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Description
NERSC Data Seminars: https://github.com/NERSC/data-seminars
Title: Intrinsi ccomputation and physics-based machine learning for emergent self-organization in far-from-equilibrium systems
Abstract: Coherent structures form spontaneously in far-from-equilibrium spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean and atmosphere dynamics. Phenomenologically, they appear as key components that organize macroscopicdynamical behaviors. Unlike their equilibrium and near-equilibriumc ounterparts, there is no general theory to predict what patterns and structures may emerge in far-from-equilibrium systems. Each system behaves differently; details and history matter. The complex behaviors that emerge cannot be explicitly described mathematically, nor can they be directly deduced from the governing equations (e.g. what is the mathematical expression for a hurricane, and how can you derive it from the equations of a general circulation climate model?). It is thus appealing to bring the instance-based data-driven models of machine learning to bear on the problem. Supervised learning models have been the most successful, but they require ground-truth training labels which do not exist for far-from-equilibrium structures. Unsupervised models that leverage physical principles of self-organization are required. To this end we will make connections between structural organization and intrinsic computation to motivate the use of physics-based unsupervised models called local causal states. As local models they are capable of capturing structures of arbitrary shape and size in a visually interpretable manner, due to the shared coordinate geometry between observable spacetime fields and their associated latent local causal state fields. We will show the local causal states can capture patterns in cellular automata models as generalized spacetime symmetries and coherent structures as localized deviations from these generalized symmetries. To demonstrate their applicability to real-world systems, we show the utility of the local causal states for extracting coherent structures in simulations and observations of complex fluid flows, including promising results highlighting extreme weather events in the water vapor field of the CAM5.1 climate model. These results require high-performance computing, and we will briefly describe how we were able to process almost 90TB in under 7 minutes end-to-end on 1024 Haswell nodes of Cori using a distributed implementation in Python.
A
B
I
think
everyone,
thanks
for
being
here,
I
may
have
gone
a
little
overboard
with
the
title
here.
It's
really
interesting
concepts
of
emergence,
I,
don't
think
for
time
sake.
I'm
gonna
go
into
as
much
detail
on
those
as
I
originally
intended,
and
what
I
want
to
get
across,
though,
is
that
this
phenomenon
of
self-organization
presents
real
challenges
for
traditional
tools
and.
C
B
But
machine
learning
offers
some
new
opportunities
for
progress,
so
gene
learning
approach,
I've
been
developing
based
on
this
idea
of
intrinsic
computation,
argue
that
it's
particularly
well
suited
for
this
problem
of
self-organization
the
motivating
example
or
problem
of
self-organization.
This
talk
is
extreme
weather
events
and
climate
I'll
give
a
brief
introduction
to
that
and
some
work
using
supervised,
deep
learning
approaches
to
identify
these
events
and
large
climate
datasets
from
a
machine
learning
perspective.
This
is
a
hard
problem
because
ground
truth,
labels
for
these
events
do
not
exist.
B
So
our
approach
in
this
talk
is
in
essence,
going
to
be
to
try
and
define
a
ground
truth
for
these
events
from
physical
principles,
and
we
want
to
do
this
coming
from
a
more
general
perspective,
we'll
review
extreme
weather
events
as
these
more
general
coherent
structures.
So
I'll
talk
a
bit
about
what
those
are
and
give
an
introductory
example
of
coherent,
vortices
and
2.
D
turbulence
get
a
little
preview
of
what
our
method
does
there
and
how
it
compares
to
some
state-of-the-art
methods.
C
B
B
C
B
B
These
long
storm
structures,
atmospheric
rivers,
provide
most
of
the
water
for
California.
We
would
like
to
know
if
those
storms
are
gonna
change
track
at
some
point
and
stop
giving
us
the
water
that
we
very
much
need
so
a
powerful
tool.
We
have
to
try
and
answer
these
questions
or
these
high
resolution
general
circulation.
Climbing
mountains
see
an
example
of
in
this
picture,
where
we
can
simulate
alternative
climate
scenarios
and
see
what
happens.
B
But
if
you
want
to
ask
these
detailed
questions
about
these
weather
events,
like
our
atmospheric
River,
is
going
to
keep
hitting
California's
very
specific
question
that
we
need
to
be
able
to
identify
these
storms
ideal
and
that
pixel
level
identification
is
the
so
called
segmentation
problem,
rather
than
doing
that
by
hand
with
mspaint
as
I've
done
for
a
demonstration
here.
