►
Description
Niels Leadholm, a visiting researcher, discusses the research he has done over the course of his time at Numenta. His work builds on and extends the Thousand Brains Theory of Intelligence to the visual domain. Most machine learning networks stumble when integrating sequential samples across an image if the sequence does not follow a stereotyped pattern, while our brain does this effortlessly. In a continuation of the introduction he made during October 5, 2020’s research meeting, Niels explores how grid cell-based path integration in a cortical network can enable reliable recognition of visual objects given an arbitrary sequence of inputs.
If you want to follow Niels' work, you can follow him on Twitter (@neuro_AI).
Interested in being a visiting researcher at Numenta? Apply to our Visiting Scholar Program here: https://numenta.com/company/careers-and-team/careers/visiting-scholar-program/
- - - - -
Numenta is leading the new era of machine intelligence. Our deep experience in theoretical neuroscience research has led to tremendous discoveries on how the brain works. We have developed a framework called the Thousand Brains Theory of Intelligence that will be fundamental to advancing the state of artificial intelligence and machine learning. By applying this theory to existing deep learning systems, we are addressing today’s bottlenecks while enabling tomorrow’s applications.
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B
So
the
kind
of
motivation
for
this
research
was
that
I
was
really
interested
in
these
papers
from
numenta
that
came
out
last
year.
Looking
at
how
grid
cells
could
be
used
to
enable
robust
object,
recognition
in
particular
enable
a
sensor
to
integrate
information
over
various
locations,
and
so
in
this
paper
from
marcus.
This
was
kind
of
shown
with
these
synthetic
objects,
and
given
that
my
background
is
in
kind
of
more
vision,
I
was
interested
to
see.
B
If,
if
you
imagine
a
situation
where
the
input
to
a
sensor
is
too
large
for
it
to
be
processed
all
at
once,
all
in
parallel,
as
as
would
be
the
case,
for
example,
with
an
embodied
agent
that
is
sequentially
applying
a
sensor
such
as
a
camera
or
an
eye
to
the
environment.
Then
then
you
need
to
sample
that
space
somehow.
B
But
the
kind
of
challenging
part
of
this
is
how
you
integrate
the
information
across
those
samples
now
most
kind
of
leading
systems
such
as
a
recurrent
neural
network.
If
you
were
to
feed
it
image
patches
in
order
for
it
to
perform
well,
the
the
sequence
that
you
follow
would
have
to
be
the
same
during
both
training
and
testing
and
on
every
time
that
you
want
to
apply
the
system.
B
Then
you
could,
for
example,
sample
this
input
in
a
principled
way,
and
you
know
you
might
see
this
part
first
and
then
very
quickly
identify
what's
in
the
image.
So
that's
that's
kind
of
the
the
key
motivation
from
the
the
machine
learning
side.
From
the
neuroscience
point
of
view,
it's
there's
been
a
lot
of
focus
in
the
kind
of
for
many
years
now,
in
how
primate
vision
can
be
modeled,
particularly
with
parallel
systems.
B
Sorry,
that's
right,
but
yeah,
but
but
of
course
we
know
that
this
is
how
we
experience
the
world,
and
so
we
there
must
be
some
mechanism
for
us
to
integrate
this
information.
But
at
the
moment
this
remains
an
open
question.
How
our
brain?
Does
this
the
kind
of
concept
of
cortical
grid
cells
and
object?
Reference
frames
provides
a
neural,
neurologically
plausible
solution,
but
beyond
kind
of
numenta's
interest
in
this
there's
been
interest
elsewhere
in
the
literature.
B
An
important
caveat
is
that
so
they
they
developed
a
model
that
was
able
to
be
fed
in
an
image
of,
for
example,
a
face
and
then
recall
that
face
so
essentially
memorize
an
image
and
recognize
that
same
image,
if
shown
again,
but
the
system
wasn't
tasked
with
generalization.
