells.
E
They
did
not
present
any
ideas
about
how
the
2d
cells
might
come
back
and
do
these
guys
and
the
other
thing
that's
going
on
is
yeah.
That's
the
general
answer,
question
with
vision.
You
know
you
you're
you're,
going
to
be
constantly
getting
sensory
input
as
you
move,
either
forward
or
backward
with
your
finger.
You
won't
right
with
your
finger.
You'll
get
you
won't
get
any
sensory
input,
you'll
get!
Maybe
proprioceptive
input
saying
oh
you're,
moving
your
finger
up
and
moving
your
finger
down,
but
there'll
be
no
sensory
data
to
to
re-anchor
these
cells.
E
E
Where
is
when
we
really
think
about
composition
of
objects?
It's
not
some
feature
at
some
location,
it's
really
other
objects
at
some
relative
pose
or
relative
location
and
orientation.
So
if
I
want
to
learn
this
coffee
cup,
I
don't
relearn
all
the
details
of
the
mental
logo
and
say:
oh
I'm
going
to
learn,
there's
an
a
on
the
top
of
the
key
or
the
t
on
there.
I
just
say
no
there's
a
mental
logo
somehow
instantly.
E
I
can
associate
the
entire
logo
with
the
entire
cup
and
all
that
knowledge
is
done,
and
so
that's
a
really
challenging
problem,
and
I
I
don't
know
who
came
up
with
the
idea,
but
I
know
that
was
marcus,
ua
and
scott
when
they
came
in
and
presented
at
a
reference
research
meeting
and
they
proposed
part
of
the
solution
and
part
of
the
solution.
Was
this
idea
of
of
a
way
of
saying?
E
Okay,
we
have
a
way
of
determining
the
relative
displacement
between
a
grid,
mod,
a
grid
cell
module
in
the
coffee
cup
and
grits
module
on
the
loco,
so
that
we
can
we
can
go
from
one
location
to
another
location.
So,
given
the
location
of
the
cup,
I
can
tell
you
the
location
on
the
on
the
logo:
I'm
not
going
to
walk
through
the
whole
thing,
but
I
think
I
think
that
general
idea
was
really
really
right
and
again
we
made
the
same
mistake
we
made
with
grid
cells.
E
What
you
end
up
with
is
a
unique
representation
for
the
logo
on
the
coffee
cup,
so
that
was
really
cool.
There
were
several
other
things
that
were
it
didn't
work
here,
and
we
pointed
them
out
in
this
paper.
One
of
them
was
that
this
didn't
deal
with
orientation.
There's
no
way
of
translating
you
know
what.
If
what,
if
the
logo
is
in
an
angle
on
the
cup
we
couldn't
handle,
that
there
was
there's
no
mechanism
for
it
and
the
other
one
was
scale,
the
logo
has
a
certain
size.
E
E
If
I
find
the
displacement
between
a
point
on
the
cup
and
the
point
and
logo,
that
tells
me
the
relative
position
to
cut
from
the
logo.
However,
if
I
just
take
two
points
on
the
cup
and
I
find
the
displacement,
I
use
the
same
basic
mechanism
in
the
same
reference
frame.
Then
it
represents
the
distance
on
the
cuff,
and
it's
basically
about
that's.
You
know
how
I'd
have
to
move
to
get
from
one
patient,
the
other.
E
E
Oh,
thank
you
yeah.
The
part
of
the
show
I
pointed
out
that
those
are
sort
of
back
and
forth
between
grid
cells
and
displacement
cells.
So
this
this
is
the
idea
here
that
if
I,
if
I
have
a
location
in
one
reference
frame,
plus
a
displacement,
I
would
now
get
the
same.
What
the
correct
location,
the
second
reference
frame,
but
if
I
had
two
locations
in
the
same,
you
know
if
I
start
with
two
locations
and
I
subtract
them-
I
get
a
displacement.
E
So
it's
just
like
this
going
back
and
forth
and
then
I'm
sorry.
I
guess
it
wasn't
ripple
before
that.
But
then
we
then
we
did
one
step
further.
We
realized
that
if
I
took
two
components
of
an
object
like
a
stapler
in
this
case-
and
we
said
well,
there's
a
displacement
between
the
top
part
and
the
bottom
part.
As
that
part
moves,
our
top
part
moves.
E
You
go
through
a
series
of
displacements
and
if
you
can
learn
that
series
as
a
sequence,
then
you
would
learn
the
behavior
of
this
object,
how
the
stapler
would
open
or
how
it
flows,
how
things
move
relative
to
each
other.
So
displacement
tells
you
where
things
are
relative
to
each
other
and
then
a
sequence
of
them
will
tell
you
how
those
things
move
relative
to
each
other
somewhere
along
the
way.
