July 18, 2018 • 26 mins
In Part 2 of this two-part interview, Numenta Co-founder Jeff Hawkins and host Matt Taylor have an in-depth discussion on how HTM sequence memory builds object representations in space through movement.
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Episode Transcript
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Matt (00:09):
Welcome to Numenta On intelligence, a monthly podcast
about how intelligence works inthe brain and how to implement
it in non biological systems.
I'm Matt Taylor.
Today, I'll be talking with JeffHawkins about the latest
research Numenta has been doingwith regards to grid cells and
hierarchical temporal memory orHTM.
While this is the first episodeof the Numenta on Intelligence
(00:30):
Podcast, Jeff and I will begoing very deeply into the
theory very quickly.
Therefore, I prepared in theshow notes a bunch of
educational resources so you canlearn at your own pace about HTM
and grid cells.
If you like this conversationand you don't know how HTM
sequence memory works, I suggestyou watch through the HTM School
videos on YouTube.
Just search for HTM School orsee the show notes for links.
(00:58):
This is part two of a two partinterview with Numenta founder
Jeff Hawkins.
This recording continues wherepart one left off after an in
depth discussion of how HTMsequence memory builds object
representations in space throughmovement.
A couple of things about gridcells.
Jeff (01:18):
Yeah
Matt (01:18):
There's head direction cells, there's border cells,
there's stripe cells, there'sspeed cells.
Do we have to pay attention toall these different types of
cells and what, what did welearn from all these different
things?
Jeff (01:28):
Well, we're going to have to pay attention to some types,
but maybe not all of them.
Uh, now again, the basic theorywe're working on here is that
you have this old part of thebrain that evolved for many,
many eons to allow animals tonavigate and map out
environments and know where theyare.
Matt (01:44):
Hippocampus, entorhinal cortex...
Jeff (01:47):
Yeah, hippocampus, entorhinal cortex are older
structures.
They've been under a lot ofevolutionary pressure.
They are designed to solvespecific problems of navigation
of an animal in an environment.
What we think happened is thatevolution co-opted those
mechanisms and stuck them in theneocortex in a more regular,
orthogonal way.
Matt (02:06):
Which happens all the time in biology.
Jeff (02:07):
It does, yes it does, but it doesn't mean all the
mechanisms can't transfer itover and some of them are going
to be very specific to theproblem of the rat navigating in
a maze or in some dark channelunder your house or something
like that.
Um, and they may not work in thecortex.
(02:28):
So I think what's happened inthe, in this case, you have some
very highly tuned specificmechanisms in the entorhinal
cortex and the hippocampus,solving very specific problems,
evolved over many, many eons sothat they're fairly well tuned
and then the evolution to sayhey, I can take the best of
those and rejigger them a bit soI have something very generic.
(02:49):
So now I can apply it torecognize lots of stuff, how to
use cell phones and how to usecomputers and tools and language
and all these other things whichwasn't originally evolved for.
So how many of those thingstransfer over, we don't know.
The idea of like for example,orientation, is clearly
something with head directioncells.
Head direction cells say, hey,which way am I facing in this
(03:11):
room?
You know?
And as I, if I just sat in onespot and rotated in my chair, my
head direction cells wouldchange.
Matt (03:15):
Right.
You certainly need to know thatwhen you're sensing objects.
Jeff (03:18):
You need to know that.
You can say where am I, but whatyou're going to sense is
depending on not only where youare, but which way you're facing
and where are you going to bewhen you move depends not only
where you are, but where you areand which way you're facing.
Some of those concepts are goingto apply in the cortex because
thinking about my finger, whatdo I sense on my finger?
Well, not, it depends not onlywhere my finger is touching an
(03:40):
object, but it's orientation.
Like I can rotate my fingeraround that.
Matt (03:44):
Oh yeah, you can turn it on, on an axis.
Jeff (03:46):
I'm touching the top of my Coffee Cup right now and I'm
rotating, pivoting on the samelocation, but I'm sensing
different things.
So also where my finger is goingto move if I flex my finger
depends on where its currentorientation is.
So some of those concepts aregoing to come across.
Matt (04:02):
So the idea of orientation could be represented in every
cortical column based on someaspect of sensory input.
Jeff (04:08):
Yeah.
Yeah.
And it will be, um, this is anarea we don't understand as well
as we'd like to understand.
It's quite complex.
Um, so at the moment the paperswe're writing, we're not
addressing specifically themechanisms of orientation
because the concepts you and Italked about earlier about
composition of objects and so onreally don't require we solve
(04:29):
that problem.
The concepts themselves withholdregardless of exactly how the
orientation problem is solved.
And they're really big conceptsif you, if you are interested in
intelligence and how brainswork, um, that those concepts
are, they stand on their own.
And then the orientationcomponent, it's more of a
detail.
Matt (04:47):
You certainly can't figure out everything at once.
Jeff (04:49):
No, right.
We need to do, as I always liketo quote Francis Crick who wrote
an essay nearly 40 years ago.
We need a framework and we don'tneed detailed theories, right?
We need a framework.
We were not thinking even abasic framework for
understanding how we perceivethe world.
And so the locations, um, uh,really give you...
grid cells really provide thatframework and then we can start
(05:11):
filling in more of the detailslater about exactly, well for
example, there was a, youmentioned these border cells and
you know, when an animal, a ratis near an edge of a room, these
border cells detect that.
Are their border cells in thecortex?
I don't know, maybe not.
You know, is there an equivalentto border cells when I'm doing
language?
Probably not.
Matt (05:31):
But I mean rats or specific organisms could develop
specific cells that detectspecific things that only exist
in their environment.
Jeff (05:37):
Exactly right.
You know, a bat flying around,you know, he doesn't follow
walls, right?
Or she.
Matt (05:44):
It might follow sound.
Jeff (05:45):
Obviously, but you know, rats literally like to run along
walls.
They don't like to be out inspace.
They don't want to be away fromthe wall.
So they have these cells attunedto knowing I'm near a wall.
I want to be near walls all thetime.
Matt (05:57):
Less chance of death there.
I know that's their modusoperandi.
That's how they get around.
They follow walls and homeowners know this.
That's the problem.
That's why we don't have, that'swhy you have rats in the walls
and not walking around the floorof the kitchen.