So,
given
a
series
of
examples
of
say
a
particular
digit,
can
it
can
the
system
recognize
a
novel
example
of
that
digit?
B
So
it's
worth
just
kind
of
mentioning
a
bit
why
this
kind
of
interesting
grid
cells.
I
appreciate
this
is
familiar
to
many
of
those
listening,
but
for
anyone,
who's
less
familiar
with
this,
so
grid
cells
fire
with
these
regular
patterns
of
activity,
as
typically
an
agent
travels
through
space,
but
also
in
this
kind
of
theoretical
framework,
as
a
sensor
travels
through
space
and
so
by
looking
at
the
activity
of
a
given
grid
cell.
B
What's
quite
useful,
however,
is
that
a
combination
of
grid
cells,
so
different
grid
cells
have
different
scales
and
different
orientations,
and
a
combination
of
these
can
therefore
uniquely
encode
a
particular
location
in
space.
But
in
addition
to
this
encoding
capability
grid
cells
are
able
to
update
their
firing
with
self
movement,
so
perform
path.
Integration,
and
this
means
that
information
about
where
a
sensor
is
moving
to,
can
also
be
encoded
robustly
and
so
in.
B
This
the
kind
of
location
representation
can
then
predict
the
sensory
input.
That
is
likely.
The
sensory
input
is
then
received
and,
together
with
the
prediction,
changes
the
representation
here
and
then
the
sensory
representation
can
update
the
location
representation
and
then
this
can
process
can
continue,
iteratively,
so
adapting
one
of
the
figures
from
marxist
paper.
B
B
Yet
the
kind
of
nothing
really
happens
at
this
point
and
there's
no
prediction
for
the
sentry
layer,
the
first
sensory
input
arrives
and
because
there's
no
prediction,
the
columns
that
are
activated
become
active
indiscriminately,
and
so
the
the
kind
of
sensory
representation
is
essentially
consistent
with
a
multitude
of
digits
that
might
be
represented
by
that
feature.
So,
for
example,
both
a
nine
and
a
zero
have
a
can
have
a
similar
feature
at
the
top.
B
This
then
predicts
a
where
the
kind
of
object
is
where,
where
the
feature
is
in
in
that
object,
reference
frame
and
gives
the
kind
of
location
representation.
So
the
kind
of
idea
here
is
that
one
believes
one
is
either
at
the
kind
of
the
top
of
a
nine
or
top
of
a
zero,
but
one
is
unsure
which
of
these
is
the
case.
B
The
kind
of
sensory
information
is
then
provided,
but
this
time,
because
some
of
these
columns,
some
of
these
cells,
whether
were
correctly
predicted
and
some
were
not,
the
activity
is
sparse
and
in
particular,
in
this
case,
the
activity
is
consistent
with
a
subset
of
the
different
examples
of
nine
that
have
been
learned
in
the
past,
but
does
not
contain
examples
of
any
other
learned
digits,
and
so
classification
at
this
point
is
considered
successful.
So
the
the
representation,
although
it's
may
still
be
in
a
sense
ambiguous
as
to
exactly
what
this
nine
is.
B
B
This
algorithm
has
kind
of
two
failure.
Cases
that
are
possible.
One
is
that
the
system
does
converge
to
a
subset
of
another
class's
targets,
in
which
case
the
the
system
has
misclassified
or
the
kind
of
other
failure
cases
that
the
system
never
converges
to
a
single
to
a
subset
of
any
target
representation.
So
it
always
remains
in
kind
of
this
ambiguous
territory,
in
which
case
it
fails
to
classify
the
input.
B
A
kind
of
natural
issue
that
one
might
expect
in
this
situation
is
that,
as
the
kind
of
number
of
learned
examples
grows,
then
the
the
union
of
location
representations
grows
as
well
and
and
can
potentially
jeopardize
the
the
kind
of
sparsity
of
the
the
system
and
therefore
its
ability
to
perform,
as
it
should
in
practice,
as
long
as
the
kind
of
the
dimensions
of
the
grid
cell
modules,
for
example,
were
set
at
reasonable
values.