We
came
to
the
realization
that
all
representations
of
of
objects
in
the
world.
E
We
never
store
a
feature
at
a
location,
we're
always
just
storing
displacement.
So
a
bicycle
is,
I
don't
have
a
picture
of
a
bicycle.
The
bicycle
is
a
bunch
of
other
objects,
all
at
some
relative
displacement
to
each
other
and
and
each
of
those
objects
like
a
wheel
or
a
pedal
or
a
seat
is
composed
of
other
objects
that
are
on
the
little
alternative
location.
So
the
entire
model
of
the
world
is
basically
objects
and
relative
locations.
The
object
with
control
of
the
patient's
object
in
sort
of
a
hierarchical
fashion,
all
right.
E
Now,
let's
just
think
what
a
displacement
is,
I'm
just
going
to
verbally
walk
you
through
this.
What
a
displacement
means
if
I
have
a
displacement
cell,
what
should
it
respond
to
it's
going
to
say?
Well,
if
I
move
a
certain
amount
in
the
in
the
location
module,
let's
say
I
move
from
one
cell
down
to
another
cell.
E
That
is
a
displacement,
but
I
want
the
cell
to
respond
when
I
do
it
from
this
cell
to
this
cell
or
from
the
next
cell
down
to
the
next
cell
down
next
so
down
to
the
next
one
down.
So
it's
like
saying
like
it's
a
movement
of
three.
It
doesn't
matter
where
you're
starting
from
or
movement
of
five,
it's
it's
like
you're
moving
a
certain
amount
in
this
direction,
but
I
want
the
cell
to
respond
regardless.
It
doesn't
matter
where
you
start
from
it's
displacement:
it's
a
delta.
E
You
know
that
we're
trying
to
calculate-
and
it
was
very-
it-
was
always
difficult
for
me-
to
figure
out
how
a
displacement
modulus
could
learn
that.
How
could
a
cell
learn
to
represent
this
cell
of
this
cell
and
this
cell
is
its
own?
It's
like
a
big.
You
know
complicated
or
function
right
and-
and
then
I
had
this
idea
this
last
week
that
it's
actually
easy
for
the
displacement
cells
to
be
calculated,
and
we
just
didn't
think
about
it
right.
So
I'm
going
to
have
to
just
try
to
walk
you
through
this
here.
E
E
E
E
E
Yeah,
okay
upside
down,
so
the
next
thing
I'm
gonna,
I'm
gonna
put
this
all
together
in
a
moment
now.
The
other
thing
I
I
just
want
to
talk
about
a
little
bit
about
orientation
cells
and
I've
mentioned
this
in
the
past.
I'm
gonna
mention
again
now
you
know
orientation
cells.
Basically,
it's
like
you're
moving
and,
as
you
move,
your
orientation
changes.
You
think
about
the
head
direction.
But
again
this
could
be
in
any
any.
If
it's
a
three-dimensional
world,
I
have
a
three
three.
E
I
need
at
least
three
variables
represent
my
orientation
that
I'm
facing,
and
and
so
it's
just
a
different
type
of
movement
instead
of
moving.
You
know,
instead
of
moving
through
space
from
one
location
to
the
other,
I'm
just
changing
my
my
direction
of
gaze
or
my
orientation
of
my
fingers
or
something
like
that,
and
we
have
to
do
all
the
same
things
with
orientation
cells.
We
have
to
do
with
grid
cells,
meaning
I
have
to
do
path
integration.
E
I
have
to
be
able
to
say
like
well
if
I
were
to
turn
so
many
degrees
to
the
left.
What
would
be
my
new
orientation?
I
have
to
do
anchoring.
Basically,
when
you
come
into
a
new
environment,
you
have
your
your
head
direction.
Cells
have
to
anchor
based
on
sensory
input,
and,
and
so
we
and
and
and
because
we're
doing
this
path,
integration
we're
going
to
have
a
bunch
of
modules
just
like
we
had
before.
E
So
I'm
going
to
argue
here
that
orientation
is
going
to
be
basically
the
exact
same
thing,
that's
going
on
with
with
location.
It's
just
that
the!
If
I
think
about
the
1d
modules.
Imagine
these
modules
now
representing
orientation.
What's
driving.
These
is
not
moving
forward
or
backwards
in
a
particular
direction,
but
turning
left
and
right
in
a
particular
direction.
If
you
will
and
everything
else
stays
the
same,
there's
almost
no
difference.
E
If
you
put
us
all
together,
yeah,
let's
get
that.
So
what
are
we
talking
about
so
far?
Well,
you
can
group
this
in
two
basic
groupings
here:
there's
orientation
and
there's
location
and
I'm
not
certain.