So, you know, again, that couldbe something very specific to
rats and probably doesn'tpertain to other animals in the
(06:18):
entorhinal cortex and probablydoesn't carry over to the
cortex.
But the basic idea oforientation is something that,
or head direction cells in the,in the entohrinal cortex, they
call them head direction cells.
We just said that's anorientation.
So that's the term we'vedeveloped, genericizing that
term.
That makes sense, um, aboutobject representation.
(06:39):
I have another question, butthat is a misunderstanding that
I had initially.
It made a lot of sense to me tothink about how we represent
objects in the brain, to thinkof it as a map.
But I know Marcus initiallythought about this and we
changed our thinking about it,but I want to walk through this
because it's sort of aneducation for me and I want you
to explain it for other people.
So it made sense to think of,okay, I've got an object in my
(06:59):
brain.
It's essentially a map oflocations in space using some
type of grid codes to sensationsthat I felt at that location,
that makes sense.
And you can do some operationson that structure, but that's
not actually the way it seems tobe working, right?
It's more about movement ordisplacements or changes, but
going from point a to point band what is sensed during that.
Jeff (07:21):
Well first of all, let's talk about the word maps.
We're not using it heavily rightnow and because there's multiple
ways you can interpret the wordmap.
And so at one point we weretalking about the entire space
of all points is one big map islike the universe.
And um, and, but maybe the mapis just a map of the phone or
(07:41):
the map of a coffee cup.
Matt (07:42):
I'm thinking of it that way, just the map of an object.
Jeff (07:44):
So, uh, that's a fine term.
We are not using that term rightnow in our language, in our
description of this.
Um, it's just a personaldecision that we made.
Now the second question youasked about is, we described it
in the Columns paper, theOctober 2017 paper, we described
(08:06):
how you learn an object bysensing at all different
locations, and there's sometruth to that, but it's more
complicated than that.
As we were talking aboutearlier, we really want to
represent objects is compositionof other objects, right?
So when I learn a Coffee Cup, Idon't really want to have to
(08:26):
touch it everywhere to recognizeevery single feature I'm going
to sense.
Um, I can start feelingsomething that feels like a
handle.
And I say, oh, that's a handle.
I don't need to touch everysingle spot on the handle to
verify it's a handle.
Matt (08:40):
You don't have to fill in.
Jeff (08:41):
Well, I, I kind of say it's an object I felt before.
When you're born, yes, youprobably know nothing.
So you have to learn everything,but you start building up this
sort of language of componentsand objects.
And so when I learn a newobject, I don't really, you know
what, I don't just move myfinger over everything and sense
every single point on theobject.
Matt (09:01):
No, you sense it enough to associate it with things you
already know.
Jeff (09:04):
That's right.
So the idea that you are movingand sensing and moving and
sensing is of course correct.
But what you're really doing isyou're moving in and inferring
substructure that-- So I see, ohthis is the, this is a circular
rim and this is a handle andthis is a cylinder.
I don't.
And so it's not like I have todisassociate the raw sensory
(09:25):
input with the location.
I'm using the location to infera structure that I already know
and then and say, oh I'm nowtouching a handle.
Matt (10:31):
I know where the handle is and now I'm touching a cylinder
and I know where it is.
(11:03):
And I didn't have to touch allthe points on this handle.
I didn't have to hit all thepoints of the cylinder, but, but
now I can associate the handlewith a cylinder.
So it's close to what we wroteabout in the Columns paper.
It's close to what you said.
It's, we're moving and sensingand moving and sensing, but in
reality what we're doing iswe're moving and inferring
structure more than what I cansense.
It's not like I have to goaround- It's like a, it's like
(11:24):
if I want to learn a map of aroom in my living room for
example, I don't have to go andtouch every part of every piece
of furniture to say, where doesthis chair extend to?
And then you know what'sexactly...
I can say, oh, that's a chair.
And, and, and now I can justsay, oh, given my point in the
room, I know there's a chairhere and given I know where the
location of chair is, I canpredict there's going to be an
arm or back or something.
So it's, it's a, it's a bit moresubtle than just sense,
location, sense, location.
So you can operate upon itwithout really knowing what it
is.
Jeff (11:29):
Yeah you can operate.
And this is what grid cells, themagic of them is.
And so the only way to buildyour quote map of the world or
map of an object is you have tosay, start in one place, move
and, and then say, Oh, here's mynew location.
Like, here's some random numberof thing that hit my
notification.
What do I see it there?
And then move again.
And what do I see there and moveagain, what do I see here?
So, uh, unlike high school mathyou'd say, oh, x, Y, and Z,
(11:54):
that's my location and now I'mgoing to move, you know,
increase x by two.
You can't do that.
You have some sort of, um, theonly way these points are tied
together is through movement.
Speaker 1 (12:05):
That's the only way they're tied together.
Matt (12:07):
That's the tricky thing.
And then trying to get to thecenter of here-
Jeff (12:10):
it takes honestly, it took us a while to really get, get
it.
Matt (12:14):
Because I always felt like, oh, each grid cell code
was a, like a coordinate orsomething, eh, not really.
Jeff (12:21):
We should come up with a good analogy.
Matt (12:23):
I wish.
I like that people call themcodes.
I guess that's something.
It's better than nothing.
Jeff (12:29):
Yeah.
Matt (12:30):
But the idea that objects are defined as, as sort of as a,
as a transition between thesetwo movements and a sensation.
Jeff (12:36):
No, it's really the oobject is defined by different
locations you're in and the onlyway to get between those
locations is through movement.
Um, and there's no other way.
Like if I say what's over there,I can't say what's over there, I
have to say, oh, I have to move.
Matt (12:50):
Because that's the only way you were ever able to
experience the object.
Jeff (12:54):
There's that plus that's the way grid cells work.
If grid cells worked likeCartesian coordinates we learned
in high school, then youwouldn't have to do that.
But they don't work that way.
That's by the way, here's oneway to think about it.
People who do computer graphicsor animation or 3D cad.
So those programs all work on X,y's and z's.
(13:16):
You know, I have a referencepoint and I say, okay, I'm going
to make a cad model of my CoffeeCup and I'll say, here's the
point, the zero point, and thenI can define all the features
that are related to that zeropoint.
That is not what the brain does.
The brain doesn't have a zeropoint.
It just has a bunch of pointsthat are tied together by
movement.