This
wasn't
something
that
I
ever
encountered.
B
C
I
mean
this
is
this
has
been
a
sort
of
a
bugaboo
for
us
for
a
long
time.
This
issue
about
unions
only
worked
up
to
a
certain
level
and
I
don't
think
correct,
be
from
wrong
or
something
I
don't
think.
We've
ever
really
analyzed
this
completely,
but
my
my
intuition
is
that
as
long
as
you
maintain
some
level
of
sparsity
in
the
union
you're
going
to
throw
away
a
lot
of
information
like
you,
you
can't
form
a
union
of
too
many
things,
but
the
system
won't
settle.
C
But
if
you
keep
sensing
over
time,
eventually
you'll
hit
a
combination
where
it
does
settle.
I
don't
think
we've
ever
proved
that
it's
sort
of
like
in
your
picture
with
the
tiger
in
the
woods
like
you,
can
scan
over
that
and
for
a
long
time
you
won't
see
what
it
is.
I
didn't
see
it
right
away,
but
then
you
hit
some
features
which
are
sort
of
unique,
more
unique
and
those
features
then
lead
to
a
better
sort
of
union,
and
then
you
can
settle
right.
C
C
D
C
B
Yeah
one
one
to
mention
so
I
did
just
kind
of
out
of
curiosity.
I
did
shrink
the
grid
cell
modules
to
see
if
I
could
kind
of
break
the
system
in
this
way
and
of
course
it
is
eventually
possible
to
to
do
that.
But
I
guess-
and
I
don't
have
any
specific
numbers
on
this,
but
what
was
interesting
was
that
I
had
to
get
closer
to
where
the
kind
of
the
the
actual
capacity
of
the
system
met
the
the
kind
of
maximum
possible
capacity.
B
C
We
don't
believe,
that's
a
realistic
number.
I
mean
it's
too
high,
as
I
don't
believe
it
is,
but
on
the
other
hand,
I
think
the
two-dimensional
nature
of
grid
cells,
I
think,
is
as
a
some
it's
it's
likely
to
be
a
an
artifact,
but
not
reality.
I
mean
the
the
theories
I've
been
working
on
and
we've
been
discussing
over
the
last
couple
years
is
that
perhaps
grid
cell
modules
are
really
path,
integration
in
1d
and
and
that
what
we
see
as
a
grid,
so
module
is
a
some
sort
of
a
2d
projection
of
that.
B
C
It's
okay
to
go
forward
as
it
is
right
now,
just
pointing
out
that
from
kevin's
question
it's
it's!
This
is
a!
We
don't
think
this
is
actually
it's
really
slightly
different
than
we're
thinking
about
it
here.
It's
the
same
idea
applies.
It's
nothing
wrong
with
the
idea.
It's
just
that
requiring
40
grit
cell
modules
of
2d
like
we
see
them,
does
not
seem
what's
going
on
in
the
brain,
so
I
think
there's
a
lot
of
one
degree
with
some
modules.
E
E
C
I
think
I
think
it
would.
I
mean
your
perceptual
experience.
Is
that
you
settle
you
make
a
decision.
You
know
it's
like
the
it's
like
the
example
of
the
vas
versus
faces
that
that's
common.
I
use
that
in
the
book
right
you
don't
you
can't
see
them
both
at
the
same
time,
they're
both
consistent
with
the
data
and
so
in
theory.
You
could
have
a
union
of
authors
and
phases
here.
You
could
have
a
union
of
two
different
digits
and
say.
C
E
Well,
but
in
a
continual
learning
scenario
I
mean
the
environment
is
usually
non-stationary
and
if
the
environment's
non-stationary,
then
when
you
don't
you
don't
assume,
you
ever
have
stable
representation,
so
those
representations
are
going
to
be
evolving
with
time.
