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From YouTube: Meta-Learning Paper Reviews - July 15, 2020
Description
In this research meeting Subutai and Karan focus on reviewing 4 related meta-learning papers. Subutai (after an initial surprise reveal) summarizes MAML, a core meta-learning technique, by @chelseabfinn et al, and a simpler variant, Reptile, by Alex Nichol et al. Karan reviews two probabilistic/Bayesian variants of MAML by Tom Griffiths et al.
Papers: Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks (https://arxiv.org/abs/1703.03400), On First-Order Meta-Learning Algorithms (https://arxiv.org/abs/1803.02999), Recasting Gradient-Based Meta-Learning as Hierarchical Bayes (https://arxiv.org/abs/1801.08930), and Reconciling meta-learning and continual learning with online mixtures of tasks (https://arxiv.org/abs/1812.06080).
B
So
so
I
guess
we
have
a
session
on
meta-learning
thing,
so
I'm
going
to
talk
about
this
paper,
which
is
the
mammal
paper
model,
agnostic,
meta
learning
and
then
I'm
going
to
briefly
touch
on
something
called
reptile,
which
is
a
variant
on
metal.
It's
simpler
than
mammals
and
then
I
think
Karan
is
going
to
talk
about
two
papers
that
are
variations
of
this
as
well.
B
B
A
B
E
B
So
if
you
look
at
split
imagenet,
they're,
all
kind
of
image,
recognition,
paths
and
they're
going
to
be
somewhat
similar,
and
so
we
want
to
discover
a
network.
That's
going
to
be
good
at
many
different
many
of
these
different
tasks
and
in
this
particular
paper,
good
means
sort
of
how
quickly
can
you
learn
each
task
right?
B
So,
if
you're,
if
you've
trained,
if
you
have
a
network
that
is
going
to
be
trained
on,
you
know,
cats
versus
dogs,
how
many
samples,
how
many
training,
samples
of
cats
and
dogs
do
you
need
before
it's
gonna,
get
a
reasonable
accuracy
right
so
in
in
in
her
case,
K
is
how
many
samples
so
and
K
is
fixed.
So,
let's
say
you're
given
five
samples
of
cats
and
five
samples
of
dogs.
How
well
can
you
classify
cats
versus
dogs?
It's
a
pretty
challenging
situation,
so
the
measure
of
goodness
is
how
quickly
you
can.
B
You
can
learn
it
and
the
basic
intuition
behind
it.
I
drew
it
a
bit
a
little
differently
than
what
you
did
in
the
paper.
I
think
I
saw
this
version
somewhere
else
and
it
made
more
sense
to
me.
They
say
imagine.
This
is
like
your
space
of
weights,
so
you
have
a
network.
You
know
that
has
a
you
know
a
lot
of
different
weights
that
are
possible
and
let's
look
at
task
one,
and
this
blue
line
here
are
all
the
points
in
the
white
space
that
are
good
at
doing
task.
One.
B
Okay,
so
that's
gonna
be
some
manifold
and
in
the
white
space
in
this
red
line,
there's
all
the
set
of
weights
that
are
going
to
be
good
at
task
two,
so
task
one
might
be
cats
versus
dogs,
and
this
one
might
be.
You
know,
cars
versus
trucks
or
something
and
then
task
three,
this
green
line.
This
is
all
the
set
points
in
weight
space
that
are
going
to
be
good
at
task.
Three
and
the
thing
is
you
want
it
to
be
very
good
at
all
of
these
tasks
with
a
small
number
of
samples.
B
Now,
if
you
just
do
normal
weight
initialization,
you
know
you
might
end
up
with
your
space
of
parameters.
You
know
somewhere
here.
That's
you
know
be
somewhere
near
zero.
When
you
initialize-
and
you
know,
it's
gonna-
take
some
number
of
gradient
steps
to
be
good
at
task.
Two.
It's
gonna
take
an
even
longer
number
of
gradient
steps
to
be
good
at
past
three,
but
you're
kind
of
far
away
from
all
of
these.
But
if
you've
kind
of
discovered
a
good
Network,
then
you
might
want
to
start
here.
B
You
know
this
would
be
your
theta
start,
and
if
you
could
start
there,
then
you
could
see
that
with
a
very
small
number
of
ingredients,
steps
you're
gonna
be
good
at
all
all
of
these
different
tasks.
Okay,
so
that's
kind
of
the
goal.
As
can
we
discover
what
this
theta
star
is,
and
you
can
think
of
it
as
a
way
of
initializing
the
network
and
it,
but
the
mammal
is
a
technique
for
coming
up
with
this.
So
it's
a
pretty
kind
of
cool
thing.