It
has
to
be
this
well
separated,
but
I'm
going
to
go
with
that
for
now
I
think
it's
probably
right,
and
so
what
might
I
have?
Well,
let's
just
talk
about
the
location.
E
First
right,
I'm
going
to
have
I'm
going
to
have
a
bunch
I'm
going
to
have
in
a
particular
column,
I'm
going
to
have
a
I'm
going
to
have
one
2d
location
module,
so
I'm
going
to
have
one
what
we
call
a
grid
cell
module,
I'm
going
to
have
a
bunch
of
1d
location
modules
that
are
actually
driving
these
guys,
and
these.
These
are
the
remaining
columns
of
a
particular
layer.
E
E
And
because
I
need
those
to
calculate
my
displacements-
and
I
don't
know
if
I
need
to
have
a
2d
displacement
module,
it's
not
clear
that
I
need
that.
I
might
need
that,
but
it's
not
clear.
I
need
that,
and
so
I
put
a
question
mark
here,
but
I
definitely
gonna
in
my
in
my
mini
column,
I'm
going
to
have
some
columns
that
are
being
driven
by
this.
These
are
all
these.
E
This
layer,
cells
and
this
layer
cells
are
all
been
driven
by
the
same
motion
in
some
direction
and
and
I'm
going
to
be
doing
path,
integration
over
and
then
I'm
going
to
end
up
with
my
grid
cell
module,
I'm
going
to
have
the
same
thing
going
on
with
orientation,
and
I
am
gonna
have
a
I'm.
Gonna
have
a
a
set
of
orientation
cells
which
we
can
consider
like
a
two.
It's
it's
2d
in
the
in
the
sense,
it'll
look
like
2d!
Now,
it's
it!
E
E
What
what
the
distinction
here
is
that
the
cell
here
you've
seen
them
talk
about
this
little
thing,
though
this
is
our
classic
grid
cell
module,
a
cell
here,
fires
at
some
location
in
an
environment,
and
it
doesn't
matter
which
way
you're
facing
it,
doesn't
matter
which
way
you're
moving
it'll
precess
depending
between
moving
but
it
it
basically
represents
some
location
and
environment,
and
that
could
be
a
3d
environment.
It
could
be
a
2d
environment,
maybe
a
1d
environment.
E
When
I
said
2d
here
it
was
a
2d
layer
sheet
of
cells,
but
this
is
not
restricted,
two
dimensions.
These
are
restricted
to
one
dimensions,
but
these
are
not
restricted
to
true
dimension.
The
same
thing
here
I
have
a
bunch
of
one
dimension:
orientation,
movement,
column,
cells.
This
would
be
a
layer
of
cells
and
then
I'm
going
to
calculate
a
my
classic
head
direction
cell
or
would
be
one
of
these
cells,
which
it
says.
Yes,
you
know
I'm
good,
no
matter
where
I
am
I'm
going
to
be.
E
You
know
facing
I'm
facing
this
direction.
I
should
I
should
also
again
remind
us
that
if
I
look
at
the
activity
of
cells
in
a
grid
cell
in
these
1d
modules,
if
I
look
at
which
cells
are
active
in
the
1d
modules-
and
I
add
them
all
up-
it's
it-
it's
going
to
be
unique
to
the
environment,
it's
a
unique
representation,
so
we
still
have
our
large
spaces
and
the.
If
I
add
up
all
the
displacement
cells,
they'll
be
unique.
Per
two
unique
objects
and
same
thing
happens
here
interesting.
E
E
E
This
is
the
cell
that
we're
projecting
the
thumb
it's
this
cell,
these
cells
here
say
what
is
my
you
know
my
my
current
orientation
of
of
one
object
to
another
object,
or
something
like
that
or
from
my
current
movement,
to
the
object
I'm
observing
so
anyway,
so
at
a
minimum,
I
think
each
each
quarter
column
has
to
have
each
mini
column
has
to
have
two
or
four
there
have
both.
There
has
to
be
at
least
all
these
different
components.
I'm
not
sure
about
this
one
nacho
valve
this
one.
E
It's
interesting
that
the
orientation
movements
and
the
location
movements
are
not
the
same,
so
it
doesn't
necessarily,
you
know,
there's
one
mini
column
which
just
expands
all
of
these,
and,
if
you
recall
in
the
past,
I
I've
shown
pictures.
If
I
have
one
right
here.
No,
I
don't
have
anything.
I've
shown
pictures
of
the
upper
layers
of
the
quadratics
and
the
lower
laser
projects.