So,
as
you
see
new
samples
that
union
is
going
to
change.
C
Well,
when
we
say
a
stable
world,
I
mean,
if
you're,
looking
at
a
particular
thing
and
trying
to
learn
that
thing,
then
in
theory
it's
stable
if
you're.
If
you're,
if
I
walk
into
a
room,
I
look
at
the
furniture
in
the
room.
I
can
build
a
model
that
room
by
looking
at
the
different
features
of
the
room.
If
I'm,
if,
if
things
are
flying
back
and
forth
in
front
of
me,
I
might
I
mean
I,
I
it's
not
going
to
be
stable.
C
If
I'm
looking
to
the
left-
and
I
see
some
trees
and
I
look
to
my
right
and
I
see
some
buildings-
no,
that's
not
going
to
be
stable
in
that
regard,
but
it'll
be
stable
during
the
trees
and
be
stable
during
the
buildings.
I
I
I'm
not
sure.
Maybe
I'm
misunderstanding
your
question
lucas,
but
it
seems
like
it's
a
very
dynamic
system.
It's
stable
while
you're.
Why
you're
perceiving
a
particular
object
or
a
particular
thing,
and
then
it
quickly
goes
on
to
the
next
one.
C
E
B
B
Naturally,
this
leads
to
some
loss
of
information,
but
in
practice
I
found
that
a
linear,
classifier
fed
these
features
could
achieve
99
plus
accuracy
on
amnest
and
that
a
decoder
could
accurately
reconstruct
the
input
images.
So
in
practice
it
didn't
appear
to
have
significantly
affected
the
amount
of
information
and
just
to
kind
of
show
a
bit
more
concretely
what
this
might
look
like
in
practice.
B
So
the
this
k
wanna
take
all
layers
of
five
by
five
dimension
of
grid,
roughly
corresponding
to
the
2d
shape
or
the
kind
of
2d
regions
of
the
input
image,
and
the
idea
is
that,
okay,
so
the
k
want
to
take
all
is
a
play,
is
applied
channel
wise
at
each
of
these
locations
and
the
after
kind
of
binarization.
This
means
that
there
are
25
sdrs
that
can
be
fed
as
features
across
this
2d
grid,
and
so
all
the
the
kind
of
classifiers.
B
B
These
sparse
distributed
representations
and,
in
particular,
the
the
entropy
essentially
so
how
many
of
these
cells
are
active
at
some
point
in
this
representation
so
kind
of
so
what
I'm
showing
here
is
so
the
duty
cycle
is
essentially
the
proportion
of
time
that
a
cell
is
a
winner
in
the
k
winner,
take
all
algorithm,
and
so
a
kind
of
target
duty
cycle
can
be
set.
This
is
the
desired
duty
cycle
for
each
cell,
and
this
can
be.
B
So
then,
the
kind
of
the
main
result,
then
is,
as
mentioned,
in
the
kind
of
the
basic
task:
there's
a
fixed
input
sequence
that
is,
of
these
features.
That's
given
to
the
classifiers
and
the
the
setting
that
I'm
looking
at
here
is
a
few
shot.
Learning
on
these
and
this
digits
so
anywhere
from
one
to
twenty
examples
of
each
class
are
being
fed
and,
in
addition
to
the
k-nearest
neighbor.
B
So
the
the
recurrent
neural
network
has
mode
with
both
only
one
epic
of
training
and
one
thousand
epics
of
training.
The
reason
for
the
one
epic
of
training
is
because
the
k-nearest
neighbor
and
the
the
grid
cell
net
essentially
observe
each
feature
for
a
given
example,
only
once
and
perform
in
the
case
of
chris
on
a
single
weight
update
for
that
feature.
B
C
D
D
C
I
mean
the
correlation,
the
correlation
between
even
on
a
single
digit
like
five,
the
correlation
between
the
upper
left,
part
of
the
image
and
the
bottom
right
part
of
the
image
is
going
to
be
less
than
you
know,
two
adjacent
segments.