You
know
if
we
want
to
look
at
these
and
hundreds
of
terabytes
what
kind
of
data
we
need.
Some
automated
and
robust
methods
to
do
this.
B
B
C
B
B
B
So,
as
I
said,
we
kind
of
want
to
step
back
and
take
a
different
approach
for
this
and
come
up
with
a
rather
than
the
supervised
training
paradigm,
see
this
as
a
fundamentally
unsupervised
paradigm
and
then
again,
try
and
can
we
come
up
with
a
ground
truth
for
more
physical
principles
and
we're
going
to
do
this
in
this
perspective
of
coherent
structures.
So
here's
an
image
and
the
message
you
know
spacecraft
of
Jupiter,
just
off
the
bat.
B
Obviously
the
dynamics
here
you
can
tell-
are
pretty
chaotic
and
turbulent
at
very
small
scales
but
large
scale.
There
is
some
organization
here,
some
quote-unquote
structure.
This
idea
of
coherent
structures
is
a
sort
of
like
underlying
lower
dimensional
skeleton
that
greatly
organizes
the
overall
dynamics
of
the
system
and
it's
they're
particularly
influential.
B
Processes
so
with
Jupiter
or
the
zonal
belts
that
form
and
the
barrier
is
between
those.
Are
these
strong
jet
streams
that
act
as
north
north
south
transport
barriers
that
define
these
some
own
belts
throughout?
You
can
also
see
their
vortices
and
all
different
scales,
including
the
famous
big
ol
red
spot
there.
These
are
known
to
be
responsible
for
so-called
levy
flights
in
turbulent
systems,
where
particles
objects,
kind
of
get
sucked
up
into
a
vortex
and
go
for
a
ride.
B
It's
known
as
anomalous
diffusion,
so
that's
a
little
taste
of
what
cocaine
structures
are,
from
a
physics
perspective,
add
a
very
challenging
problem
again,
there's
no
general
theory
for
these
structures
or
how
to
predict
how
they
all
merge.
There
are
a
few
things
we
do
know,
though,
but
it's
that
system,
details
and
histories
matter
in
these
cases
and
that
kind
of
motivates
the
sort
of
instant
based
modeling
of
machine
learning.
B
So,
instead
of
trying
to
kind
of
come
up
with
an
explicit
description,
can
we
teach
an
algorithm
to
learn
principal
description?
So
in
general
this
is
an
active
and
open
problem
again,
there's
no
ground
truth,
but
from
the
this
Lagrangian
approach
to
coherent
structures,
as
gained
popularity
in
recent
years,.
B
So
in
this,
as
I
mentioned,
coherent
structures
are
impactful
in
transport,
so
you
want
to
try
and
identify
their
signatures
based
on
Lagrangian
transport
in
the
system.
So,
for
example,
the
art
methods,
the
geodesic,
which
views
coherent
structures
as
these
four
material
surfaces
that
have
characteristic
deformation
properties.
So
imagine
every
point
on
the
surface
being
about
flow.
B
It's
like
a
smooth
information
on
the
surface
and
particular
weights
that
surfaces
get
deformed,
might
define
them
as
structures
like
the
green
circles,
outline
a
narrow
segmentation
for
these
coherent
vortices
and
the
one
next
to
it
in
the
bottom
right
corner
and
the
state-of-the-art
method,
particularly
designed
for
these
vortices.
And
you
see
they
agree
on
some
but
là
bébé,
except
some
extra
things
like
circles
that
geodesic
does
not.
So
we
got
hold
of
this
data
set
and
applied
our
method
to
it.
B
So
what
we
see
here
on
the
far
left
is
the
observable
vorticity
field,
I've
added
some
annotated,
bounding
boxes
here
to
outline
the
these
identified
by
the
previous
methods
you
just
looked
at
so
the
green
bounding
boxes
are
white
geo.
That's
akin
le
VD,
both
capture
red
or
additional
things
at
le
BB
captures,
then
yellow
are
some
new
things
that
we
capture
so
our
it's,
a
latent
state
representation
model,
so
they're
the
two
other
images
in
the
middle
and
right,
our
latent
representation
fields.
B
So
each
pixel
in
the
observable
field
gets
mapped
to
a
local
latent
state
value,
so
the
individual
colors,
you
see
in
the
middle
of
the
right
are
particular
unique
labels
for
these
states,
so
in
particular
in
the
middle,
we
see
that
the
background
potential
flow
all
gets
mapped
to
the
same
state
and
that
creates
a
sort
of
local
euclidean
symmetry
in
the
latent
field
and
the
other
states
and
horsies
break
that
symmetry.