E
We
know
that
there's
at
least
two
parts,
two
layers
in
the
cortex
that
are
detecting
movements,
the
lower
layer,
three
complex
cells
in
the
lower
layer,
five
complex
cells,
and
so
this
may
be
what's
going
on
in
the
lower
layers,
and
this
may
be
what's
going
on
in
the
upper
layers.
So
just
because
I
have
I
might
go
down
through
a
mini
com
doesn't
mean
that
all
the
cells
in
an
income
are
representing
the
same
thing.
E
One
could
be
changing
an
orientation,
one
could
be
changing
forward
direction
or
back
or
there
could
be,
it
could
be
another
ring.
I
don't
really
know
yet
about
that.
So
I
want
to
point
out
one
more
thing
about
sequences.
You
know
these
one
deal.
1D
modules
are
ideal
for
learning
sequences;
they
are,
they
are
the
foundation
of
our
temple
cooler.
E
So
if
I
have
a
series
of
1d
displacement
modules
like
I've
shown
here
or
one
of
these
spatial
modules,
I've
shown
here
if
I
want
to
learn
a
sequence
of
behaviors
like
the
stapler
opening
up
in
the
stapler
closing,
I
basically
just
have
to
take
these
cells
and
apply
our
temple
pool
to
our
temple.
Member
to
it.
These
these
are
basically
very
you
know,
sparsely
activated
in
any
columns.
Not
all
the
many
columns
have
activity
on
them.
E
There'll
be
only
some
of
the
many
columns
in
cortical
column,
and
this
layer
would
be
active.
You
know,
but
so
it's
it's
just
exactly
what
our
our
our
temple,
our
temple
memory,
does.
So
we've
really
been
beautifully
set
up
to
take
existing
stuff.
We've
already
had
to
learn
the
behaviors
of
objects
here,
if
I'm
doing
that
or
to
learn
my
behaviors
as
I
move
through
the
world
by
by
short
learning
sequences
here
right.
If
I
learn
how
this
is,
this
is
actual
movement
through
the
space.
This
is
displacement.
E
Modules
are
now
excuse
me.
I
said
that
incorrectly
the
displacement
modules
are
the
movement
or
remember
the
displacement
modules
are
movements
or
displacement
modules
can
learn
behaviors
of
objects.
So
anyway,
the
point
is,
we
now
have
the
trick
I
thought
of
which
is
just
re-anchoring.
The
displacement
cells
at
the
beginning
of
movements
gives
me
my.
It
was
a
very
simple
way
of
calculating
displacement,
and
now
we
have,
and
by
going
to
1d
modules
like
this,
it's
very
simple:
those
are
sequences
of
them.
D
E
E
If
you
think
about
a
cortical
column,
I
think
the
smallest
cortical
column
I
can
imagine,
would
have
a
hundred
mini
columns.
So
that
would
be
like.
Let's
say
it's
I
don't
know
pic.
I
can
pick
any
number
here
making
that
might
have
let's
say:
400
microns,
like
400
microns,
for
a
mini
com
and
let's
say
each
eats.
I
mean
for
a
big
column
and
let's
say
there
was
40
microns
for
each
mini
column,
so
it'd
be
10
by
10.
So
you
might
have
a
you
know.
E
I
think
that's
a
good.
A
100
is
sort
of
a
good
lower
limit
for
the
number
of
minicoms
you
might
have
as
500
or
even
a
thousand
would
be
a
good
upper
limit.
So
we
have
that
range
to
work
from
and
and
so
I'm
gonna
you
know
I
if
I
I
don't
know
how
to
divide
it
up
kevin,
but
there
they'll
at
any
point
in
time
I
mean
so
so
you
might
have
you
might.
E
Of
these
things
to
work
from
it
may
be
not
that
big,
I
don't
know,
but
now
they're
not
all
going
to
be
active
at
once.
But
the
point
is
that
you
could
you'll
have
a
lot
of.
If
you
just
put
this
through
a
spatial
pooler
like
like
I
talked
about
in
the
past,
you
put
the
flow
bits
into
a
spatial
cooler.
E
You
end
up
dividing
this
up
into
n
number
of
mini
columns
and
if
I
I
might
have
100
dimensions,
I
can
work
with
and
and
that's
certainly
well
more
than
I
possibly
could
use
or
need.
So
I'm
not
saying
we're
going
to
use
all
of
them,
but
there's
plenty
and
see
you
know.
Ideally,
obviously,
if
I'm
representing
3d
space,
I'm
going
to
do
3d
three
three
of
these
things,
but
they're
gonna,
they're
gonna,
be
over
complete,
there's
gonna,
be
quite
a
lot
of
them
and
they're
all
gonna
be
different
right.
D
Yeah,
I
was
just
thinking
that
there
are.
There
are
experiments
in
other
directions
in
looking
at
orientation
such
like.
How
many,
how
much?