So
it's
just
hard
to
find
those
dependencies
right.
Isn't
that
the
interpretation.
B
Yeah,
so
I
I
I
you
know,
I'm
not
suggesting
that
this
is
a
obviously
rnn's.
There
are
forms
of
rnns
that
are
designed
to
kind
of
address
this
issue,
but
it
it
it
just
points
to
to
one
of
the
kind
of
yeah
potential
limitations
already.
But
but
the
kind
of
more
interesting
result,
then,
is
if
the
this
sequence
follows
an
arbitrary
pattern
and
for
the
grid
cell
net.
B
This
essentially
has
no
influence
on
its
performance,
but
for
the
other
classifiers
it
it
clearly
does,
and-
and
I
mean
the
kind
of
one
thing
that's
worth
noting
is
you
can
see,
can
given
sufficient
time
and
potentially
examples.
It
looks
like
the
the
rnn
might
be
able
to
improve
and
get
up
to
a
similar
position,
but
but
this
just
kind
of
emphasizes
again
that
the
the
point
of
this
system
is
to
emulate
the
capabilities
of
some.
C
Not
a
fixed-
and
it's
not
it's
not
following
some
pattern,
but
we
definitely
pick
out
the
brain,
picks
out
salient
features
or
various
types
of
things
which
are
more
likely
that
are
more
likely
to
read
to
a
better
representation
or
a
rapid
settlement.
So
so
we're.
This
is
sort
of
a
worst
case
scenario,
but.
B
C
Even
if,
even
if
you
just
say
we're
only
going
to
look
at
the
elements
that
have
you
know
an
edge
in
them,
you
know
we're
not
going
to
look
at
sections
of
the
image
that
that
are
blank.
You
know
that
would
improve
it's
dramatically,
just
doing
that.
Okay,
but
anyway,
I
know.
If
you
had
a
question
yeah.
B
A
C
C
B
D
E
E
E
B
B
Yeah,
because
even
kind
of
many
examples
of
few
shot
training
still
provide
the
the
classifier
as
much
time
kind
of
as
it
wants
to
to
learn
from
those
five
examples
or
whatever,
but
but
that's
not
necessarily
very
realistic
from
a
biological
point
of
view.
So
this
is
kind
of
getting
towards
what
you
were
talking
about.
B
So
in
both
of
these
cases,
it's
with
the
the
arbitrary
input
and,
as
you
can
kind
of
see,
the
k
n
is
essentially
constrained
to
just
key
off
the
kind
of
key
features
that
were
or
kind
of
key
information.
That
was
already
present
in
a
single
representation.
It
doesn't
really
gain
much
from
additional
information.
C
B
B
We
assume
that
there
are
no
further
kind
of
input
sensations
and
that
the
rest
of
the
image
is
tiled
with
blue,
so
the
predictions
of
the
system,
the
these
actual
kind
of
sequence
of
sensed
and
predicted
features,
can
be
taken
from
the
system
and
fed
to
a
decoder.
So
a
neural
network.
That's
been
trained
separately
on
these
sdr
features
to
reconstruct
the
input,
image
and
oops.
Sorry.
E
B
B
E
E
C
B
E
E
B
Yeah
no
noise,
yeah,
I
mean,
I
guess
the
only
thing
I
can
say
is
I
so
this
is
from
so
also
I
had
to
decide.
You
know
how
many
examples
this
is
when
it's
been
trained
with
five
examples
per
image,
but
you
know
I
briefly
plotted
the
other
ones
and
they
had
similar
curves.
It
wasn't
anything
kind
of.
I.
C
B
Yeah
so,
but
anyway,
so
then
predicting
these
the
kind
of
representation
in
the
system.
So
what
that's
showing
here?
