►
Description
Marcus Lewis further elaborates and discusses some ideas outlined in "The Tolman-Eichenbaum Machine” paper in a continuation of Feb 15's research meeting. He first gives a quick review of the grid cell module presented in the paper and outlines 2 extreme scenarios of the mechanisms within the module to address the team’s skepticism of a multi-scale grid cell readout.
“The Tolman-Eichenbaum Machine: Unifying Space and Relational Memory through Generalization in the Hippocampal Formation” by James Whittington, et al.: https://www.sciencedirect.com/science/article/pii/S009286742031388X
Feb 15 research meeting: https://youtu.be/N6I3M3pof5A
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B
A
C
A
Memory
that
spans
multiple
scales
and-
and
we
were
a
little
hesitant
about
this
because
of
just
our
intuition-
about
grid
cells
and
what
happens
when
you
combine
multiple
scales,
and
so
this
is
a
follow-up
on
that.
I
learned
a
little
bit.
It's
not.
Let's
see
our
intuition
was
partly
right,
but
I
learned
something
by
really
trying
to
create
some
figures
here
that
demonstrate
this.
This.
B
A
A
Here
and
I
kind
of
want
to
share
it,
some
quick
review
on
what
we
talked
about
last
week.
This
is
copy
and
pasted
from
my
last
presentation,
the
the
model
of
their
hip
of
the
hippocampus
and
to
rhino
cortex,
where
the
top,
the
the
place
cells
form
an
auto-associative,
retractor
network,
storing,
feature
location,
pairs,
location,
sensory
pairs,
the
bottom,
medial,
internal
cortex
is,
of
course,
grid
cells
and
lateral
is
sensory
input
and,
and
they
have
different
temporal
skills
on
the
sensory
input.
A
A
future
location
pair
is
encoded
by
the
population
of
place
cells
across
multiple
modules,
and
so
this
picture
down
on
the
bottom
shows
basically
everything
you
the
lateral
end
to
rhino
cortex,
the
sensory
input
on
the
bottom
sort
of
anoints
a
set
of
columns
in
this
picture.
It
says
you're
allowed
to
be
active,
the
grid
cells,
sort
of
anoint,
a
set
of
rows
and
say
you're
allowed
to
be
active
and
the
intersection
of
them
is
what
becomes
active
and
the
only
the
only
crosstalk
between
modules
is
at
the
level
of
these
cells.
A
They
learn
these
attractor
states
like
this,
so
this
is
the
review.
This
is
me
just
getting
you
to
page
back
in
what
we
talked
about
last
week.
Now,
our
intuition
our
background
on
this.
Why
why
part
of
this
jeff-
and
I
agreed
that
that,
like
part
of
it,
felt
a
little
wonky
and
I'm
trying
to
display
that
to
you
right
here
we're
a
little
bit
skeptical
of
the
multi-scale
grid
cell
readout.
A
Here
I've
shown
three:
oh
sorry,
five
grid
cell
modules
and
before
and
after
a
movement,
so
I've
used
blue
to
denote
another
grid
cell
representation.
So
here
I'm
depicting
two
good
cell
representations
and
I've
made
it
kind
of
cartoonish
where
one
of
them
changes
a
lot
most
of
them
don't
change
at
all
and
the
the
point.
A
A
Here
is
that
to
read
out
this
code
is
hard
to
to
read
out.
Neuron
would
have
to
be
very
precise
to
discriminate
between
the
black
and
blue
representations,
especially
when
you
adopt
the
mindset
that
know
that
neurons
are
noisy
and
dendrites
need
to
be
fault.
Tolerant,
so
dendrites
need
to
not
expect
an
exact
number
of
matches.
So
so
something
felt
off
about
this
with
with
multiple
scales,
and
so
this
intuition
has
kind
of
pushed
us
away
from
thinking
grids
of.
C
You
would
say:
no,
that's
not
part
of
this
pattern,
so
you
just
wouldn't
the
a
local
ruling
learning
rule
on
a
dendrite
would,
as
we've
always
thought
about
it.
That
doesn't
mean
it's
right,
but,
as
we've
thought
about
it,
a
local
learning
role
in
dendrite
would
say:
hey
the
thing.
That's
changing
a
lot
looks
kind
of
like
noise.