What
degree
of
overlap
do
you
need
between
these
things
to
kind
of
make
it
clean
and
but
if
you're
saying
that
they're
just
kind
of
randomly
oriented
but
we'll
we'll
deduce
a
direction
via
space
of
pooler,
somehow
they're.
E
Not
well
they're,
not
randomly
oriented
they're,
going
to
be
learned,
you're
going
to
take
these
slow
bits
and
you're
going
to
put
them
to
a
temp
spatial
cooler
and
said
it
will
learn
to
divide
up
the.
What
the
trick
about
this
thing.
The
column
doesn't
know
what
it
what
it's
representing.
It
doesn't
know
what
the
sensor
represents,
and
it
doesn't
know
what
movement
it's
going
to
experience
in
the
world.
E
So
it
just
observes
the
movements
of
the
flow
bits
as
I've
talked
about
before,
and
it's
going
to
say,
I'm
going
to
divide
those
up
into
a
bunch
of
different
a
bunch
of
different.
You
know
representations
just
like
the
spatial
puller
does,
and
so
it's
not
like
randomly
chosen,
they're
gonna
be
learning.
If
my
sensor
never
moved
in
the
third
dimension,
I
would
never
represent
the
third
dimension.
E
You
know
it
wouldn't
be
there
if
my
essentially
moves
in
four
dimensions,
I'll
represent
four
dimensions
so
and
so,
and
and
and
even
if
here's
another
weird
one
theory-
I'm
not
sure
that
these
always
have
to
be
straight
movements.
It's,
like
you
know
I
think,
of
like
a
rat
moving
forward
straightly.
But
you
know,
as
marcus
talked
about
these
grid
cells,
get
really
kind
of
distorted
a
bunch
of
places.
E
So
I
technically
all
we
can
say
is
that
these
flow
bits
are
coming
in
and
the
the
column
doesn't
know
what
they
what
they
mean,
but
it
just
divides
them
up
into
like
a
nice
set
that
it
can
work
with,
and
so
you
know
movements
could
involve.
You
know
weird
things
too.
I
mean
there
could
be
kerdi
movements
that
are
also
changing
orientation.
E
At
the
same
time,
I'm
I'm
not
sure
it's
a
little
confusing
to
me
still,
but
the
easiest
to
think
about
it
right
now
that
the
location,
1d
modules
are
all
sort
of
straight
line,
trajectories
in
different
directions
and
the
orientation
ones
are
similar
changes
in
and
you
know,
changes
in
orientation
when
the
orientation
changes
all
these
different
planes.
You
could
be
changing,
you
know,
so
I
I
I
need
three
like.
I
could
look
up
and
down
looking
left
to
right
and
I
can
rotate
along
the
axis
of
my
vision.
E
That's
me:
I
need
to
do
orientation,
but
I
could
look
up
to
40
degrees
and
up
to
the
right
at
30
degrees
and
also
we
have
to.
I
should
I
should
point
out
as
mark
as
I
mentioned
earlier.
If
I
have
three
dimensions,
I
actually
need
six
of
these
modules
because
I
have
to
represent
both
directions
at
the
same
time.
So
three
dimensions
require
six,
so
I
misstated
myself
there,
but
we
we
might
have
a
hundred
to
work
with
or
200
or
400,
so
a
lot
of
stuff
going
on.
E
Okay,
yeah
there's
some.
You
know
I
can
I
just
talk
briefly
here.
I
remember
I
mentioned
on
the
orientation
cells.
These
are
head
direction
cells.
They
are
not
specific
to
a
an
environment,
a
particular
orientation
head
direction
cell
says:
I'm
moving
it
this
direction
in
this
environment,
but
that
cell
could
represent
a
different
direction
in
a
different
environment.
So
it
doesn't
tell
me
what
an
environment
is,
but
these
guys
do
these
1d
cells.
E
If
I
look
at
them,
they
could
flex
on
them,
but
what's
interesting
what
I
need
to
compensate
the
for
orientation
changes
in
the
transform.
I've
talked
about
the
thalamus.
Is
these
guys?
I
want
to
send
a
signal
to
the
thalamus.
It
says
you
need
to
convert
this
input
based
on
some
orientation.
I'm
not
going
to
review
that
again
today,
but
we
talked
about
that,
but
I
want
to
tell
this:
I
don't
want
to
tell
the
thalamus.
Oh
I'm
in
room
a
and
you
change.
You
need
to
change
your
orientation.
E
F
E
F
E
Yeah
but
but
but
I
I
am
assuming
that
the
transform
of
the
thalamus
is
occurring
constantly
and
and
so
as
I
change
my
orientation,
the
input
from
the
thalamus
is
being
swapped
at
the
same
time,
and
I
haven't
worked
it
through
in
detail,
but
I
worked
it
through
enough
to
convince
myself.