B
The
problem
is
that
this
is
a
huge,
very
high
dimensional
search
space.
So
most
optimization
techniques
are
not
good
at
searching
these,
you
know
high
dimensional
spaces,
and
so
what
they
did
in
this
paper
is
basically
in
mammal.
These
are
the
different
kind
of
properties
of
it
they
formulated.
So
you
can
use
gradient
descent
to
find
this
find
this
point,
and
we
know
back
prop
and
gradient.
Descent
is
quite
good
at
that
seems
to
be
pretty
good
at
solving
high
dimensional
problems.
So
that's
the.
F
F
B
They
would
just
be
worse
because
if
you're,
let's
say
you're
here,
you
would
be
good
at
solving
task
two.
But
if
you
are
given
task
one,
it
would
take
you
many
steps
to
get
there.
So
you
know
your
error.
If
you're,
given
a
fixed
number
of
training
samples
like
five
samples,
you're,
not
gonna,
be
able
to
achieve
good
performance
there.
Okay.
B
I
mean
if
you
had
an
infinite
number
of
training
samples,
then
no
matter
where
you
start,
you
know,
you'd
be
able
to
get
to
there
and
that's
sort
of
you
know
typical
imagenet.
We
don't
really
care
about
as
much
about
the
initialization
I
mean
there's
initialization
matters,
but
because
we
have
so
many
training
samples
and
we're
gonna,
you
can
repeatedly
train
through
them.
You
know
you
you're,
okay,
with
having
a
large
number
of
gradient
steps.
The
the
formulation
here
is:
how
quickly
can
you
learn
it?
I
was.
B
F
B
F
B
Hopefully,
and
now
they're
interesting,
so
they
formulated
to
use
gradient
descent
to
solve
this
problem
and
back
prop.
Another
interesting
thing
is
that
there's
no
additional
parameters
introduced
by
this
method.
It
just
uses
the
same
parameters
as
your
network.
This
is
not
exactly
true,
there's
a
couple
of
hyper
parameters,
but
basically
there's
no
no
new
weights
or
anything
else,
that's
introduced.
B
It
can
work
with
any
differentiable
Network,
so
it
just
uses
leverages
back
prop
on
the
network
itself,
and
so
this
is
a
very
general
solution.
We
can
use
it's
applicable
to
lots
of
different
paradigms,
like
reinforcement,
learning,
classification,
regression
and
so
on.
So
it's
again,
it's
a
very
general
purpose
thing.
The
basic
way
she
formulates
it
here
is
that
for
the
objective
function
is
going
to
be
how
well
you
generalize
on
a
newt,
ask
after
K
gradient
steps,
okay,
so
I'll
formula
formalize
that
a
little
bit
in
a
second
and
you
can
think
of
intuitively.
B
What
it's
doing
is.
It
sticks
discovering
a
representation,
a
network
structure
that
is
kind
of
optimal
for
this
set
of
tasks.
So
if
it's
image
that
maybe
it's
discovering
image
features
and
things
that
are
going
to
be
very
transferable
to
other
tasks
and
that's
really
what
at
the
end
of
the
day
mammal
is
doing,
and
so
if
your
tasks
are
very
similar,
it's
going
to
actually
it's
going
to
work.
Well,
if
the
tests
are
completely
different,
it
may
not
work
well,
so
I
think
it's
a
very
general
formalism.
B
The
other
thing
and
whether
the
reasons
that
kind
of
backed
into
this
is
that
you
know
we'll
talk
about
continuous
learning
and
animal
and
oml
a
bit
next
week
and
both
of
those
kind
of
rely
on
on
meta
learning
and
they
formulate
the
objective
function
a
little
bit
differently
to
sort
of
focus
on
catastrophic
forgetting.
But
you
know,
because
it's
so
general
purpose,
you
could
kind
of
use
this
for
lots
of
different
types
of
tasks.
I
think
it's!
It's
a
really
good
kind
of
tool
to
have
in
your
in
your
back
pocket
back
pocket.
B
B
So
if
you,
if
you're
feeding
in
you,
know
images
as
one
task-
and
you
know
the
GSC
audio
things,
that's
another
task,
those
are
like
completely
different
things
and
then
watching
the
features
you
detect
would
be
completely
different,
but
four
images,
one
versus
nine
or
five
versus
six
or
whatever
you
know
lines
are
still
important,
and
so
those
are
good
features
to
detect.
You
know:
random
network
wouldn't
have
lines
in
there.
So
if
you,
if
their
network
already
discovers
lines
and
curves
and
stuff
like
that,
it
would
be
quicker.