So
we
identify
the
coherent
vortices
in
this
case
as
broken
symmetries.
B
B
C
B
We'll
come
back
later
and
see
videos
of
the
other
two
cases
sort
of
seeing
involved
here
where
these
are
moving
under
the
flow
I
should
mention
the
because
each
point
in
space-time
gets
mapped
to
a
local
latent
variable.
There's
a
shared
coordinate
geometry
between
the
observable
space-time
field
and
the
latent
space-time
field
is
probably
see
from
the
video
and
that's
a
key
property
of
our
method.
We'll
come
back
to
that
a
few
times,
yep.
A
B
B
D
B
B
If
you
think
of
pattern,
you
might
think
in
your
head
and
an
exact
symmetry
pattern
like
you
see
here,
and
these
great
algebraic
description
in
terms
of
group
theory.
So
that's
the
set
of
all
transformations
that
return,
the
object
to
itself
and
compositions
of
those
transformations
that
together
give
another
transformation
that
return
the
object
to
itself
in.
B
Okay,
so,
let's
get
even
more
simple.
We
have
a
binary
string
here.
We
can
see
that
it's
translation
very
stick.
It
shifted
over
I
get
that
string
again.
So
there
is
a
group
that
describes
these
translations
and
how
they
relate.
Is
there
a
different
representation
that
we
can
have
that
captures
that?
So
we
want
to
look
at
these
finite
state
machines,
these
machine
presentations
as
they're
called,
and
you
can
think
of
as
describing
the
set
of
all
indexed
by
infinite
streams
that
have
this
repeating
pattern
of
three
zeros,
three
one,
three
zeros.
B
We
won
that
second.
So
this
the
study
of
these
kind
of
sets
of
buying
it
infinite
strings
with
particular
patterns
is
known
as
symbolic
dynamics
that
this
interesting
interface
between
dynamical
systems
theory
a
computation
theory.
It
serves
as
the
mathematical
foundations
for
the
theory
pattern
structure
we
want
to
develop
here,
so,
in
particular,
for
translation,
American
strings.
We
can
see
that
this
machine
presentation
actually
captures
the
quotient
group
of
the
symmetry.
B
So
that's
the
set
of
all
transformations
that
do
change
my
object,
but
sequentially
we'll
bring
it
back
to
itself
internal
structure
of
the
symmetry,
so
it's
like
the
internal
States
and
if
transitions
are
like
a
counter,
attractive
phase
of
the
pattern.
So,
if
I
had
my
in
the
string
and
its
index,
I
can
ask,
in
my
current
index,
I
see
a
1.
B
Is
that,
like
the
first
one
in
a
block
of
3
of
the
middle,
the
last
moment,
the
same
or
state
C,
and
this
notion
of
internal
states
and
their
relations
and
among
each
other
are
key
to
our
development.
Those
are
like
the
local
latent
States
I
was
mentioning
before
so
it's
nice
that
they
capture
exact
symmetry
in
this
way.
B
Here,
though,
we
have
another
by
infinite
string.
It
is
not
translation
invariance,
but
it
does
contain
I
know
if
anyone
happens
to
see
the
pattern
here,
you
stare
at
it
long
enough.
You'll
notice
that
blocks
of
ones
always
come
in
even
likes
founded
by
zeros,
so
the
set
of
all
indexed
rings
with
this
pattern,
where
there
are
no
odd
link
blocks
of
ones
about
by
zero.
This
is
called
the
even
process
or
the
even
shift
in
symbolic
dynamics.
B
It's
machine
presentations
here
is
a
nice
visual
interpretability
that
the
the
structure
of
this
machine,
it's
organization,
restricts
the
strings
that
it
produces
to
enforce
the
pattern.
So
if
I'm
in
state
a
I
can
omit
a
zero
or
one
by
mid-2012,
go
to
state
B
and
then
I'm
forced
to
admit
another
one
ensuring
that
one's
come
in
odd
length
blocks.
B
B
B
B
Combined
with
that,
the
one
on
the
left
similarly
ensure
that
larger
blocks
of
odd
length
ones
get
back
to
e,
so
again,
just
wanted
to
give
to
show
that
there
is
an
algebraic
description
of
patterns
in
this
way
and,
as
we
just
saw
it,
can
capture
exact,
symmetries
and
attract.