Matt (13:33):
But the interesting thing is you can take two points in
cad and you can define atranslation between them and you
can't do that with grid codestoo.
Jeff (13:40):
You can, but in a very different way.
Matt (13:42):
Yes, it's not a Cartesian distance formula at all.
Jeff (13:46):
Yeah, Cartesian coordinates are pretty easy.
You just do a little bit of mathand you get your answer.
Here it's not that way and thisgets to this displacement
transform that we've, we'vediscovered here that allows you
to say, okay, given two pointsthey look kind of random.
How can I establish a vectorthat says where, where, how far
(14:09):
apart they are and whatdirection are they are from each
other and you can do that andyou do that going back through
the grid cells.
It's Kinda like, it's, I'm notgoing to try to explain to here.
It's complicated
Matt (14:19):
Okay.
Okay.
I got to ask a question aboutthis.
So say you have an object andyou have two points and you have
a transition, something thatmoves from one point to another.
Can you apply that to any pointon the object and expect the
same movement to occur in thatspace?
Jeff (14:35):
Uh, we're, we're mixing a couple things up here, Matt.
Essentially there's, the brainuses grid cells in two different
ways.
One is to build maps orstructured defined objects, and
the other is to tell me how tomove my body.
Okay?
Okay.
There's really two separate waysof doing that.
So I can apply grid cells andsay, Oh, my finger's at one
(14:55):
location and I wanted to go toanother location.
How do I move my finger to getthere?
Then I could say that- it turnsout the mechanism that does that
- animals had to solve this along time ago.
Like, Oh, I'm, I'm in the woods.
How do I get home?
I may go a way I've never gonebefore, but I know which way to
(15:15):
go.
So then we think what hashappened is the cortex has taken
that same mechanism but appliedit to a very different purpose.
Matt (15:21):
Now you're talking about path integration, right?
Jeff (15:24):
Path integration is when you physically move, what is
your new location?
So I'm saying,I wasn't reallytalking about path integration.
I was talking about given, if Icould tell you here's a point in
space and here's another pointin the same space, like here's
where I am in the woods rightnow and here is my home is and I
(15:45):
know those two representationsof location and, and they're in
the same space because as Iwander through the woods to get
to where I am now, I pathintegrated.
They're in the same cloud ofpoints, but.
And so that's important.
Yes, but now I can say I know Ican calculate even though I can
calculate the straight way fromwhere I am home, even though
that's not how I got here.
Matt (16:04):
Right.
Jeff (16:04):
I wandered around in the woods and now I'm saying, okay,
I need to get home.
I can calculate the straightpath home.
That's kind of clever, um, thatyou do this without using the
Cartesian math.
Matt (16:15):
Yeah it is.
Jeff (16:15):
Okay.
So there's a, there's amechanism for doing that.
Uh, we think we understand thebasics of that mechanism and now
that same mechanism is, is usedto figure out how to move my
finger from the Coffee Cup to mynose.
Like it's the same problem.
Like, Hey, my finger's overhere, how do I get to my notes?
So that's very analogous.
I hope you can see the analogy,the analogy between like I'm in
(16:36):
the woods, I need to get homeand from I'm on the Coffee Cup
and I want to touch my nose.
I'm on a coffee cup, I want totouch the wall or something like
that.
Yes, that's going on in thecortex.
But that's what we call thewhere pathway to the cortex.
Now that same mechanism can useto be used to define object
compositions.
Right?
This is a tricky idea, but if Ihave two different objects and
(16:56):
they have their own spaces,right?
If I move in one object, I don'tactually move into the other
space, I just don't do that.
But imagine these two objectsphysically or in the same world
together.
So there's a point.
Let's go back to the Coffee Cupof the logo.
I have a space around the logodefining the logo, right.
(17:17):
And I have a bunch of pointsaround the cup, defining the
cup.
There are two different parts ofthe world where there's two
separate things (17:22):
there's a cup and there's a logo.
Now, right now they're in someon my cup those two things have
a fixed relationship to eachother.
Matt (17:29):
They're sort of on top of each other.
Jeff (17:31):
It doesn't even have to be on top of each other.
They have a fixed position.
That's the important part.
They're fixed.
Now it turns out that the logois on the cup, but that doesn't
really matter.
At this point, it's not movingrelative to the cup.
If I take a point on the logo isa location logo at any point in
time there'll be an equivalentlocation on the cup.
(17:52):
It happens to be the samephysical location, but there are
two different representationsfor it.
One's in the space of the cup,one's in the space of the logo.
Matt (18:01):
That makes sense.
Jeff (18:01):
So now I have two points, two locations.
They turn out to be physicallythe same spot in the world, but
they're literally two differentlocations because one's relative
of the Coffee Cup and one'srelative to the logo.
Matt (18:15):
Two different locations in two different reference frames.
Jeff (18:17):
That's right.
But right now, because I'm notmoving the logo, the logo's
fixed relative to the cup,there's a one to one
correspondence between points inthe logo space and points and
the cup space.
Doesn't matter, because they'refixed relative to each other.
Yeah.
And so now I have these twopoints and what I'm going to
(18:38):
tell you is I can take the samemechanism that was used to
navigate from the woods to homeor from the cup to my nose,
which is two points in the samespace.
How do I get from the point in,you know, in the woods to the
point of where my home is,that's the same space, the same
environment.
Or now I'm gonna apply it to sayhow do I get from a point on the
cup to a point on the logo?
Matt (19:00):
Between spaces.
Jeff (19:01):
Between spaces but physically actually not moving
at all.
Physically, it's the same pointin the world.
Matt (19:06):
Right.
Right.
Jeff (19:06):
But I'm going between one point in logo space and the
equivalent point in cup space.
So I'm converting between twopoints.
Matt (19:14):
And you're not moving at all.
Jeff (19:15):
I'm not physically moving at all but by-
Matt (19:18):
This kind of trippy, like a wormhole or something.
Jeff (19:23):
That's a good analogy.
It's kind of like like a littlewormhole.
How do I get to another place byjust not moving?
Matt (19:29):
In your brain, it's easy apparently.
Jeff (19:32):
Yes, it's a very clever idea.
And Marcus came up with theunderpinnings of it and um, um,
we were working on this problemtrying to figure how it does it.
And he came up with some of thebasic of the solutions that was
really clever.