B
B
I
do
think
that's
possible,
so
it's
but
I
bite.
You
know
if
you
make
the
more
different
the
tasks
are
that
harder.
This
problem
is
gonna
get,
and
you
know
it
may
be
harder
to
find.
You
know
something
as
good
as
what
I
drew
on
there,
but
I
do
think
there
are
a
lot
of
different
modalities
and
share
things
sure,
okay,
so
the
algorithm
is
conceptually
pretty
simple.
B
So
app
is
a
network
with
weights
data,
okay,
so
the
basically
there's
two
loops
to
this
thing:
there's
an
outer
loop
and
an
inner
loop.
So
yeah,
you
start
by
initializing
theta
and
you
can
just
use
you
know
whatever
initialization
you
want,
and
so
what
you're
gonna
do
in
the
inner
loop
is
that
you're
going
to
sample
a
set
of
tasks?
So
if
you're
doing
split
imagenet,
you
might
you
know
with
two
categories
at
a
time
you
might
do
you
know
cat
versus
dogs?
You
know
cars
versus
trucks,
tables
versus
chairs.
B
Those
might
be
a
few
different
castes
that
you
pick
and
then
for
each
test.
You're
gonna
train
your
network,
the
network
that
you
did
start
that
you
initially
is
here
on
K
samples
using
kind
of
the
standard
gradient
descent,
so
you're
going
to
compute
the
loss
on
the
task
from
from
your
network,
take
a
gradient
step
and
update
the
weights
and
you
get
your
theta
prime
I,
okay,
so
theta
and
you're
gonna.
Do
this
k
times
for
K
samples
and
so
theta?
B
Prime
I
is
the
network
that
was
trained
on
task,
I,
okay,
so
you're
gonna
end
up
here
with
a
bunch
of
different
networks,
one
for
each
task.
Okay!
So
for
each
one
you
start
with
the
initial
with
data
and
you
train
it
and
you
get
somewhere.
You
start
from
theta
again
and
you
train
it
and
you
get
somewhere
else.
You
gotta
end
up
with
a
bunch
of
that
works
for
each
of
them,
so
that's
your
inner
loop
and
then
on
the
outer
loop.
B
B
B
Okay
and
then,
basically,
you
keep
doing
that.
You
keep
sampling
new
tasks,
updating
the
weights,
and
then
this
is
your
your
your
meta
loss
function
and
you
update
the
original
network
and
then,
after
you've
done
all
of
that.
Hopefully
you
end
up,
but
you
will
end
up
with
some
theta
star,
and
hopefully
it's
kind
of
in
this
sweet
spot.
B
Is
that
any
questions
and
I'm
there's
one
one
slightly
tricky
thing
here
is
that
this
involves
computing,
a
second
derivative
because
you're
doing
gradients
on
gradients.
So,
in
some
sense,
what
you're
trying
to
do
is
you're
trying
to
find
a
gradient
such
that
a
small
number
of
gradients
works.
Well
and
apparently
this
is
supported
by
PI,
torch
and
tensor
flow
as
well
and
there's
code
out
there,
but
it
is
a
little
slow.
B
She
mentions
that
there's
a
first-order
version
of
this,
which
seems
to
work
pretty
well,
which
is,
as
it's
not
really
clearly
described
in
the
paper.
But
what
I
think
it's
doing
is
it's
just
taking
the
last
gradient
step
for
each
of
these
tasks
and
then
just
summing
those
up
and
then
using
that
to
update
the
weights.
So
here
you're,
taking
K
gradient
steps
for
each
test,
I
think
she's,
just
looking
at
the
very
last
gradient
step
for
each
of
the
of
the
tasks,
adding
them
up
and
then
updating
I
think
that's.
B
B
B
If
you
want
to
you
know,
you
don't
want
to
test
on
the
categories
that
that
you
trained
on
it's
a
completely
new
set
of
tasks
and
then
for
each
of
these
tasks,
you're
going
to
train
on
K
samples
and
compute
the
generalization
error,
so
you're
gonna
see
okay,
now
this
new
network,
how
well
does
it
adapt
to
each
new
test
that
it
hasn't
seen
during
this
Mediterranean
phase?
How
well
kind
of
generalize
given
on
the
case
apples.
D
B
So
it's
it's
a
pretty.
You
know
conceptually
it's
a
pretty
simple
formula.
Zhim
and
you
know
again
it
there's.
No
additional
parameters
use
the
network
itself.
You
just
have
this
kind
of
two
two
loops
a
loop
within
a
loop.
Of
course
you
got
to
have
a
reasonable
number
of
tasks
to
be
able
to
assemble
from
in
order
to
do
this.