It's
not
part
of
this
pattern,
therefore
we
wouldn't
form
synapses
to
it,
but
the
system
requires
you
to
do
so.
C
In
this
case,
you
show
three
of
these
units
being
the
same,
but
in
a
more
general
case,
most
of
them
would
be
different,
and
you
know
only
as
you
go
to
the
right.
There'd
be
more
stability,
but
in
the
left,
almost
everything
very
quickly
things
get
walking
on
the
left
side.
So
it's
it's
more
than
just
a
being
able
to
decode
the
pattern.
It's
also
a
learning
rule
about
how
synapses
are
formed.
That
would
seemingly
fail
under
this
kind
of
scenario,.
A
Yeah,
so
this
this
was
laying
out
the
review
in
the
background
now
now
to
show
where
I
kind
of
learned
something
by
creating
exact
diagrams.
Basically,
the
question
I'm
asking
is
now
that
we
move
now
that
we're
moving
this
multi-module
code
up
to
the
place
cells
up
to
the
feature
location
pairs.
Does
this
problem
carry
through?
Does
it
remain
or
does
it
does
it
change?
Is
it
no
longer
quite
as
bad
or
is
it
a
different
problem
and
so
yeah
should
this
multi-skill
readout
is
bad
intuition
carry
over
to
this
model?
B
A
Scenario
here
is
consider
a
small
movement,
much
like
much
like
what
I
showed
here,
a
movement
where
only
one
of
these
modules
changes
essentially
essentially
only
one
of
them
changes
and
in
case
one.
So
so
it's
important
to
distinguish
between
these
two
cases,
because
they
keep
in
mind
they're,
also
modeling,
lateral
and
torino
cortex
as
having
different
temporal
skills
and
so
kind
of
in
their
mindset.
It's
likely
that
case
one's
going
to
occur
where
only
one
module
sensory
input
is
going
to
change
this.
A
The
sensory
representation
here
I'll
bring
in
the
figure
in
a
second
the
the
sensory
representation
that
was
going
to
stay
the
same
in
most
of
it.
So
what
the
way
I
show
this
is
the
leftmost
module.
Has
this
location
change?
That's
the
blue.
Moving
down
and
the
leftmost
module
also
has
a
sensory
input,
change
the
red
I
drew
it
moving
right.
It
didn't
have
to
be
a
translation
of
the
two,
but
that's
just
what
I
did.
A
A
These
are
the
two
attractor
states
that
are
going
to
be
learned
and
the
two
attractor
states
are
going
to
be
overlapping.
One
of
them
is
going
to
be
this,
this
top
the
the
the
top
set
of
cells.
The
other
is
going
to
be
the
bottom
sub
cells
which
contain
many
of
the
same
cells
and
the
the
the
second
case
in
some
ways.
A
A
C
A
A
C
In
the
lower
one,
the
lower
case
is
they're
all
changing
yeah,
which
is
a
little
hard
to
imagine.
If
the
location's
not
changing.
How
does
the
sensory
input
change?
I
mean
you
know
it's
like
if
you
think
about
the
different
modules,
the
different
regions
of
visual
cortex.
You
know
the
sensory.
If
you
look
at
the
receptive
field,
size
of
a
cell
in
v2,
it's
much
larger
than
v1
and
v4
is
much
larger
than
v2,
or
something
like
that.
A
C
A
Okay,
so
I'll
move
on
so
so
now
the
two
questions
I'm
going
to
ask
are:
first
of
all,
can
a
location
predict
a
feature
I'll
get
to
the
second
question.
The
second
question
is
going
to
be:
does
readout
work,
but
but
the
more
fundamental
question
for
their
model
is
given
a
location.
Can
you
will
this
attractor
successfully
predict
a
feature,
and-
and
so
you
see
the
answers
here-
that
I
that
I'm
stating
but
I'll
walk
through
them
here.
A
So
I
mean
you
see
that
I
mean
going
back
and
forth
between
these
two
slides.
I
should
have
animated
differently
so
back
and
forth.
I've
just
taken
these
same
two
pictures
and
removed
a
bunch
from
it
and
said
that
if
you,
if
you
activate
a
given
location,
a
given
grid
cell
in
each
module,
it's
going
to
provide
excitatory
input
to
these
rows
of
cells,
and
so
the
the
question
is:
is
this
going
to?
Is
this
attractor
going
to
successfully
activate
this
pattern
of
dark
red?