I
think
I
think
it'll
work
that
that
that
it's
so
yeah,
so
I
said
it,
I
can
say
it
again,
but
I
think
that
I
think
that
obviates
the
need
you
just
said,
as
as
the
orientation
is
changing.
E
F
E
Well,
they
can
observe
it.
Let's
say
I
have
a
camera
and
they
can
observe
the
flow
bits
right
and
I'm
turning
it
to
the
right.
So
there
will
be
a
set
of
modules
here
up
actually
here
these,
these
are
the
1d
orientation
modules
they'll
be
set
up
now.
Maybe
this
middle
column
here
represents
movement
to
the
right,
so
that
one
updates
maximal
frequency
right.
This
one,
maybe
is
representing
movement.
F
E
Yeah.
Well,
if
I
have
sensory
input
that
I'm
I
can,
I
can
do
everything
right.
I
think
you
brought
up
a
new
question
earlier.
If
I
don't
have
sensory,
it's
a
challenge,
but
if
I
have
an
essential
impress
which,
in
a
vision
system,
let's
assume-
I
always
have
that
for
the
moment,
then
the
visual
input
will
tell
me
how
each
of
these
modules
should
be
updated.
I
don't
need
anything
else
to
do
that.
E
I'm
not
disagreeing
with
you.
I'm
not
saying
that
there
isn't
a
need,
like
you
said,
with
the
finger.
If
I
lift
it
off,
I
have
no
sensory
input
telling
me
how
the
fingers
moving-
I
just
I
I
might.
I
have
proprioceptive
input,
perhaps
so
I
I
think
those
are
some
interesting
opening
open
questions,
so
I'm
not
disagreeing
with
you,
but
I
think
it's
not
as
obvious
to
me.
At
least
it's
not
as
obvious
of
the
need
for
that
that
you
need
to
have
this
to
represent
the
path
integration
here.
E
If
you've
got
your
sensory
data
or
or
you
have
an
efferent
copy
motor
command,
which
I
didn't
talk
about,
but
I
also
think
you
could
do
this,
which
serves
the
same
purpose
as
the
sensory
data.
Then
I
think
it
could
update.
But
you
know
you
might
be
right
I'd
like
to
if
you,
if
you
could
make
it
make
the
argument
convince
me.
E
That
would
be
good.
I
I
I
didn't
go
that
far,
yet
I'm
just
I'm
just
sort
of
laying
things
out,
but
to
me
the
big,
the
big
it's
just
getting
closer
to
figuring
out.
Okay,
what
are
all
the
components
that
we
have
to
be
doing
here?
How
might
they
actually
be
working
and
and
then
to
me
the
big
extra
thing
was
the
displacement
modules
like
oh,
I
got
a
whole
way
of
doing
the
displacement
mods,
which
is
simple,
because
I
I
remember
when
you
presented
the
original
displacement
model
concept.
E
I
really
had
struggling
with
it
at
first
and
understanding
it,
and
then
I
said
to
myself:
oh
you
know
how's
the
cell
going
to
learn
this.
How
can
a
cell
learn
to
respond
to
all
these?
You
know
crazy
combinations
of
other
cells,
and
now
I
realize
you
don't
have
to
do
that
at
all.
You
just
have
to
do
past
immigration,
just
like
the
other
guys,
so
that
was
to
me
it
was
a
big
big
plus
for
me
this
week
and
then
that
could
and
now
that
I
can
do
secrets
as
well.
E
E
I
don't
I
don't
really.
I
had
a
couple.
I
said:
there's
some
there's
some
things
you
could
predict
from
this.
I
don't
need
to
go
through
that.
Oh
well,
this
is,
I
guess
things
in
my
notebook
here.
Here's
one
more
thing
just
to
remind
ourselves
that
phase
procession
is
going
on
here
everywhere,
so
so
in
the
1d
columns
and
the
2d
modules,
the
there's,
actually
not
just
one
cell,
that's
active,
but
at
different
parts
of
the
theta
phase.
E
Different
cells
are
active
and
so
you're
you're
sort
of
running
through
little
sequences,
little
subsets
of
sequences
constantly
in
these
guys
as
you're
moving
based
on
the
phase
possession.
I
just
put
that
in
this.
I
don't
want
to
forget
that
that's
another
thing
we
have
to
accommodate
all
right,
I'm
done
you
can
you
can
go
ahead.
F
E
Yeah,
so
the
trick
was,
I
said,
I'll,
say
the
trick
again
and
I'll
try
to
walk
you
through
it.