B
So
you're
gonna
sample
tasks
just
like
here,
you're
gonna
train
on
each
of
the
tasks
again
to
get
this
theta.
I
prime,
which
you
get
to
say
that
I
prime
so
now
you
have
a
bunch
of
different
networks
and
then
you
just
look
at
the
the
difference
in
though
in
the
weight
values
and
and
take
the
average
difference
in
the
weights
and
then
just
update
your
original
weight.
So
it's
a
much
simpler
version
of
this.
H
B
So
here
some
of
the
things
are
you're
not
directly
using
the
generalization
error
you're
using
the
training
you're
using
the
weights
that
are
resulting
from
training
using
the
training
set
and
then
you're
just
looking
at
the
difference
between
your
starting
point
and
the
end
point
for
each
of
the
tasks
and
taking
the
average
difference
in
doing
it.
So
it's
much
simpler
and
in
the
reptile
paper
anyway,
they
said
the
results
are
about
the
same.
It's
works
better
in
some
cases
and
worsen
in
some
other
cases,
but
you
know
certainly
it's
a
much
simpler
formalism.
B
E
B
So
she
applies
it
to
regression
and
classification
and
reinforcement
learning
in
any
any
network,
anything
that
you
can
formulate
using
a
deep
learning
network
or
a
differentiable
network
and
could
can
work
here
and
what
what
I'll
do
is.
I'll
just
show
some
of
the
regression
and
classification
samples,
so
the
first
simple
one
that
she
tries
it
on
is
learning
these
random
sine
waves.
So
here
the
task
is,
let's
see
you
have
a
sine
wave,
that's
dependent
on
an
amplitude
parameter
and
a
phase,
and
these
are
kind
of
chosen
randomly
within
this
range.
B
So
each
task
is
a
you
know,
a
sine
wave
with
a
random
phase
and
the
random
stretching
factor.
And
then
what
you
can
see
here
is
the
left
side
is
mammal,
went
using
K
equals
5
or
K
equals
10
samples
after
training
and
the
red
is
kind
of
the
ground
truth
and
this
this.
Finally,
that
this
sort
of
heavy
dotted
line
here
is
what
is
that?
What
the
net
the
mammal
train
network
ends
up
after
you
train
on
these
five
samples?
B
Ok,
so
you
can
see
it's
it's
pretty
close
to
the
ground
truth
and
it
kind
of
deviates
here,
but
it's
still,
even
though
it's
the
the
samples
we're
all
on
this
side
of
the
sine
wave.
This
it
still
does
pretty
well
here,
and
this
fine
green
line
is
the
is
what
the
network
outputs
before
any
training
is
done.
B
So
this
is
after
five
training
samples
and
then,
with
ten
training
samples,
it
approximates
ground
truth
really
well
the
she
compared
it
with
a
network
that
was
pre
trained
on
a
whole
bunch
of
these
tasks
and
there
that
network
does
really
poorly
because
you're,
because
each
task
is
with
a
random
phase
and
a
random
amplitude.
The
the
average
is
going
to
be
basically
a
zero,
and
so
that
the
network
gets
confused
between
all
of
these
different.
B
It
doesn't
know
what
the
phase
of
what
that
will
do
this,
so
it
just
sees
a
whole
bunch
of
these
tasks,
all
as
one
batch
training
set,
and
it
doesn't
really
generalize.
So
what
must
be
going
on
is
the
network
is
learning
you
know
if
it
really
just
has
to
fit
two
numbers.
It
has
to
fit
the
phase
and
the
amplitude,
so
just
a
couple
of
samples
in
theory
should
be
enough,
so
it
must
be
finding
some
representation
such
that
from
a
few
samples.
It
can
figure
out
what
the
phase
and
and
the
amplitude
is.
B
B
The
five
way
accuracy
is
you're
asked
to
choose
from
one
of
different
five
categories
and
you're
either
given
one
example
as
your
training
set
or
five
examples,
as
your
training
set,
so
here
the
chance
would
be
around
20%
and
it
so
mammal,
you
know,
get
that's
better
than
a
bunch
of
these
other
techniques
on
these
I.
Don't
really
know
what
they
are
so
I
think
they
all
have
like
parameters,
other
parameters
or
they're,
more
complex
or
or
something
like
that.
B
B
D
B
D
I
think
the
main
from
I
think
it
works
in
Canada,
but
I
don't
know
if
it's,
but
it
uses
more
parameters
like
learns
and
arrests
and
learns
of
function
learn
how
to
use
the
gradients
to
update
the
network.
So
there
is
an
extra
function
there
and
that
function
has
weight.