A
And
my
intuition
says:
yes,
the
the
fact
that
there
is
this
other,
these
other
two
cells
that
are
kind
of
confused
or
kind
of
very
close
to
this
attractor
point
isn't
a
problem,
because
these
cells
aren't
receiving
good
cell
input,
and
so
I
think
that
in
their
model
a
location
is
going
to
successfully
predict
a
feature,
whereas
in
ours,
when
we
talk
about
grid
cells
of
multiple
scales,
it
it
doesn't
really
work,
because
that
requires
a
readout
that
we
don't
like.
But
here
I
don't
think
there's
any
such
problem.
C
So
it
just
gets
back
to
my
my
concern
earlier.
I
tried
to
make
the
definition.
The
real
problem
for
me
of
the
different
scales
is
the
learning
problem,
and
so
the
upper
case
here
case
one
requires
that
I
learn.
I
know
if
you
want
to
call
it
two
attractors
or
one
attractor,
but
you've
got
let's
say
two
attractors
or
one
attractive
reunion.
I'm
not
sure
how
you
want
to
phrase
it,
but
there
are
two.
You
know.
Four
of
those
modules
are
all
stable,
but
the
other
going
down
to
the
one
on
the
left.
C
You
have
to
predict
two
things,
so
I
have
to
say:
okay,
I'm
gonna
predict
either
one.
You
know
either
one
location,
another
location
and
the
question
I
have
is:
how
does
that
get
learned,
especially
if
we
start
thinking
that
it's
more
than
one
location,
maybe
there's
you
know,
half
a
dozen
or
a
dozen
that
options
down
in
the
left
module
there.
It
doesn't
seem.
You
could
learn
these
attractors.
That's
that's
the
problem.
I
have
it.
If
the
attractors
were
learned,
then
yes,
it
would
work.
C
I'm
seeing
how
they
learn
practically
on
a
dendrite.
You
know
it's
like
I'm
again.
I
imagine
just
imagine
I'm
a
dendrite
suction
of
a
dendrite,
and
I
I'm
looking
at
all
these
cells
and
I'm
trying
to
learn
a
pattern
and
some
of
the
again
like
I
said
earlier,
some
of
the
cells
are
sort
of
stable
for
a
long
period
of
time,
and
then
I
get
another
pattern
and
then
I
can
know
well
it's
easier.
C
I
can
learn
those
attractors,
but
while
one
while
some
of
those
cells
are
stable
for
a
long
period
of
time,
these
other
cells
are
changing
rapidly
and
I'm
not
going
to
learn
them
as
part
of
that
attractor.
So
the
in
the
in
this
more
extreme
case
on
the
left
here,
I
might,
as
I
go
left
in
this
diagram
I'll-
have
lots
of
changes
or
lots
of
possibilities
on
the
left,
instability
on
the
right,
and
so
how
do
I
learn
that
attractor?
C
When
there's
all
this
instability
on
some
of
the
inputs,
I
have
to
somehow
say:
yeah,
I'm
going
to
learn
those
even
though
they're
I
just
don't
know
how
the
dendrite
could
do
that.
How?
How
would
I
know
to
associate
a
changing
an
action?
That's
going
by
that's
changing
radically,
while
a
bunch
of
electrons
going
by
that
are
not
changing
rapidly.
How
do
I
associate
the
changing
line
with
all
the
ones
that
are
that
aren't
changing?
C
C
C
That's
always
been
my
objection.
I've
always
imagined
myself
as
a
dendrite
section,
trying
to
look
like
okay.
What
kind
of
simple
hebbian
rule
that
I
want
to
use
to
learn
these
there's
a
pattern
out
there
and
and
if
somebody
some
of
the
potential
synapses
are
changing
rapidly
and
some
are
not.
How
am
I
going
to
learn
to
associate
the
ones
that
are
changing
rapidly
with
the
ones
that
are
not
changing?
C
A
C
C
The
second
box
shows
two
arrows
coming
in
from
the
left
and
one
out
from
the
right,
meaning,
there's
two
there's
two
different
patterns
of
oscillating
on
the
left
and
there's
one
pattern,
that's
coming
in
from
the
right,
and
this
problem
could
be
much
worse
than
two
to
one
and
so,
if
you're,
a
dendrite
in
that
block,
how
do
you
know
to
associate
the
stable
one
on
the
right
with
the
changing
ones?