From
this
perspective,
we
see
that
exact
symmetry
is
a
pretty
restrictive
property.
The
Machine
presentation,
as
we
saw
on
the
previous
one,
cannot
have
any
local
branching,
otherwise
the
and
wouldn't
necessarily
be
guaranteed
to
exactly
repeat
okay.
C
E
B
So
we
take
the
state
space
of
our
dynamical
system.
We
chop
it
up
into
finite
elements
and
those
elements
are
sort
of
the
possible
measurement
outputs
our
device.
So
if
our
state
space
is
the
unit
interval
and
ample
system
that
map
seen
an
interval
to
itself,
you
can
divide
that
in
half
and
say
the
left.
If
my
state
is
on
the
left
of
1/2,
it's
a
zero.
If
it's
on
the
right,
it's
a
1,
my
output
measurement
will
then
be
zeros
and
ones.
Okay.
This
is
a
little
character,
change,
yeah
and
so.
B
So
from
observed
data,
we
define
the
internal
states
of
our
machine
presentation
based
on
this
notion
of
equivalent
histories,
so
two
paths
are
considered
causally
equivalent
if
the
distribution
of
futures
that
follow
from
those
paths
is
the
same
and
the
ones
classes
of
those
equivalence
classes
generated
by
this
equivalence
relation
are
the
internal
states
of
the
machine,
what
we
call
causal
States,
so
this
is
actually
defining
internal
states
of
finite
state
machines,
as
:
histories
goes
way
back.
Huffman
and
Minsky
worked
on
this.
This
is
kind
of
just
a
stochastic
generalization,
for
various
reasons.
C
B
So
these
produce
minimal
the
states
that
produce
our
presentations
for
a
minimal
machine
and
there
are
also
optimal
predictors
of
the
process,
so
these
como
states
to
find
that
it's
called
relation
can
show
our
unique
minimal,
sufficient
statistics
of
the
past
for
predicting
the
future.
Yes,
if
my
string
say
has
a
pattern,
I
can
get
a
compressed
representation
that
optimally
produces
it
I've
sort
of
captured
that
pattern.
B
When
we
go
to
space
time
as
we're
interested
here,
the
idea
is
to
apply
this
locally
and
have
this
local
notion
of
causal
equivalents
in
internal
states.
So
we
need
local
oceans
of
pasts
and
futures
and
we
use
light
cones
for
that
and
these
physical
systems
that
self-organizing,
though
that's
a
product
of
local
interactions
and
how
they
propagate
in
the
system.
So
the
light
cones
capture
the
extent
and
history
of
local
interactions
and.
A
B
The
current
value
in
space
on
the
point
in
space
time
to
past
light
cone
is
the
set
of
all
points
in
the
past
that
could
possibly
influence
the
current
position
through
these
local
interactions.
Likewise,
the
future
light
cone
is
the
set
of
all
points
that
the
present
could
possibly
influence
through
local
interactions,
so
having
defined
light
cones,
we
can
now
just
apply.
C
B
B
So
the
epsilon
in
the
middle
here
is
the
function
that
maps
from
past
light
cones
to
their
equivalence
classes.
So
two
light
cones
will
be
mapped
to
the
same
value
under
the
epsilon
that,
but
they
have
the
same
conditional
distribution
over
futures.
We
can
use
that
to
take
a
spacetime
field
and
map
every
point
locally
to
its
corresponding
latent
internal
state.
B
E
E
B
B
B
Can
only
make
finite
horizon
cut-offs,
so
we
need
some
approximations,
so
I
think
think
clustering
here.
This
is
gonna
proceed
through
two
stages
of
clustering.
First,
if
we
have
real
valued
like
combs,
vector,
they're,
never
gonna,
exactly
repeat
right,
so
we
can't
build
counts
of
those.
So
we
want
to
do
first.
This
clustering
here.
C
B
Cone
distance
has
tempore
exponential
decay
so
again
think
you
know
in
our
present
and
we're
going
back
some
time
steps
as
you
go
further
and
back
in
time
we
sort
of
care
less
about
how
much
they
agree
there.
So
this
is
exponential
decay
so,
rather
than
saying
I'm
going
to
equally
weight
everything
within
my
finite
horizon
and
add
footnote
beta
stuff
behind
it.