So
it's
more
complex
and
memo
and
I
think
that
they
have
similar
with.
They
have
better
results
right
so
which.
D
E
D
Existing
classes,
all
right,
no
so,
for
example,
one
of
them
is
the
product,
it
cannot
work
and
the
idea
of
the
vertical
networks
that
when
you
get
a
new
class,
you
just
you
divide
the
space
between
all
these
classes.
You
know
and
then
you
just
look
which
one
is
closer
and
then
you
assign
the
probability
to
be
of
that
class.
I
mean.
E
D
B
You
can
ask
him
when
he
gets
back
so
let's
it's,
this
one
is
the
mini
image
net
task,
where
it's
basically
a
split
image.
Net
task
and
you're
asked
to
you're
the
network
is
asked
to
distinguish
between
five
different
categories,
so
20%
is
chance
and
you're
either,
given
one
training,
example
or
five
training.
B
Examples
and
mammal
here
is
significantly
better
than
the
other
techniques
on
this
task
and
with
five
examples
it
gets
to
about
63%
and
the
first
order
version
is
very
close
and
it
actually
does
a
little
bit
better
in
the
in
the
five
shot
case,
which
is
interesting,
but
it's
probably
not
significant.
It's
they're
about
the
same.
B
You
know
so
many
networks
get
in
the
high
70s,
no
80%
accuracy,
and
this
is-
and
that's
where
the
thousand
category-
if
this
is
a
five
category
task,
so
I
would
expect
optimal.
If
you
knew,
if
you
were
to
train
on
the
entire
training
set,
would
be
much
higher
than
63%,
but
it
would
have
been
nice
to
have
that
as
a
baseline,
just
to
see
how
close
it's
able
to
get
to
that
baseline.
So
right
now,
it's
really
hard
for
me
to
tell
okay.
D
B
It's
very
few,
so
I
think
as
a
comparison
with
these
other
techniques.
That's
fine,
but
it
still
would
be
good
to
know
how
far
away
are
we
from
the
absolute
optimal
that
you
could
do?
I
mean
a
human
might
do
way
better
than
five
shot,
bully
better
than
63%
right,
even
with
one
shot.
Humans
can
often
learn
a
category
completely,
and
so
you
know
what
what
is
the
best
you
can
do
four
or
five
way
accuracy.
If
you
had-
and
you
know
the
full
training
set,
though
that
would
be
just
an
interesting
comparison.
B
Let's
see
what
else
this
was
just
for
completeness.
This
was
the
reptile
paper
from
opening
I'd
came
out
a
couple
of
years
ago,
and
they
had
similar
kind
of
Omni
gladdened
and
many
omission
had
results
in.
In
the
case
of
many
imagenet,
reptile
was
a
little
bit
better
than
mammal
and
in
Omniglot
it
was
a
little
bit
worse
than
Mamo.
B
B
Yeah,
it's
a
weird
phrase,
as
best
as
it
could
tell
is
so
remember
in
reptile
the
basic
way
it
does
not
use
the
test
that
at
all
transduction
they
include
the
test
set
in
the
as
part
of
the
training
as
well
mammal
uses,
both
the
training
set
and
the
test.
You
know
only
train
it.
Trains
on
the
training
set,
but
then
computes
lost
on
the
test
set.
So
I
think
in
in
here.
E
B
D
You're
gonna
show
several
different
classes
like
let's
say:
you're
gonna
show
classes
a
to
EE
and
then
you're
gonna
ask
to
predict
how
well
it
it
doesn't
that
in
tasks
H,
we
write
like
you're
just
going
to
show
an
image
of
each
other
of
the
past
and
how?
How
are
we
doing
each
one
of
these
tasks?
Yeah.
I
E
B
D
I
D
I
I
I
Okay,
so
the
the
couple
papers
that
I'm
going
to
talk
about
today
are
have
to
do
with
looking
at
mammal
through
the
lens
of
Bayesian
statistics.
So
let's
just
recap
what
Supachai
talked
about.
So
he
said
you
know
in
mammal
you
have
this
objective
L
of
theta,
where
theta
is
the
meta
parameter,
it's
the
one,
the
pet
parameter.
You
learn
where
you
try
to
work
from
which
you
can
easily
step.
Take
a
few
gradient
steps.
I
You
can
perform
a
new
particular
task
and
the
objective
there
is
just
to
minimize
this
law
switches
on
each
individual
task.
J.
If
the
parameter
is
basically
a
gradient
step
on
that
specific
loss
function
for
that
task
from
theta,
then
you
want
to
get
you
want
to
perform.
Well,
that's
just
a
mammal
objective
and
so
I
think
su
batalla
on
the
white
board.