On
the
left?
C
Yeah,
but
tens
of
fireworks
means
that
that
they're,
not
that
that
they
tend
to
fire
with
if
the
ones
in
my
left
in
this
diagram
are
changing
rapidly.
Then
I
can't
assume
that
they're,
if
they
only
one
out
of
ten
times
they
fire
with
the
ones
on
the
right,
then
I
would
say
nope
they're
not
flying
together.
C
Be
finessed,
maybe
it
could
be
finesse,
I'm
I'm
not
claiming
that.
I
I
just
it's
the
way
I've
been
thinking
about
it.
Maybe
I
can
I
can
I'm
imagining
myself
saying
well
what
have
I
modified
my
heavier
learning
rule
and
thought
about
a
little
differently,
maybe
I'll
get
to
work.
So
let's
go
with
that
for
a
moment.
C
A
C
God
it's
it's!
The
heavy
learning
thing
you
know
take
away
the
way.
Spatial
pull
over
the
spatial
cooler
basically
says
it's
constantly.
It's
constantly
forgetting
connections
that
don't
occur
reliably
enough
with
other
ones
right.
So
there's
gonna
be
some
threshold.
That
says
you
know
you're,
just
not
firing
together,
often
enough
you're
out
of
here.
C
So
that's
that's
the
basic
of
heavy
learning.
You
have
to
have
some
level
of
yeah.
These
are
firing
together
enough
enough
of
the
time
and
as
soon
as
they
it
seems.
You
know
fire
enough
of
the
time.
Then
I
have
to
assume
you're
you're,
just
you're,
not
part
of
this
group.
You
know
you
have
to
you
have
to
we're
just
going
to
forget
you
and
that's
that
problem
exists
here
now.
The
bottom
picture
here
you're
saying
here.
Well,
I'm
not
sure
what
the
picture
shows.
A
So
yeah
the
the
bottom
picture
is
in
the
other
extreme
case,
where
all
of
the
inputs
have
changed.
That
means
the
conjunctive
look,
representations
have
changed
the
place
different
place.
Cells
are
active,
then
the
the
two
attractor
states
don't
overlap,
and
so
what
will
happen
when
you
burst
these
rows,
given
the
location
input
as
well?
First
of
all,
what
will
definitely
happen
is
it'll
resolve
down
to
all
these
dark
red
cells,
and
then
the
open
question
is
whether
it's
going
to
be
powerful
enough
to
then
silence
these
two
and
these
two,
the
wrong
ones.
A
C
C
A
A
C
Yeah,
I
guess
it's
always
been
the
learning
issue
for
me
so
yeah
I
just
heard
something
yeah,
so
that's
I
brought
up
earlier
when
you
put
up.
I
said:
no,
it's
really
a
learning
issue,
so
yeah
I
mean,
I
think
it's
a
very
interesting
question
to
ask
that
you
know
to
question
that
assumption.
I
mean
you
recall
marcus
when
we
started
talking
about
multiple
visual
modules.
C
I
immediately
objected
to
the
idea
that
we're
mixing
scale
and
it
was
for
this
reason
and
then
we
found
out
later
that
oh
it
doesn't
seem
to
be
much.
You
know,
interaction
between
the
scales,
the
different
modules
of
different
scales.
It
didn't
seem
to
find
the
connections
that
spans
different
scales
and
we
say:
okay,
that's
consistent
with
that,
but
you
know
maybe
there's
maybe
we're
wrong
about
that.
Maybe
I
was
wrong
about
that.
Maybe
there
is
a
way
to
get
it
to
work,
and
I
mean
in
this
case
you
also
pointed
out.
C
Oh
they're,
not
really
talking
good,
sell
the
grid
cell
they're
talking.
You
know,
they're
they're
doing
this,
this
sort
of
place
cell
union
connections
across
so
maybe
those
connections
do
exist.
So
I
think
it's
worth
and
I
think
it's
worth
putting
this
back
in
the
potential
toolbox
of
like.
Oh
maybe
we
got
that
part
wrong
or
I
got
that
part
wrong
and
maybe
maybe
there
is
a
way
of
getting
it
to
work.
I'm
not
sure
yet,
but
I'm
going
to
give
that
a
try.