But it was actually motivated bysome work that was previously
done about how animals canfigure out their way home in the
woods literally.
(19:53):
How does an animal navigate fromhere to here?
There was a proposed mechanismfor that and we said, oh, that's
kind of similar to the problemwe want to solve instead of the
question, would it solve thatproblem?
So we think it does.
And so, so it's the samemechanism, but now I'm not
moving at all.
I just like saying it's themovement of like an attentional
shift.
I'm saying attend to the logo,attend to the cup.
(20:14):
Attend to the logo.
Attend to the cup.
Matt (20:15):
Oh yeah, yeah.
Yeah.
Jeff (20:16):
And as I do that, I switch spaces.
And I can say, now I can say thefollowing, I can say, well, my
hand, my finger is touching thetouching the logo right now.
Where will it be on the cup?
And I can figure that out byusing this transform.
I can say, oh, I know where itis on the cup.
(20:36):
So now I move my finger relativeto the cup.
I can say where's my fingerrelative to the logo.
Uh, in this case I can't reallyfeel the logo, but in general
that's the general idea.
So a clever idea.
It's an old mechanism thatevolved a long time ago.
We think it's been repurposed todo this thing and I realized
some of these concepts are verykind of bizarre.
(20:57):
They're actually very elegantand beautiful once you
understand them.
Matt (21:00):
Oh, it just takes so long to distill them into the
simplest form.
Jeff (21:06):
And, and part of our challenge is to pick out the
right language to do this andwhat's the right metaphors with
right examples.
But I don't think it's any moredifficult than other things um,
a lot of the listeners willknow.
If you know how computers workor how deeply how software
works.
For example, like the first timeI learned about a real time
operating systems and reentrantcode and how the stack point it
(21:26):
works when you're doing, you'remanaging code.
And these are details mostprogrammers don't know, but some
programmers do this.
That stuff is mind blowing atfirst.
It's like, oh my God, how doesthat really work?
Is it really possible, all thestuff does it like that and can
it do it fast enough?
And, and you know, it tookawhile for me to really
internalize the nature of a realtime operating system.
And why does it look like it'sdoing all these things
(21:47):
simultaneously when it's reallynot.
Um, so it's kinda like that.
It's not that hard.
Anyone can learn it, if youknow, but you got to work out a
little bit, right?
So the first time if you'venever seen a computer before and
somebody just dumped on you, ohthere's this reentrant code and
it works by moving the stackpoint around and we use
temporary variables that arecomplicated and moved over here.
And it's like, well what thehell are you talking about?
Matt (22:09):
There's a lot of new concepts coming in neuroscience
right now and people are tryingto keep up with it.
Jeff (22:14):
These concepts are, uh, are sort of similar difficulty I
would say, but if you've spent alittle time,we're trying to
write these papers in a way thatanyone could read them and get
it.
I'm not gonna sugar coat it.
These are not obvious things,um, the nature of grid cells and
(22:34):
how they work.
It's kind of bizarre and even alot of neuroscientists don't
really understand it.
Matt (22:41):
Nobody said the brain was easy, that's for sure.
Jeff (22:43):
But it's not ridiculously complicated.
It's more like the concepts arenew.
Matt (22:48):
When I first got what grid cells are doing, I was blown
away to see that, that, thatprocess was happening in your
brain like almost just byitself, it just emerged.
It's amazing.
Jeff (23:00):
Yeah.
It's a very clever idea, butit's no more clever than
Cartesian math.
You just said you learnedCartesian math when you were in
high school and you were exposedto it for many years, now you
get it.
You know, if you'd never beenexposed to any kind of
mathematics like that and Itried to teach you, you know,
it'd be hard, it'd take awhile.
So grid cells are like that.
(23:21):
They just work on completelydifferent principles than anyone
new until fairly recently andum, it takes a little while to
sort of internalize it and getit and go, oh, now I know what's
going on.
Matt (23:31):
Now it's almost hard to keep up.
There's so much literature outabout it.
Jeff (23:34):
Yeah, but the basic premises aren't changing.
It's all these little detailsaround the idea, I think what
we've done is, is significantlyextend it.
We've significantly extended thetheoretical basis for grid
cells, uh, understanding whatthey do, how they can do object
compositions, how they canrepresent behaviors.
These are ideas that I don'tthink anyone's ever thought of
(23:55):
before.
I'm not aware of it.
And even the idea that thecortex is using grid cells to
build models of the world, uh,in the same way that the
entorhinal cortex andhippocampus is using to build
models of environments.
The cortex is learning models ofobjects.
Even that idea is new.
I mean, there are peopletouching on the edge of it, but,
(24:16):
um, it's a pretty big idea.
So we're not aware of thatexisting out there in the
literature right now.
So we think those arecontributions that we can help
make.
Matt (24:29):
So Jeff, I think we're running out of time.
I have a couple more questionsfor you, but I think I'll just
put that off until the nexttime.
Jeff (24:36):
Alright, well that'd be great.
I think we should check in everyonce in a while on this and see
what's new.
Matt (24:40):
Yeah.
Um, well we've got a podcast nowso we'll have you as a guest
another time.
Jeff (24:45):
Things are happening here rapidly here at Numenta.
We are learning, you know, thesesort of pieces are falling into
place.
I've said this before, it's sotrue.
Um, so it's an exciting time andum, and that means it's going to
be new things all the time.
Matt (24:59):
A lot going on this fall.
So stay tuned to Numenta, keepwatching numenta.com and follow
our YouTube channels and stuff.
Thanks Jeff for joining me forthis chat and it was a pleasure.
Jeff (25:10):
Thanks Matt.
It's always fun talking to you.
Matt (25:11):
All right, take care and don't forget to subscribe to our
podcast.
Thanks Jeff Hawkins.
This has been Numenta OnIntelligence.
If you like what you hear on thepodcast and you want to discuss
ideas like this withintelligent, friendly people, be
sure to join HTM forum atdiscourse.numenta.org.
Our online community was createdaround the Numenta open source
(25:34):
project and continues to thriveon HTM forum.
Hundreds of folks interested inHTM and related theories, share
ideas, experiments, and opensource code.
If you are an HTM theorist,engineer or a programmer or just
a hobbyist, HTM forum is afriendly place to keep up with
the latest on HTM technologies.
Thanks for listening to NumentaOn Intelligence.