I
He
mentioned
he
used
theta
star
as
the
task
specific
parameter
for
each
each
task,
but
I'm
going
to
change
up
the
notation
here
and
use
Phi
or
fee
I'm,
not
sure
how
it's
supposed
to
be
pronounced,
Phi,
J
and-
and
it's
the
data
for
each
task,
that
we
are
all
the
observations
that
we
have
during
learning.
So
if
we
think
of
the
loss
at
each
for
at
being
a
negative
log
likelihood,
then
you
basically
end
up
with
this,
which
is
it
so
all
I've
done
is
I've
replaced
the
ALJ's
with
minus
log
probability.
I
So
in
this
case
here
the
parameter
is
this
guy,
so
theta
minus
the
gradient
step
from
theta,
and
this
whole
thing
is
a
loss
function
here
and
that's
just
at
a
specific
parameter,
because
it's
just
a
gradient
step
away,
so
in
the
maximum
likelihood
setting.
This
is
what
the
mammal
objective
looks
like.
Okay.
I
So
now
so
we're
gonna
go
from
there
and
so
assume
that
you
know
exit
X
just
be
the
data
that
we
all
the
data
we
have
for
all
the
tasks
we
can.
We
can
have
a
likelihood
function
for
the
for
the
meta
parameter
and
that's
just
independently
and
that's
just
independent
over
all
the
tasks,
because
we're
assuming
like
each
task
is
sort
of
separate,
and
this
is
what
the
I
forget
the
term
for
this
type
of
diagram.
But
this
is
sort
of
graph
looks
like
you
assumed
the
theta
generate
there.
I
You
have
one
theta,
the
matter
parameter.
It
generates
the
all
of
the
task,
specific
parameters
and
then
that
generates
the
there
are
observing
observations
that
you
have
so
from
here.
We
have
this
product
of
individual
likelihoods,
and
what
we
can
do
is
say
is
basically
say
this
is
this
is
equivalent
to
integrating
over
the
task
specific
parameter,
Phi
that
we've
introduced
here.
So
if
we
just
integrate
over
the
files,
we
just
get
this
this
likelihood
back
here
and
from
that,
and
so.
B
Now
we
have
done
yeah
yeah,
quick
question
with
the
with
this
formulation.
So
you
know
mammal
works
particularly
well
when
the
tasks
are
have
some
shared
characteristics
and
representations.
So
does
this
independence,
assumption
kind
of
you
know
and
doesn't
you
know,
obviously
it
assumes
all
the
tasks
are
independent,
that
they're
not
sharing.
B
B
G
I
F
B
I
I
Making
the
same
assumption
of
what
the
tasks
being
somewhat
similar,
just
like
the
original
mammal
people?
Okay,
so
once
we
write
this,
the
individual
likelihood
for
each
task
as
this
as
this
integral
here
we
have
a
likelihood
term
and
a
prior
term
where
the
prior
is
the
prior,
basically
influences
what
what
the
meta
with
the
task
specific
parameter
is
given
data,
and
then
here
this
is
just
a
likelihood
for
the
task,
given
the
task,
specific
parameter
and
the
main
assumption
here,
what
they
do
for
for
a
computational,
I
guess
to
make
it
simple.
I
Is
they
assume
that
this
that
this
distribution
here
the
prior
on
the
on
the
task
specific
parameter,
is
a
Dirac
distribution?
So
here
this
Dirac
distribution?
Okay?
Well,
it's
not
one!
It's
all!
The
mass
of
this
distribution
is
concentrated
at
the
point,
which
is
just
a
gradient
step
from
the
from
the
meta
parameter.
That's
where
all
the
mass
is
concentration
and
the
distribution
is
just
zero
everywhere
else,
so
this
is.
I
This
is
equivalent
to
doing
empirical
base
because
in
empirical
Bayes
you're
estimating
the
prior
distribution,
based
on
the
observations
that
you
have,
the
x's
and
here
as
you
can
see,
they're
they're
they're
determining
what
the
where
the
mass
of
this
distribution
lies
based
on
the
x's.
So
the
x's
are
actually
involved
here
in
computing.
This
prior
and
so.
I
I
I
And
and
the
and
so
the
real
reason
they
one
of
the
main
reasons
they
do.
This
is
just
so
that
you
know
if
you,
if
you
think
of
this
prior
distribution
as
just
being
a
single
as
just
having
all
its
mass
Center
at
a
single
point
and
then
basically
the
this.
This
whole
function
that
you're
integrating
here
just
becomes
zero,
except
for
at
one
point,
so
you
don't
really
have
to
compute
the
integral
you
just
this.