B
I
feel,
like
my
intuition,
like
you
say,
marcus,
is
that
kind
of
with
a
basic
heavy
rule
like
what
you
see
kind
of
in
case.
One
should
be
possible,
but
that
maybe
or
like
would
occur,
but
that
maybe
kind
of
along
the
lines
of
what
you're
saying
jeff,
that
this
could
lead
to
issues
further
down
the
line.
And
I
I
feel,
like
kind
of
we
mentioned
last
time
about
how
they
reset
the
weights,
the
heavy
weights
between
environments
and
that
sort
of
thing,
and
so
it
would.
C
C
C
If
I
accept
that,
okay,
we're
going
to
be
doing
some
heavy
learning
here
and
we're
going
to
group
things
that
fire
together,
but
they
don't
fire
together
all
the
time.
In
fact
they
don't
have
to
fight
again.
Very
often,
you
know
every
once
in
a
while.
They
fire
together
we're
gonna
form
that
that
connection
okay.
Well,
I
could
have
a
heavy
role
like
that,
but
then
what
I
would
end
up
doing
is
forming
synapses
to
confront
the
tunnel
things.
I
don't
really
want
to
form
synapses
dude.
They
really
weren't
causally
connected.
C
C
Yeah
well,
but
then
you
know,
then
you
have
to
go
through
the
math
and
see
what
is
your
chance
of
error?
We've
done
this
kind
of
work
in
the
past,
but
like
okay,
what
if
I'm
forming
connections
to
think
I
shouldn't
connect
to,
but
so
what's
the
harm
in
that
right?
What's
the
harm
in
that?
Well,
the
harm
eventually
becomes
at
some
point.
You
recognize
a
pattern
that
really
wasn't.
You
know
a
real
pattern
at
all.
C
C
I
could
be
presenting
some
other
pattern
on
the
into
the
system
and
I'm
picking
one
cell
from
you
know
and
by
chance
there's
a
there's
like
I
have
a
by
chance
or
the
each
of
these
cells
is
used
in
multiple
patterns.
So
I
have
some
different
patterns
on
the
left
that
shouldn't
be
part
of
this
union.
There
shouldn't
be
part
of
this,
this
stable
pattern,
but
I
just
randomly
picked.
You
know
by
chance.
C
C
If
I
start
forming
all
these
extra
synapses,
I
will
start
having
mix
and
match
errors
and
I'll
get
I'll
get
I'll,
detect
patterns
that
I
really
shouldn't
have
detected,
that
there
wasn't
a
pattern
there,
but
just
by
chance
there's
enough
active
cells
and
across
the
different
patterns,
and
so
there
that's
the
downside
to
this.
There's
this
tension
between
you
know
being
too
specific
in
your
learning
or
being
so
unspecific.
C
C
You
know
you
can
you
can
just
they're
technically
discernible
right,
you
can
say
well,
I
have
two
patterns
and
they
share
90
or
80
of
the
same
cells,
but
still
they're
separate.
So
I
can
differentiate
them,
but
from
a
neuronal
neuron
point
of
view,
it
gets
very,
very
difficult
to
differentiate
so
from
pure
mathematical
point
of
view.
Sure
you
can
do
that
no
problem,
but
from
a
from
a
neuron
point
of
view,
it's
like
no,
I
don't
think
I
could
do
that.
A
I
have
one
more
slide:
it's
not
super
important,
so
I'll
just
go
through
it
quickly
and
then,
if
we
have
any
more
so
the
the
the
final
one
is
well,
let's
go
back
to
readout
like
what
we
were
talking
about.
I
say
it's
less
important,
because
their
model
doesn't
really
rely
on
reading
out
these
codes
at
all.
It
really
treats
them
as
a
big
attractor
and
that's
it.
A
C
A
C
B
A
C
A
C
C
Yeah
I'll
just
say
like
well,
it's
pretty
hard
for
me.
I
understand
how
it's
going
to
work,
but
I'll
think
about
it.
You
know
there's
other
ways
to
skin
this
problem
I
mean
well,
I
mean
we're
mixing
up
a
bunch
of
things.
You
know
one
fundamental
problem
we've
been
trying
to
deal
with
like
well.
If
I
don't
have
multiple
modules,
a
different,
you
know
to
work
with.
How
do
I
get
my
unique
representations?
How
do
I
do
all
these
things?