So
a
lot
of
these
kind
of
features
that
are
being
fed
to
the
decoder
are
just
vectors
of
zeros,
and
then
the
this
kind
of
highlighted
window
is
telling
us
where
the
system
is
currently
predicting,
so
the
kind
of
next
sequence.
So
you
can
see,
for
example,
here
it's
predicting
this
location.
B
And
then
the
system
can
kind
of
fill
in
the
rest
of
the
space
with
its
predictions
alone.
And
then
this
kind
of
fill-in
is
based
on
a
prior
learned
example,
which
in
some
cases
can
be
quite
close
to
the
ground.
Truth
and
but
what's
interesting
to
know,
is
so
I'm
showing
examples
where
the
at
inference
time.
B
The
system
has
converged
to
a
single
representation
of
a
single
location
representation,
sometimes
that
inference
it's
a
union
of
location
representations,
particularly
for
digits
such
as
two,
which
I
believe,
have
more
variance
in
how
they're
written
so
some
people
do
twos
with
like
a
loop
at
the
bottom.
For
example,
some
people
do
them
with
a
kind
of
a
flat
bottomed
to
the
two
and
and
the
decoder,
because
it's
only
been
trained
on
examples
of
single
sdrs.
B
It's
unable
to
to
kind
of
deal
with
these,
so
that's
another
kind
of
future
thing
to
do,
would
be
to
train
it
on
these
unions
and
see
what
the
outputs
look
like.
It
could
be
interesting
if
this
is
actually
a
way
of
the
system
to
kind
of
given
a
an
unfamiliar
representation,
use
a
union
to
encode
kind
of
almost
interpolate
between
two
known
examples
to
get
closer
to
the
input
you
know.
C
When
I
was
doing
a
handwriting
recognition
software,
one
of
the
things
the
simple
observation
we
came
across
is
that
the
way
people
write
letters
can
be
completely
different
and
therefore
you
can't
generalize
you
can't
generalize
between
one
person's
letter
of
I
don't
know
pick
a.
I
can't
remember
these
specific
examples
not
like,
like
an
e
or
something
and
another
person
they're,
just
literally
different,
there's,
there's
nothing
so
essentially
your
brain
has
to
classify
them
as
saying.
Oh,
that's
a
separate
object
that
I
know,
but
I'm
giving
it
the
same
class.
C
So
it's
a
it's
a
fallacy
to
you.
Don't
want
to
fall
into
the
trap
of
trying
to
say
well
this
I'm
trying
to
figure
out
what's
common
between
all
these
different
ways
that
people
write
a
six.
It
may
not
be
anything
common,
I'm
not
saying
that
applies
here,
but
the
general
principle
applies
in
handwriting
that
you
can
write
these,
like
you
said
the
two:
they
can
they're
really
separate
characters
and
we
and
our
brain
learns
them
separately,
and
then
we
assign
them
to
the
same
class,
which.
D
So
deals,
I
think
this
is
a
really
cool
result
and
in
picture
it's
just,
I
think
that
the
image
itself
might
be
really
confusing
to
people
like
I'm,
not
sure
exactly
like.
What's
what
you
know,
why
are
you
starting
at
sensation,
two
not
at
sensation,
one
and
what
is
what
exactly
is
this
square
and
where,
where
has
it
looked
before,
and
where
has
it
not
looked
before.
D
B
B
C
B
E
B
So
I
can't
really
compare
that
in
a
sense
to
an
auto
encoder,
because
it's
using
an
auto
encoder,
but
it
so
it's
more
so,
for
example,
one
comparison
might
be
to
train
an
rnn
on
the
kind
of
first
12
sensei
sensations,
and
for
it
to
predict
the
last
13
and
then
see
how
that
compares
that's
kind
of
one
way
of
doing
it
but
yeah.
I
ultimately
didn't
do
it
partly
because
of
time,
but
partly
because
yeah,
it
felt
unsatisfying.
B
Part
of
part
of
what
makes
the
system
interesting
is.
The
number
of
sensations
before
prediction
starts.