I
Just
this
just
ends
up
being
the
likelihood
at
at
a
certain
point,
which
is
the,
which
is
the
estimate
that
we
obtained
here
so
so
Phi
hat
is
the
is
the
gradient
step
from
the
for
the
meta
parameter
and
then-
and
this
ultimately
becomes
the
likelihood
this
ultimately
becomes
the
objective
so
using
what
we
just
obtained
on
the
last
slide.
If
we
go
back
to
the
maximum
likelihood
setting
negative
law,
the
negative
log
likelihood
is
just
this
guy
and
this
thing
which,
which
is
the
empirical
estimate
of
the
TAS
specific
parameter,
is
just
you
just.
I
We
can
just
unroll
it
as
being
all
this,
so
beta
minus
the
gradient
step
of
the
loss
on
that
task,
and
the
nice
thing
about
what
someone's
gonna
get
here.
This
this
actually
looks
very
familiar
because
basically,
this
inner
part
here
is
just
the
in
mammal.
It's
just
the
loss
on
each
individual
task,
and
this
whole
thing
here
is
just
is
just
basically
the
loss
on
it's
just
the
loss
for
each
for
each
task
on
mammal.
B
I
This
is
so
we
have
this
likelihood
on
this
prior.
So,
ultimately,
what
we're
doing
is
we're
integrating
this
posterior
probability,
and
this
posterior
is
just
a
posterior
over
the
task,
specific
parameters
and
what's
happening
here.
Is
that
so
originally
what
what?
What
actually
earlier,
is
that
you
know,
since
we
are
using
wind,
since
we
are
using
a
point
estimate
for
the
prior.
What
we're
essentially
doing
here
is,
instead
of
integrating
this
whole
posterior
function,
we're
just
taking
a
single
point,
estimate
and
saying:
okay.
This
is
our
approximation
to
this,
integral
that
we
want
to
that.
I
We
want
to
compute,
and
that
can
be
that
can
be
sometimes
we
used.
That
can
be
useful
if
your
posterior
function
is
very
peaked
around
the
point
where
you
take
your
point
estimate.
So
if
you're,
if
you're
a
posterior
function,
looks
sort
of
like
this
I'm,
not
a
nindroid,
but
it
looks
like
this,
then
that
that's
good.
But
then
in
the
case,
where
it's
a
really
wide
posterior
function,
then
that's
you're
not
really
getting
a
good
approximation
of
this
integral
another
technique
that
they
tried.
I
So
there,
instead
of
using
the
point
estimate
they
they
replace
that
with
the
Laplace
approximation
which
I
don't
know
too
much
about.
But
maybe
someone
here
does
so
you
can
correct
me
if
I'm
wrong,
but
in
the
Laplace
approximation,
what
they're
doing
is
they're
picking
a
single
they're
taking
their
finding
with
the
mode
for
this
posterior
function
is
I,
think
based
on
some
assumptions
and
then
basically
fitting
that
mode
with
a
with
the
Gaussian,
and
then
you
can
integrate
that
Gaussian
and
so
you're,
basically
finding
the
area
under
this.
I
I
So
we
also
wanted
to
show
everyone
on
this
page.
So
if
you,
if
you
look
back
to,
let's
go
back
to
the
slide,
one
of
these
slides
here
yeah,
so
this
whole
integral
here
becomes
this
just
this
guy
right
here.
So
if
you
ignore
the
the
PI,
it's
this
integral
turns
into
this.
Just
this
value
right
here,
where
you're
evaluating
the
likelihood
based
on
this
estimate
of
the
task
specific
parameter.
I
But
if
you
then
that's
if
you're
using
the
single
point
estimate,
but
if
you
use
the
Laplace
approximation,
what
happens
is
that
you
get
what
you
get
good
information
with
the
curvature,
and
so
this,
and
so
this
integral,
which
is
the
same
one
I
had
on
my
slide.
It
tends
to
have
this
determinant
of
this
Hessian
matrix
of
the
posterior
distribution.
I
Don't
think
so,
I
think
it's
I
mean
so
I,
don't
know
too
much
about
Laplace,
approximations,
either
and
I.
Didn't
I
didn't
really
read
up,
read
too
much
into
it,
but
from
what
I
understand
it's
a
way
to
integrate
somewhat
hard
functions
to
integrate
and
that
so,
like
it's
a
form,
if
you
have
the
integral
of
e
to
the
f
of
X,
then
it's
a
way
to
sort
of
approximate
that
integral,
but.
I
B
D
B
I
I
They
all
influence
how
the
task
specific
parameter
Phi
is
what
would
that
ends
up
being,
and
so
so
I
said:
I.