(25:55):
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service.
To learn more about Numenta andthe progress we're making on
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our newsletter.
Welcome to Numenta On intelligence, a monthly podcast
about how intelligence works inthe brain and how to implement
it in non biological systems.
I'm Matt Taylor.
Today, I'll be talking with JeffHawkins about the latest
research Numenta has been doingwith regards to grid cells and
hierarchical temporal memory orHTM.
While this is the first episodeof the Numenta on Intelligence
(00:30):
Podcast, Jeff and I will begoing very deeply into the
theory very quickly.
Therefore, I prepared in theshow notes a bunch of
educational resources so you canlearn at your own pace about HTM
and grid cells.
If you like this conversationand you don't know how HTM
sequence memory works, I suggestyou watch through the HTM School
videos on YouTube.
Just search for HTM School orsee the show notes for links.
(00:58):
This is part two of a two partinterview with Numenta founder
Jeff Hawkins.
This recording continues wherepart one left off after an in
depth discussion of how HTMsequence memory builds object
representations in space throughmovement.
A couple of things about gridcells.
Jeff (01:18):
Yeah
Matt (01:18):
There's head direction cells, there's border cells,
there's stripe cells, there'sspeed cells.
Do we have to pay attention toall these different types of
cells and what, what did welearn from all these different
things?
Jeff (01:28):
Well, we're going to have to pay attention to some types,
but maybe not all of them.
Uh, now again, the basic theorywe're working on here is that
you have this old part of thebrain that evolved for many,
many eons to allow animals tonavigate and map out
environments and know where theyare.
Matt (01:44):
Hippocampus, entorhinal cortex...
Jeff (01:47):
Yeah, hippocampus, entorhinal cortex are older
structures.
They've been under a lot ofevolutionary pressure.
They are designed to solvespecific problems of navigation
of an animal in an environment.
What we think happened is thatevolution co-opted those
mechanisms and stuck them in theneocortex in a more regular,
orthogonal way.
Matt (02:06):
Which happens all the time in biology.
Jeff (02:07):
It does, yes it does, but it doesn't mean all the
mechanisms can't transfer itover and some of them are going
to be very specific to theproblem of the rat navigating in
a maze or in some dark channelunder your house or something
like that.
Um, and they may not work in thecortex.
(02:28):
So I think what's happened inthe, in this case, you have some
very highly tuned specificmechanisms in the entorhinal
cortex and the hippocampus,solving very specific problems,
evolved over many, many eons sothat they're fairly well tuned
and then the evolution to sayhey, I can take the best of
those and rejigger them a bit soI have something very generic.
(02:49):
So now I can apply it torecognize lots of stuff, how to
use cell phones and how to usecomputers and tools and language
and all these other things whichwasn't originally evolved for.
So how many of those thingstransfer over, we don't know.
The idea of like for example,orientation, is clearly
something with head directioncells.
Head direction cells say, hey,which way am I facing in this
(03:11):
room?
You know?
And as I, if I just sat in onespot and rotated in my chair, my
head direction cells wouldchange.
Matt (03:15):
Right.
You certainly need to know thatwhen you're sensing objects.
Jeff (03:18):
You need to know that.
You can say where am I, but whatyou're going to sense is
depending on not only where youare, but which way you're facing
and where are you going to bewhen you move depends not only
where you are, but where you areand which way you're facing.
Some of those concepts are goingto apply in the cortex because
thinking about my finger, whatdo I sense on my finger?
Well, not, it depends not onlywhere my finger is touching an
(03:40):
object, but it's orientation.
Like I can rotate my fingeraround that.
Matt (03:44):
Oh yeah, you can turn it on, on an axis.
Jeff (03:46):
I'm touching the top of my Coffee Cup right now and I'm
rotating, pivoting on the samelocation, but I'm sensing
different things.
So also where my finger is goingto move if I flex my finger
depends on where its currentorientation is.
So some of those concepts aregoing to come across.
Matt (04:02):
So the idea of orientation could be represented in every
cortical column based on someaspect of sensory input.
Jeff (04:08):
Yeah.
Yeah.
And it will be, um, this is anarea we don't understand as well
as we'd like to understand.
It's quite complex.
Um, so at the moment the paperswe're writing, we're not
addressing specifically themechanisms of orientation
because the concepts you and Italked about earlier about
composition of objects and so onreally don't require we solve
(04:29):
that problem.
The concepts themselves withholdregardless of exactly how the
orientation problem is solved.
And they're really big conceptsif you, if you are interested in
intelligence and how brainswork, um, that those concepts
are, they stand on their own.
And then the orientationcomponent, it's more of a
detail.
Matt (04:47):
You certainly can't figure out everything at once.
Jeff (04:49):
No, right.
We need to do, as I always liketo quote Francis Crick who wrote
an essay nearly 40 years ago.
We need a framework and we don'tneed detailed theories, right?
We need a framework.
We were not thinking even abasic framework for
understanding how we perceivethe world.
And so the locations, um, uh,really give you...
grid cells really provide thatframework and then we can start
(05:11):
filling in more of the detailslater about exactly, well for
example, there was a, youmentioned these border cells and
you know, when an animal, a ratis near an edge of a room, these
border cells detect that.
Are their border cells in thecortex?
I don't know, maybe not.
You know, is there an equivalentto border cells when I'm doing
language?
Probably not.
Matt (05:31):
But I mean rats or specific organisms could develop
specific cells that detectspecific things that only exist
in their environment.
Jeff (05:37):
Exactly right.
You know, a bat flying around,you know, he doesn't follow
walls, right?
Or she.
Matt (05:44):
It might follow sound.
Jeff (05:45):
Obviously, but you know, rats literally like to run along
walls.
They don't like to be out inspace.
They don't want to be away fromthe wall.
So they have these cells attunedto knowing I'm near a wall.
I want to be near walls all thetime.
Matt (05:57):
Less chance of death there.
I know that's their modusoperandi.
That's how they get around.
They follow walls and homeowners know this.
That's the problem.
That's why we don't have, that'swhy you have rats in the walls
and not walking around the floorof the kitchen.
So, you know, again, that couldbe something very specific to
rats and probably doesn'tpertain to other animals in the
(06:18):
entorhinal cortex and probablydoesn't carry over to the
cortex.