Taking
place
is
is,
is
varies,
it's
not
a
fixed
quantity,
whereas
again
generally
yeah
often
a
train
system
will
expect
a
certain
number
of
sequences.
Although
I
guess
that's
not
necessarily
the
case
so
yeah,
it's
definitely
possible
to
maybe
compare
them,
but
but
yeah.
It's
not
something.
I've
done.
E
B
So
that's
the
the
kind
of
the
last
of
the
results
so
then
kind
of
tying
this
all
kind
of
together.
So
one
I
mentioned
that
you
know
this
idea
of
kind
of
making
do
with
fewer
sensations
than
than
the
maximum
possible
is
interesting
from
a
predictive
point
of
view.
But
I
was
kind
of
alluded
to
at
the
start
of
this
and
and
by
jeff.
B
It's
also
interesting
from
the
point
of
view
of
an
embodied
agent
which,
as
kind
of
noted
earlier,
you
don't
want
to
be
doing
a
raster
scan
or
whatever
you
want
to
be
able
to
intelligently
sample
the
input,
and
so
this
would
definitely
be
an
interesting
area
for
future
work.
I
think
to
actually
combine
this
with,
for
example,
a
reinforcement
learning
agent
that
learns
to
control
the
the
motor
outputs
in
such
a
way
that
it
efficiently
recognizes
digits
rather
than
doing
an
arbitrary
order.
B
B
This
system,
at
the
kind
of
at
the
at
the
sort
of
the
grid
cell
level,
at
that
the
at
the
the
column
network
level
is
really
by
design,
should
be
quite
robust
to
translation
and
variance
because
it's
it's
performing
object,
recognition
in
the
reference
frame
of
the
object,
and
so
so
should
work
quite
well.
The
difficulty
then,
is
feeding
in
the
appropriate
features,
because
at
the
moment
the
system
for
generating
the
sdrs
is
itself
not
neither
translation
invariant
nor
equivalent.
C
B
Though
exactly
so
I
mean
it's,
it's
just
the
because
it's
it's
just
learned
how
the
yeah,
the
the
features
will
relate
to
one
another
as
it
travels
through
the
the
kind
of
grid
cell
location
representation.
So
if,
if
a
particular
feature
is
active,
it
doesn't
matter
if
it
was
learned
in
this
location,
but
it's
presented
in
this
location.
It
will
know
that
by
moving.
C
D
B
Yeah
definitely
at
the
moment
it's
yeah
just
2d
shifts,
but
yeah.
The
the
difficulty
is
how
the
the
features
are
fed
in
and
and
also
just
the
this
idea
of
going
from
kind
of
a
relatively
continuous
input
space
28
by
28
pixels
to
a
very
discrete
input.
Space
of
five
by
five
again
has
its
own
problem,
so
that
would
definitely
need
to
be
resolved
before
this
question
could
be
properly
addressed.
But
but
I
think
this
would
be
another
really
interesting
avenue
for
future
research.
B
So
in
summary,
using
these
kind
of
good
cells
definitely
seems
to
offer
some
tangible
benefits
for
what
is
a
challenging
task.
These
kind
of
arbitrary
sequences
and
and
the
fact
that
this
works
on
actual
images
suggests
that
it
could
be
something
that
the
the
primary
brain
might
use,
but
I
would
say
the
kind
of
the
main
limitation
so
far
is
that
the
the
method
I
use
to
derive
these
sers
is
is
quite
contrived.
B
C
A
B
A
Right
well
sure
so
the
the
paper,
as
is
like
we
trained
it
on
specific
instances
of
objects,
basically
and
and
then
recognize
those
objects.
So
the
the
fact
that
he
got
this.
Where
he's
training,
where
he's
recognizing
novel
digits,
that
I
wasn't
sure
that
would
work
at
all
and
and
and
it's
cool
that
it
did,
it's
called
it
and
he
pulled
it
off
yeah.
I
agree.