The
trick
again
is
that
the
difference
between,
let's
say
the
difference
between
the
displacement,
module
and
location
and
the
displacement
and
a
location
model
right
between
a
grid
cell
module
and
a
displacement
module
is
they're,
almost
identical
it's
about
what
they
anchor
on.
E
So
when
you
enter
an
environment,
the
grid
module
the
midsub
module,
or
these
one
data
visual
modules
will
anchor
on
a
particular
cell
and
and
that's
happening
over
and
over
again
right.
You
know
you're
constantly
up
you're
constantly
using
sensory
data
to
re-anchor,
but
the
idea
ideally
was
once
you've
got
an
anchor
there
and
you
start
moving
that
cell
just
keeps
going
and
you
and
you're
moving
here
when
the
it's
the
same
thing,
but
what
you
anchor
every
time.
E
You
start
the
movement
every
time
you
start
moving
the
cell
anchors
and
it
always
anchors
on
the
same
cell
pick
the
top
one
and
and
that's
the
difference
between
them
now.
So
this
one's
anchoring.
Every
time
you
get
to
the
you
start
a
movement.
This
is
re-anchoring
based
on
centering
data
all
the
time,
and
I
don't
even
know
how
that
happens,
but
it's
gonna.
So
what
what
occurred
to
me?
Maybe
this
will
help
you
mark
this.
E
What
occurred
to
me,
I
was
thinking
about
a
good
cell
module
and
I'm
thinking
like
okay
and
then
I
was
thinking
about
a
displacement
cell
module.
I
said
well
what
what?
What?
What
if
I,
how
would
the
displacement
modules
cells
change
as
I
move?
Well,
as
I
move
between
you
know
as
I'm,
what
would
happen
is,
as
I
move
relative
to
two
points
in
the
world
that
the
active
cell
and
displacement
module
would
change
slowly,
just
like
the
active
cell
in
the
grid
cell
module.
E
That
is
my
displacement
changes
as
I
move
through
the
world.
If
I,
if
I'm
trying
to
say,
what's
my
displacement
between
point
a
and
point
b,
I
say
well
that
cell
will
be
changing
slowly,
just
like
the
cell
they'll
be
moving
at
the
same
speed
actually,
and
so
then
I
just
realized
well
the
distance
it
traveled.
E
Here
is
your
displacement,
and
so
here
I'm
trying
to
say
oh
yeah,
the
distance
on
the
on
the
midsole
module
that
just
the
distance
traveled
could
be
between
this
cell
and
this
cell
orchid
between
another
cell
and
another
cell,
and
this
one
another
cell,
but
here
it's
just
from
the
beginning
of
the
end,
and
so
the
cell
that
I
end
up
on
after
I
start
at
the
top,
and
I
move
down
the
cell
that
I
end
up
on
is
the
distance
I've
traveled.
It
doesn't
matter
where
I
was
in
the
world.
It's
just
the
distance.
E
I
traveled
and
that's
my
displacement.
You
know.
Remember:
displacement
cells
represent
movement
between
two
points
or
they
represent.
You
know
the
equivalent
is
the
displacement
between
two
points
and
two
different
grids
of
the
two
different
reference
frames.
So
it's
the
same
thing.
So
it's
actually
just
all
you
have
to
do
is
just
track.
How
far
you
moved
in
this
direction
from
when
you
left
point
a
until
you
get
the
point
b
and,
and
the
cell
that
is
active,
is
represents
any.
E
E
I
think
here
we
talked
about
displacement
cells,
could
represent
the
difference
between
a
point,
a
in
the
one
space
at
a
point
x
in
another
space
or
point
a
in
the
same
space
at
the
point
b
in
the
same
space
between
different
spaces
of
the
same
space.
It's
the
exact
same
thing,
there's
there's
no
difference
between
them
and
so
the
same
module
and
I
haven't
worked
out.
The
detail
here
could
represent
both
at
one
point,
I
think
I
think
remember.
Scott
said
this.
E
E
It
was
the
idea
of
the
same
grid,
a
displacement
cell
module,
the
same
displacement
module
could
could
serve
both
purposes
one
at
one
moment:
it's
exactly
how
far
you're
moving
and
then,
when
you
switch
to
it
it's
then
it's
now
going
to
represent,
as
I
re-anchor
when
I
re-anchor
my
this
on
my
grid
cell
it'll,
now
represent
the
displacement.
52
points
all
right.
E
I
didn't
explain
it
very
well,
but
the
same
we
we
described
that
in
here
somewhere
in
here
that
the
same
module
can
do
both
and
and
so
what
it
there's
some
trickiness
to
it.
If
I
and
I
didn't
talk
about
that,
the
trickiness
gets
to
the
it's
like.