We
kind
of
smooth
that
out
with
this
exponential
decay-
and
it
actually
gives
them
more-
the
temporal
decay
rate
gives
us
more
nuanced
inference,
parameter
to
control.
E
B
E
B
B
E
B
C
B
We
have
seen
conditional
stationarity
in
the
system
which,
basically,
if
it's
governed
by
uniform
local
interactions,
it'll
satisfy
this,
which
would
say,
wherever
I
see
a
past
light
cone
in
space-time
I'm.
Assuming
that
the
conditional
traditional
follows
is
independent
of
space-time
location,
where
it's
found
right
so
for
real
value.
We're
gonna
do
this
clustering
for
discrete
value.
That
kind
of
comes
for
free
anyway,
so
the
clusters
are
basically
all
the
pine
cones
that
have
the
same
values
within.
D
B
B
B
B
Symmetries
in
space
and
time
with
all
this
private
second,
this
is
a
simple
of
space-time
on
CI
models,
so
horizontal
slices
or
spatial
configurations
they've
all
the
time
from
top
to
bottom,
as
almost
cried
more
in
second,
at
the
bottom,
we
have
latent
state
field.
So
again,
at
every
point,
in
space-time
here,
you
had
this
approximated
of
solid
matter
to
a
corresponding
local.
C
B
B
B
B
Can
stack
sequential
and
spatial
spatial
lattices
together
to
make
these
space-time
fields
that
we
just
saw
okay,
so
these
generalized
symmetry
regions?
This
is
what
we
call
and
they'll
have
these
symmetry
states
that
identify
regions
that
are
locally
had
the
symmetry
and
then
coherent
structures
are
defined
as
sets
of
states
that
are
especially
localized
but
temporally.
Persistent
deviations
from.
B
Again,
the
plus
particle
that's
moving
to
the
right.
It
collides
with
the
gang
to
create
the
beta.
They
have
their
unique
set
of
signature
states
of
deviate
from
a
main
region.
So
here's
an
example:
if
we
have
a
hidden
background
there
might
be
hidden
structures
here.
It
would
probably
take
way
too
long
to
stare
at
this
guess
what
structures
might
be
there.
But
if
we
filter
out
there,
these
sort
of
locally
random
walking
pairwise
annihilating
structures
there.
C
B
Invariant
sets
that
the
CA
produces
and
these
generalized
space-time
symmetries
and
our
layton
States,
so
they
really
are
doing
something
meaningful
here
in
terms
of
pattern
in
these
systems
and
structures
as
deviations
from
there.
Let's
go
back
to
flute
floats
here.
We
introduced
the
method
and
the
reconstruction
in
this
parameter.
B
B
C
B
B
B
B
C
B
C
C
B
B
C
B
B
B
Different
physical
fields,
water
vapour
temperature
pressure,
etcetera,
take
sort
of
combined
light,
cones
from
those
and
learn
equivalence
classes
in
combined
light,
cones
of
that
full
state
and
get
one
latent
filled
out.
That
is
the
combined
internal
state
for
these
fields
or
its
independently
and
then
take
the
structural
to
from
each
of
the
independents
Layton
field
combined
the
in
and
out
in
a
segmentation
analysis.
So
again,
we
can
do
that
through
this
y
coordinate
geometry
here.
So
if
I
say
at
a
point
in
my
data.
C
B
C
C
B
B
Works
great
and
it
could
apply
to
climate
and
then
stop
there
right,
because
you
know
maybe
I
don't
want
to
spend
the
time
to
write
it
and
see
your
Fortran
to
have.
It
actually
be
able
to
apply
to
this,
but
if
we
have
it
in
Python-
and
we
have
these
performing
and
optimized
libraries
where
we
can
write
basically
take
our
prototype
pipeline,
something
like
scikit-learn
and
now
flip
a
distributed,
equals
true
flag
and
run
it
on
Cory.
B
B
B
C
B
B
Error
as
an
optimization
metric
to
train
in
network,
but
I,
we
construct
these
states
from
data
actually
in
doing
that,
you
get
this
stochastic
decoding
along
with
it
the
encoding.
So
it's
not
particularly
useful
in
this
case.
But
what
is
interesting
and
useful
is
that
do
the
Markov
properties
of
the
internal
states,
you
can
actually
define
a
dynamic
inflating
space
to
a
latent
space
as
an
actual
prediction.
B
I,
don't
need
to
do
forecast
doesn't
do
super
well.