Do
these
arrows
all
different,
colors
and
different
sizes,
and
to
show
that,
like
you
know
they
could
they
can
all
have
they
can
all
influence,
how
later
little
or
more
influence
on
theta?
So
in
this
case,
what
we
do
is
we
may
introduce
introduce
this
idea
of
this
cluster
assignment
probability
so
for
task
J
the
probability
that
it
belongs
to
cluster
L.
I
So
this
this
fancy
L
right
here
it
just
indexes
each
of
the
meta
parameters.
The
probability
is
just
proportional
to
the
likelihood
p
of
x
given
theta,
which
we
computed
earlier,
and
this
can
be,
and
then
that
can
be
evaluated
just
by
plugging
this
into
this
guy
here,
which
is
which
you
evaluate
every
time
you
compute
the
mammal
loss
anyways.
So
once
we
have
this
yeah.
B
That's
pretty
cool,
so
this
is,
if
I
understand
this
correctly,
it's
you're
saying
there
isn't
a
single
you're,
not
assuming
there's
a
single
weight
point
in
weight
space
which
is
you're,
gonna,
find
but
there's
multiples,
L
such
points
and
you're
really
treating
it
as
a
mixture
of
a
bunch
of
different
networks.
Each
point
is
a
set
completely
different
network
and
now
you're
treating
the
solution
as
a
sort
of
a
it's
an
expert
system.
I
I
I
Do
a
I'm
just
that
good
next
year
you
just
compute
these
assignment
polities
for
each
individual
task
that
the
task
Pacific
parameter
was
generated
from
each
of
the
different
meta
parameters.
And
then
you
update
this
and
when
you
update
this
you're
you're
updating
it
just
like
you
do
in
mammal,
but
in
this
gradient
you're,
just
weighing
the
term
that
comes
from
so
for
each
meta
parameter.
You
just
swing
the
term
that
comes
from
each
task
based
on
the
assignment
probability
and
that's
and
that's
more
or
less
it.
I
E
I
And
then
I
think
they
didn't
talk
too
much
about
in
this
paper
about
like
a
test
time,
how
they're
gonna
actually
determine
what
the
task
specific
parameter
is,
but
I
would
assume
they
just
they
just
whatever.
Whatever
assumption
you
make
for
the
form
of
the
prior
distribution
over
the
tasks
of
a
parameter,
you
just
you
just
draw
it
from
that
mixture,
distribution
so
fairly,
straightforward
so
far,
and
then
here
they
had
mininum
it.
They
try
this
out
on
many
imagenet
five-way
classification.
I
So
this
was
the
original
nama
48.7%
and
then,
as
they
increase
the
number
of
components,
they
are
the
number
of
meta
parameters.
So
components
is
just
the
number
of
meta
parameters
if
they
had
here
the
task,
the
accuracy
sort
of
shot
up,
but
it
was
interesting
how,
from
three
components
before
it
went
when
the
accuracy
went
down,
I
don't
know
if
that
has
to
do
with
the
nature
of
the
tasks
that
you
know
having.
D
In
that
case,
you
framed
the
problem
as
like.
You
could
have
a
different
set
of
data
for
four
different
pathologies
as
well.
In
this
case,
we
are
still
in
the
same
domain.
You
know
if
they
tried
to
use
this
method
to
learn
fast
and
like
slightly
different
domain,
to
please
I
mean,
let's
say
still
computer
vision,
but
let
being
in
image,
net
and
ciphers
like
that.
D
B
D
I
H
B
B
I
E
I
I
read
out
of
time,
so
I
didn't
I
couldn't
get
into
that,
but
I
guess
they
they've
tried
that
out
on
that's
that
case,
yeah,
otherwise,
okay,
and
is
there
anything
else
yeah?
So
for
the
for
the
continual
learning
case,
these
Jewishly
process
mixtures,
which
again
I
didn't
really
get
into
so
there's
a
lot
of
stuff
in
this
paper.
I
guess
that
I
didn't
go
too
deep
into,
but
I
think
covered
the
main,
the
main
top.
The
main
points
could.
B
I
I
D
B
I
B
E
D
D
B
D
B
D
B
B
H
B
You
know
it,
you
know,
even
in
mammal,
in
a
backdrop
fundamentally,
I
think
just
assumes
that
each
each
data
point
is
somewhat
independent.
There's
none
of
an
iid
assumption
there
in
the
mammal
formulation.
The
original
I
didn't
get
into
this,
but
they
they.
She
has
a
version
where
you
can
look
at
sequences
where
you
don't
have
independence
within
a
sequence.