But the basic idea oforientation is something that,
or head direction cells in the,in the entohrinal cortex, they
call them head direction cells.
We just said that's anorientation.
So that's the term we'vedeveloped, genericizing that
term.
That makes sense, um, aboutobject representation.
(06:39):
I have another question, butthat is a misunderstanding that
I had initially.
It made a lot of sense to me tothink about how we represent
objects in the brain, to thinkof it as a map.
But I know Marcus initiallythought about this and we
changed our thinking about it,but I want to walk through this
because it's sort of aneducation for me and I want you
to explain it for other people.
So it made sense to think of,okay, I've got an object in my
(06:59):
brain.
It's essentially a map oflocations in space using some
type of grid codes to sensationsthat I felt at that location,
that makes sense.
And you can do some operationson that structure, but that's
not actually the way it seems tobe working, right?
It's more about movement ordisplacements or changes, but
going from point a to point band what is sensed during that.
Jeff (07:21):
Well first of all, let's talk about the word maps.
We're not using it heavily rightnow and because there's multiple
ways you can interpret the wordmap.
And so at one point we weretalking about the entire space
of all points is one big map islike the universe.
And um, and, but maybe the mapis just a map of the phone or
(07:41):
the map of a coffee cup.
Matt (07:42):
I'm thinking of it that way, just the map of an object.
Jeff (07:44):
So, uh, that's a fine term.
We are not using that term rightnow in our language, in our
description of this.
Um, it's just a personaldecision that we made.
Now the second question youasked about is, we described it
in the Columns paper, theOctober 2017 paper, we described
(08:06):
how you learn an object bysensing at all different
locations, and there's sometruth to that, but it's more
complicated than that.
As we were talking aboutearlier, we really want to
represent objects is compositionof other objects, right?
So when I learn a Coffee Cup, Idon't really want to have to
(08:26):
touch it everywhere to recognizeevery single feature I'm going
to sense.
Um, I can start feelingsomething that feels like a
handle.
And I say, oh, that's a handle.
I don't need to touch everysingle spot on the handle to
verify it's a handle.
Matt (08:40):
You don't have to fill in.
Jeff (08:41):
Well, I, I kind of say it's an object I felt before.
When you're born, yes, youprobably know nothing.
So you have to learn everything,but you start building up this
sort of language of componentsand objects.
And so when I learn a newobject, I don't really, you know
what, I don't just move myfinger over everything and sense
every single point on theobject.
Matt (09:01):
No, you sense it enough to associate it with things you
already know.
Jeff (09:04):
That's right.
So the idea that you are movingand sensing and moving and
sensing is of course correct.
But what you're really doing isyou're moving in and inferring
substructure that-- So I see, ohthis is the, this is a circular
rim and this is a handle andthis is a cylinder.
I don't.
And so it's not like I have todisassociate the raw sensory
(09:25):
input with the location.
I'm using the location to infera structure that I already know
and then and say, oh I'm nowtouching a handle.
Matt (10:31):
I know where the handle is and now I'm touching a cylinder
and I know where it is.
(11:03):
And I didn't have to touch allthe points on this handle.
I didn't have to hit all thepoints of the cylinder, but, but
now I can associate the handlewith a cylinder.
So it's close to what we wroteabout in the Columns paper.
It's close to what you said.
It's, we're moving and sensingand moving and sensing, but in
reality what we're doing iswe're moving and inferring
structure more than what I cansense.
It's not like I have to goaround- It's like a, it's like
(11:24):
if I want to learn a map of aroom in my living room for
example, I don't have to go andtouch every part of every piece
of furniture to say, where doesthis chair extend to?
And then you know what'sexactly...
I can say, oh, that's a chair.
And, and, and now I can justsay, oh, given my point in the
room, I know there's a chairhere and given I know where the
location of chair is, I canpredict there's going to be an
arm or back or something.
So it's, it's a, it's a bit moresubtle than just sense,
location, sense, location.
So you can operate upon itwithout really knowing what it
is.
Jeff (11:29):
Yeah you can operate.
And this is what grid cells, themagic of them is.
And so the only way to buildyour quote map of the world or
map of an object is you have tosay, start in one place, move
and, and then say, Oh, here's mynew location.
Like, here's some random numberof thing that hit my
notification.
What do I see it there?
And then move again.
And what do I see there and moveagain, what do I see here?
So, uh, unlike high school mathyou'd say, oh, x, Y, and Z,
(11:54):
that's my location and now I'mgoing to move, you know,
increase x by two.
You can't do that.
You have some sort of, um, theonly way these points are tied
together is through movement.
Speaker 1 (12:05):
That's the only way they're tied together.
Matt (12:07):
That's the tricky thing.
And then trying to get to thecenter of here-
Jeff (12:10):
it takes honestly, it took us a while to really get, get
it.
Matt (12:14):
Because I always felt like, oh, each grid cell code
was a, like a coordinate orsomething, eh, not really.
Jeff (12:21):
We should come up with a good analogy.
Matt (12:23):
I wish.
I like that people call themcodes.
I guess that's something.
It's better than nothing.
Jeff (12:29):
Yeah.
Matt (12:30):
But the idea that objects are defined as, as sort of as a,
as a transition between thesetwo movements and a sensation.
Jeff (12:36):
No, it's really the oobject is defined by different
locations you're in and the onlyway to get between those
locations is through movement.
Um, and there's no other way.
Like if I say what's over there,I can't say what's over there, I
have to say, oh, I have to move.
Matt (12:50):
Because that's the only way you were ever able to
experience the object.
Jeff (12:54):
There's that plus that's the way grid cells work.
If grid cells worked likeCartesian coordinates we learned
in high school, then youwouldn't have to do that.
But they don't work that way.
That's by the way, here's oneway to think about it.
People who do computer graphicsor animation or 3D cad.
So those programs all work on X,y's and z's.
(13:16):
You know, I have a referencepoint and I say, okay, I'm going
to make a cad model of my CoffeeCup and I'll say, here's the
point, the zero point, and thenI can define all the features
that are related to that zeropoint.
That is not what the brain does.
The brain doesn't have a zeropoint.
It just has a bunch of pointsthat are tied together by
movement.
Matt (13:33):
But the interesting thing is you can take two points in
cad and you can define atranslation between them and you
can't do that with grid codestoo.
Jeff (13:40):
You can, but in a very different way.