One
thing
we're
interested
this
in
this,
though,
is
at
an
optimization
metric
for,
say,
hyper
parameter,
tuning
or
choosing
fratres
if
I
want
to
do
run
a
bunch
of
climate
simulations,
say
extreme
weather
events,
but
the
turbulence
I
can
whom
parameters
and
they
give
physically
nice
outputs
that
just
kind
of
different
levels
of
dispersion.
So
it's
a
sort
of
objective
way
if
I
want
to
do
a
big
survey
that
picks
right.
B
This
also
opens
up
the
possibility,
training,
giving
a
more
nuanced
self
supervised
and
that
trick
the
Train
no
Matt
works
on
shell.
You
could
put
up
more
in
a
second
I
mentioned
before
in
discussing
states
that
they
are
rely
on
the
notion
causality,
but
don't
discover
causality
well
this
for
real
value
cases.
With
this
multivariate
analysis
and
I
see
you
can
combine
those
together
to
actually
have
a
potential
way
of
discovering.
D
B
Y
and
predict
x
from
that,
if
my
prediction
is
better
having
incorporated
information,
why?
Why
is
somehow
causally
influential
to
X
some
other
information,
theoretic
and
dynamical
system
approaches
to
causal
discovery,
I'm
interested
in
where
collaborate
with
some
ecologists
at
Oakridge,
interested
in
ecological
memory
and
how
they.
B
Environment
will
stimuli.
This
is
an
approach
I
want
to
work
on
in
that
context.
So,
as
a
recap
of
this
future
directions,
the
new
tools
and
analysis
and
predictive
forecasting
and
we're
really
interested
in-
is
this
idea
of
mechanism
and
not
just
identifying
structures
but
getting
towards
you
know
what
goes
into
forming
them.
What
is
the
underlying
mechanisms
underneath
I
just
described
how
we
might
go
about
looking
at
causal
mechanisms?
B
B
With
the
physical
related
by
the
equations
of
motion
that
produce
the
data
that
we
train
on
not
super
clear
how
to
do
that,
but
I
think
this
is
a
couple
of
time.
Series
case
is
a
more
simple
setting
to
play
around
with
that,
and
then
there's
this
question
of,
like
is
the
always
a
good
assumption
or
climate
there's
reason
to
believe
that
might
be
an
issue,
and
so
that's
provides
a
way,
as
I
said,
to
maybe
look
at
training
neural
networks,
so
networks
are
higher
class
of
computational
models.
B
A
B
Which
is
useful
if
you
have
infinite
states
and
that's
still
in
early
development,
so
with
that
was
like
my
buck-
are
thinking
for
BOTS
collaborators
here
at
no
risk,
Nalini
and
Victor
at
inta
disco,
collaborators
and
Intel
is
kind
enough
to
fund
us
in
this
project.
I
also
mention
that
our
HPC
implementation
was
chosen
for
this
HPC
innovation.
Excellence
awards
are
very
alright.
Thank
you.
E
E
E
D
D
Forms
a
for
memorizing
system:
it's
also
helpful
assistance
in
Kepler's
to
be
dispersed
another
good
week
for
quickly
viscosity,
so
there's
a
very
strong,
so
means
of
vortex
will
process
again
your
your
Arbonne
nail
toes
to
the
well
and
their
York.
You
have
certainly
contexts
we're
coming
back
to
your
what
rivers
jump
over,
so
they
they
represent.
More
of
a
elementary
structure
is
memory.
D
B
C
D
D
D
D
And
then
you
got
you
gotta
meet
about
the
describing
the
answers
river,
because
that's
what
refurbished
should
be
just
wondering
answered?
Burnable
all
the
politicians
around
a
source
of
something
there's
some
coming
back
to
europe,
idea
of
going
into
a
vectorial
classification
technique.
Is
that
actually
the
code
so
minimally
addressing.
A
A
B
Positively
open
all
the
exponents
are
spreading.
That
increases
the
entropy
of
the
distribution,
but
it's
still
captured
alright,
so
yeah
for
prediction,
then
I'm
sampling,
this
high
entropy
distribution
and
like
we
can
see
in
this
prediction.
If
you
don't
get
it
right,
it
leaves
the
local
instabilities
that
will
just
kind
of
wash
out
so
I.
Don't
again,
I,
don't
envision
this
as
being
like
particularly
useful
for
like
state-of-the-art
forecasting
or
something,
but
it
adds
an
interesting
dimension
of
this
and
including
the
internal
state
representations.