It's
really
easy
to
imagine
that
spice
module
representing
the
amount
of
the
distance
I
moved
in
within
the
particular
object.
But
now,
let's
say
I'm
at
a
point,
a
on
the
coffee
top
and
I
want
to
say,
what's
the
equivalent
point
on
the
logo.
E
Well,
I'm
actually
not
moving,
but
I
want
to
I
want
to
pretend
like
I
did
move,
and
so
I
I
I'm
working
on
an
id
here.
This
is
I'm
going
to
lose
everyone
on
this,
but
I
think
I'm
working
on
the
idea
that
very
quickly
the
displacement
module
will
say:
okay,
I'm
at
you're
at
point
a
on
the
coffee
cup.
What
you
know,
what
does
the
equivalent
point
be
on
the
the
point
on
the
on
the
logo?
It'll
very
rapidly
run
down
here
until
it
matches-
and
it
says:
oh
okay.
E
E
F
E
Do
they
will
move
together?
Okay,
because
they're
in
the
same
mini
column,
the
same
they're
sitting
the
same
one?
These
you
know
vectors
column,
and
so
I
don't
even
know
if
they
have
to
link
together.
Maybe
they
do
but
but
they
just
move
together
and
one
is
just
one
is
just
starting
it.
You
know
putting
a
tape
measure
down
saying
how
far
to
go
and
the
other
one's
saying.
Okay,
I'm
at
the
edge
of
the
table,
I'm
going
to
the
other
end
anyway.
E
E
F
I
guess
I'll
do
one
just
one
last
one
and
it
really
comes
back
to
the
first
point.
I
made
I'll
be
curious
to
see
you
know:
you're
you're,
really
bringing
in
this
constraint
from
the
retina
and
complex
cells,
it's
kind
of
inconvenient.
We
would
almost
want
the
rings
to
update
in
both
directions.
We
would
kind
of
want
these,
these
mini
columns
to
update
no
matter
what
direction
you're
moving,
because
that
would
give
you
path
integration
here.
Somehow
we
have
to
solve
that.
E
E
There
was
something
about
the
the
oscillatory
interference
model.
That
said,
oh,
I
know
what
it
was
is.
If
you
moved
backward,
you
would
see
it
was
something
about
the
phase
procession.
It
was
like.
There
was
something
that
said.
If
the,
if
this
worked
in
both
direction,
then
the
phase
possession
wouldn't
look
like
it
was
something
like
that.
J
E
I
fouled
that
in
my
head
and
then
I
also
said
I
also
you
know,
then
I'm
also
thinking
about
the
way.
Then
I
have
this
idea
that
the
mini
comps
in
computer
part
takes
you
right
based
on
the
visual
questions.
Are
these
sort
of
they
don't
fire
in
both
directions?
Right?
They
only
respond
to
movement
in
one
direction.
You
have
another
column
with
fires
moved
in
the
opposite
direction,
so
I
combine
those
two
things
and
say:
okay.
Well,
we'll
have
to
accept
that.
I
wouldn't
have
thought
that
I
would
have
been
confused
like
hey.
E
Why
can't
we
go
both?
You
know
forward
and
backwards.
That
would
be
nice,
but
it
doesn't
seem
to
be
so
I'm
going
with
what
it
seems
to
be,
and
I
think
I
can
make
it
work
this
way.
There's
gonna
be
some
yeah,
as
you
pointed
out
absolutely
there's
going
to
be
some
some
little
tricks.
You
have
to
resolve
to
make
that
work,
but
I
overall
okay,
but
but
I
I'm
not
discouraged
by
that.
E
E
G
E
Yeah
for
sure,
well,
that's
good!
I
didn't
want
anyone
to
be
completely
lost.
You
know
it's
strange.
I
actually
believe
these
fields
details
really
matter.
I
don't
I.
I
still
adhere
to
the
belief,
there's
nothing!
That's
what
swayed
me
from
it
that
you
know.
Oh,
we
don't
have
to
concern
about
ourselves
about
these
details.
I
think
in
the
end,
ai
systems
are
going
to
work
very
very
closely.
To
this
I
mean
yes,
there
will
be
differences,
but
I
don't
think
we've
gotten
down
far
enough
where
we
can
say
like.
E
Oh,
we
can
abstract
all
this
away.
I
don't
think
so.
I
think
these
these
mechanisms
are
going
to
apply
and
obviously
not
the
biological
details
of
the
mechanisms
like
we
don't
have
to
have
this
chemical
chemistry
in
the
biochemistry
and
all
that
stuff
and
this
convolving
model,
then
we
don't
have
voltage
gradients
and
things
like
that,
but
this
basic
representational
scheme-
that's
shown
on
this
page
here,
I
think,
is
going
to
be
essential.