Matt (13:42):
Yes, it's not a Cartesian distance formula at all.
Jeff (13:46):
Yeah, Cartesian coordinates are pretty easy.
You just do a little bit of mathand you get your answer.
Here it's not that way and thisgets to this displacement
transform that we've, we'vediscovered here that allows you
to say, okay, given two pointsthey look kind of random.
How can I establish a vectorthat says where, where, how far
(14:09):
apart they are and whatdirection are they are from each
other and you can do that andyou do that going back through
the grid cells.
It's Kinda like, it's, I'm notgoing to try to explain to here.
It's complicated
Matt (14:19):
Okay.
Okay.
I got to ask a question aboutthis.
So say you have an object andyou have two points and you have
a transition, something thatmoves from one point to another.
Can you apply that to any pointon the object and expect the
same movement to occur in thatspace?
Jeff (14:35):
Uh, we're, we're mixing a couple things up here, Matt.
Essentially there's, the brainuses grid cells in two different
ways.
One is to build maps orstructured defined objects, and
the other is to tell me how tomove my body.
Okay?
Okay.
There's really two separate waysof doing that.
So I can apply grid cells andsay, Oh, my finger's at one
(14:55):
location and I wanted to go toanother location.
How do I move my finger to getthere?
Then I could say that- it turnsout the mechanism that does that
- animals had to solve this along time ago.
Like, Oh, I'm, I'm in the woods.
How do I get home?
I may go a way I've never gonebefore, but I know which way to
(15:15):
go.
So then we think what hashappened is the cortex has taken
that same mechanism but appliedit to a very different purpose.
Matt (15:21):
Now you're talking about path integration, right?
Jeff (15:24):
Path integration is when you physically move, what is
your new location?
So I'm saying,I wasn't reallytalking about path integration.
I was talking about given, if Icould tell you here's a point in
space and here's another pointin the same space, like here's
where I am in the woods rightnow and here is my home is and I
(15:45):
know those two representationsof location and, and they're in
the same space because as Iwander through the woods to get
to where I am now, I pathintegrated.
They're in the same cloud ofpoints, but.
And so that's important.
Yes, but now I can say I know Ican calculate even though I can
calculate the straight way fromwhere I am home, even though
that's not how I got here.
Matt (16:04):
Right.
Jeff (16:04):
I wandered around in the woods and now I'm saying, okay,
I need to get home.
I can calculate the straightpath home.
That's kind of clever, um, thatyou do this without using the
Cartesian math.
Matt (16:15):
Yeah it is.
Jeff (16:15):
Okay.
So there's a, there's amechanism for doing that.
Uh, we think we understand thebasics of that mechanism and now
that same mechanism is, is usedto figure out how to move my
finger from the Coffee Cup to mynose.
Like it's the same problem.
Like, Hey, my finger's overhere, how do I get to my notes?
So that's very analogous.
I hope you can see the analogy,the analogy between like I'm in
(16:36):
the woods, I need to get homeand from I'm on the Coffee Cup
and I want to touch my nose.
I'm on a coffee cup, I want totouch the wall or something like
that.
Yes, that's going on in thecortex.
But that's what we call thewhere pathway to the cortex.
Now that same mechanism can useto be used to define object
compositions.
Right?
This is a tricky idea, but if Ihave two different objects and
(16:56):
they have their own spaces,right?
If I move in one object, I don'tactually move into the other
space, I just don't do that.
But imagine these two objectsphysically or in the same world
together.
So there's a point.
Let's go back to the Coffee Cupof the logo.
I have a space around the logodefining the logo, right.
(17:17):
And I have a bunch of pointsaround the cup, defining the
cup.
There are two different parts ofthe world where there's two
separate things (17:22):
there's a cup and there's a logo.
Now, right now they're in someon my cup those two things have
a fixed relationship to eachother.
Matt (17:29):
They're sort of on top of each other.
Jeff (17:31):
It doesn't even have to be on top of each other.
They have a fixed position.
That's the important part.
They're fixed.
Now it turns out that the logois on the cup, but that doesn't
really matter.
At this point, it's not movingrelative to the cup.
If I take a point on the logo isa location logo at any point in
time there'll be an equivalentlocation on the cup.
(17:52):
It happens to be the samephysical location, but there are
two different representationsfor it.
One's in the space of the cup,one's in the space of the logo.
Matt (18:01):
That makes sense.
Jeff (18:01):
So now I have two points, two locations.
They turn out to be physicallythe same spot in the world, but
they're literally two differentlocations because one's relative
of the Coffee Cup and one'srelative to the logo.
Matt (18:15):
Two different locations in two different reference frames.
Jeff (18:17):
That's right.
But right now, because I'm notmoving the logo, the logo's
fixed relative to the cup,there's a one to one
correspondence between points inthe logo space and points and
the cup space.
Doesn't matter, because they'refixed relative to each other.
Yeah.
And so now I have these twopoints and what I'm going to
(18:38):
tell you is I can take the samemechanism that was used to
navigate from the woods to homeor from the cup to my nose,
which is two points in the samespace.
How do I get from the point in,you know, in the woods to the
point of where my home is,that's the same space, the same
environment.
Or now I'm gonna apply it to sayhow do I get from a point on the
cup to a point on the logo?
Matt (19:00):
Between spaces.
Jeff (19:01):
Between spaces but physically actually not moving
at all.
Physically, it's the same pointin the world.
Matt (19:06):
Right.
Right.
Jeff (19:06):
But I'm going between one point in logo space and the
equivalent point in cup space.
So I'm converting between twopoints.
Matt (19:14):
And you're not moving at all.
Jeff (19:15):
I'm not physically moving at all but by-
Matt (19:18):
This kind of trippy, like a wormhole or something.
Jeff (19:23):
That's a good analogy.
It's kind of like like a littlewormhole.
How do I get to another place byjust not moving?
Matt (19:29):
In your brain, it's easy apparently.
Jeff (19:32):
Yes, it's a very clever idea.
And Marcus came up with theunderpinnings of it and um, um,
we were working on this problemtrying to figure how it does it.
And he came up with some of thebasic of the solutions that was
really clever.
But it was actually motivated bysome work that was previously
done about how animals canfigure out their way home in the
woods literally.
(19:53):
How does an animal navigate fromhere to here?
There was a proposed mechanismfor that and we said, oh, that's
kind of similar to the problemwe want to solve instead of the
question, would it solve thatproblem?
So we think it does.
And so, so it's the samemechanism, but now I'm not
moving at all.
I just like saying it's themovement of like an attentional
shift.
I'm saying attend to the logo,attend to the cup.
(20:14):
Attend to the logo.
Attend to the cup.
Matt (20:15):
Oh yeah, yeah.
Yeah.
Jeff (20:16):
And as I do that, I switch spaces.
And I can say, now I can say thefollowing, I can say, well, my
hand, my finger is touching thetouching the logo right now.
Where will it be on the cup?
And I can figure that out byusing this transform.
I can say, oh, I know where itis on the cup.
(20:36):
So now I move my finger relativeto the cup.
I can say where's my fingerrelative to the logo.
Uh, in this case I can't reallyfeel the logo, but in general
that's the general idea.
So a clever idea.
It's an old mechanism thatevolved a long time ago.
We think it's been repurposed todo this thing and I realized
some of these concepts are verykind of bizarre.
(20:57):
They're actually very elegantand beautiful once you
understand them.
Matt (21:00):
Oh, it just takes so long to distill them into the
simplest form.
Jeff (21:06):
And, and part of our challenge is to pick out the
right language to do this andwhat's the right metaphors with
right examples.
But I don't think it's any moredifficult than other things um,
a lot of the listeners willknow.
If you know how computers workor how deeply how software
works.
For example, like the first timeI learned about a real time
operating systems and reentrantcode and how the stack point it
(21:26):
works when you're doing, you'remanaging code.
And these are details mostprogrammers don't know, but some
programmers do this.
That stuff is mind blowing atfirst.
It's like, oh my God, how doesthat really work?
Is it really possible, all thestuff does it like that and can
it do it fast enough?
And, and you know, it tookawhile for me to really
internalize the nature of a realtime operating system.
And why does it look like it'sdoing all these things
(21:47):
simultaneously when it's reallynot.
Um, so it's kinda like that.
It's not that hard.
Anyone can learn it, if youknow, but you got to work out a
little bit, right?
So the first time if you'venever seen a computer before and
somebody just dumped on you, ohthere's this reentrant code and
it works by moving the stackpoint around and we use
temporary variables that arecomplicated and moved over here.
And it's like, well what thehell are you talking about?
Matt (22:09):
There's a lot of new concepts coming in neuroscience
right now and people are tryingto keep up with it.
Jeff (22:14):
These concepts are, uh, are sort of similar difficulty I
would say, but if you've spent alittle time,we're trying to
write these papers in a way thatanyone could read them and get
it.
I'm not gonna sugar coat it.
These are not obvious things,um, the nature of grid cells and
(22:34):
how they work.
It's kind of bizarre and even alot of neuroscientists don't
really understand it.
Matt (22:41):
Nobody said the brain was easy, that's for sure.
Jeff (22:43):
But it's not ridiculously complicated.
It's more like the concepts arenew.
Matt (22:48):
When I first got what grid cells are doing, I was blown
away to see that, that, thatprocess was happening in your
brain like almost just byitself, it just emerged.
It's amazing.
Jeff (23:00):
Yeah.
It's a very clever idea, butit's no more clever than
Cartesian math.
You just said you learnedCartesian math when you were in
high school and you were exposedto it for many years, now you
get it.
You know, if you'd never beenexposed to any kind of
mathematics like that and Itried to teach you, you know,
it'd be hard, it'd take awhile.
So grid cells are like that.
(23:21):
They just work on completelydifferent principles than anyone
new until fairly recently andum, it takes a little while to
sort of internalize it and getit and go, oh, now I know what's
going on.
Matt (23:31):
Now it's almost hard to keep up.
There's so much literature outabout it.
Jeff (23:34):
Yeah, but the basic premises aren't changing.
It's all these little detailsaround the idea, I think what
we've done is, is significantlyextend it.
We've significantly extended thetheoretical basis for grid
cells, uh, understanding whatthey do, how they can do object
compositions, how they canrepresent behaviors.
These are ideas that I don'tthink anyone's ever thought of
(23:55):
before.
I'm not aware of it.
And even the idea that thecortex is using grid cells to
build models of the world, uh,in the same way that the
entorhinal cortex andhippocampus is using to build
models of environments.
The cortex is learning models ofobjects.
Even that idea is new.
I mean, there are peopletouching on the edge of it, but,
(24:16):
um, it's a pretty big idea.
So we're not aware of thatexisting out there in the
literature right now.
So we think those arecontributions that we can help
make.
Matt (24:29):
So Jeff, I think we're running out of time.
I have a couple more questionsfor you, but I think I'll just
put that off until the nexttime.
Jeff (24:36):
Alright, well that'd be great.
I think we should check in everyonce in a while on this and see
what's new.
Matt (24:40):
Yeah.
Um, well we've got a podcast nowso we'll have you as a guest
another time.
Jeff (24:45):
Things are happening here rapidly here at Numenta.
We are learning, you know, thesesort of pieces are falling into
place.
I've said this before, it's sotrue.
Um, so it's an exciting time andum, and that means it's going to
be new things all the time.
Matt (24:59):
A lot going on this fall.
So stay tuned to Numenta, keepwatching numenta.com and follow
our YouTube channels and stuff.
Thanks Jeff for joining me forthis chat and it was a pleasure.
Jeff (25:10):
Thanks Matt.
It's always fun talking to you.
Matt (25:11):
All right, take care and don't forget to subscribe to our
podcast.
Thanks Jeff Hawkins.
This has been Numenta OnIntelligence.
If you like what you hear on thepodcast and you want to discuss
ideas like this withintelligent, friendly people, be
sure to join HTM forum atdiscourse.numenta.org.
Our online community was createdaround the Numenta open source
(25:34):
project and continues to thriveon HTM forum.
Hundreds of folks interested inHTM and related theories, share
ideas, experiments, and opensource code.
If you are an HTM theorist,engineer or a programmer or just
a hobbyist, HTM forum is afriendly place to keep up with
the latest on HTM technologies.
Thanks for listening to NumentaOn Intelligence.
(25:55):
Be sure to subscribe to ourpodcast on your favorite podcast
service.
To learn more about Numenta andthe progress we're making on
understanding how the brainworks, go to numenta.com.
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