Practice English Speaking&Listening with: The first class(ification)-oriented representational...

LEV GOLDFARB: All right.

This title is not a frivolous.

So I'm going to suggest to you that we don't have formalisms

for talking about classes, and we, therefore, do not

understand very well what classes are.

So this is sort of related things.

So the first third of the talk will be about the sort of

formalisms that we have and why they are inadequate for

dealing with classes and, therefore, classification.

And two thirds of the talk will be about this new

formalism that we have been working for many, many years.

And this is just hot off the press even though this is the

fifth version.

But it's a much more satisfactory version.

So let's take a look-- we have to deal with very

basic issues here.

First, what is a numeric representation?

Well, this mapping did not really appear for a long time,

historically, but eventually we began to represent objects

by numbers.

Primitive tribes are still using knots and so on.

So the numbers actually should be thought of in this way, not

really as representations of things that be can eventually

be used as a representations.

But in any case, this is sort of a view of what is a numeric

representation is.

Notice there's no concept of class here appears.

So numbers, we have natural numbers, there

are no classes there.

Natural numbers is no different, In fact, even if

you go to real numbers.

So this step is not a big step as far as the representation

of formalism is concerned.

I want to allow questions during the--

not discussions--

because then we can proceed at a reasonable pace.

Discussions we can do at the end of the talk.

So first of all, a little bit about the classes.

Well, if you look carefully at objects in the universe it

turns out there's no single object that exists outside the

environment of its class.

So these are tightly linked things.

Whatever we look at there's always associated classes.

There is no object that exists outside the class.

They are co-existent concepts.

So it's important to understand, then, that there

must be some tight link between objects and classes.

And that's sort of the business of induction, is the

reason biological information processing is so effective it

sort of relies--

it's a built-in mechanism.

And therefore it must exist in nature too.

So it's not our invention.

It must exist.

Let me propose the definition of what means class-oriented

representational formalism.

We want to have a formalism that does the mapping of

objects, but that this mapping automatically induces the

mapping of the classes.

So the way we define classes in the representational

formalism should correspond to those classes.

So we should not invent, then, what the definition class Is?

It must come with a representational formalism.

So those two postulates.

And I'm going to discuss them in greater

detail in the next slides.

So what are the implications?

I'm saying nontrivial but it's not a particularly difficult

one, we can discuss later, that first of all, that the

class must be used by object mapping.

So it's not something we should be sweating a lot

about, introducing classes.

And they should automatically capture

the classes in reality.

So here is our representational formalism.

Once a define class here, it should capture exactly the

corresponding class that exists in reality.

And we will discuss later on why conventional

representation, certainly vector space representation do

not satisfy this property.

And also, what about the general

structure of this concept?

So we are not going yet into details but there's something

about general formal structure, what we want to

have [UNINTELLIGIBLE].

We would like to have this situation.

The class representation must be expressed with basic object

operations.

If we violate this we would violate the first basic axiom.

Now I'm just drawing your attention in this slide that

we don't have the concept of class representation.

And this is not really an accident, even though it's

quite unreasonable situation to do classification without

the concept of class representation.

But I'm saying that it's not accidental.

It just happens so that conventional formalism do not

really support an adequate concept of class.

We kind of have to add it post-hoc.

So you can think about that situation where to which

extent we have the concept of class representation.

Now, moving on to this sort of structure what we want to

have. We want it to be an

inductive generative structure.

So what does it mean?

Generative structure is similar to what Chomsky was

talking about grammars.

We want to be able to generate every object in the class, and

only those objects.

And it must be inductive.

Now inductive formal grammars don't possess that property.

Inductive, it means it must be effectively, reliably,

recoverable from a small training set.

That's what inductive is.

So this is just I'm reminding there was syntactic popular

area in '70s, '80s, inductive pattern recognition, where

they tried to adopt formal grammars to describing classes

of parents.

But it sort of fizzled out because of the problems I will

discuss in a moment.

So what is it related to, the inadequacy of formal grammars?

Well Chomsky actually never believed, as I mentioned here,

he never believed in induction.

Because first of all, on the one hand he couldn't see

connection between formal grammars and induction because

there's no tight link between set of strings

and the formal grammars.

Sort of formal grammars is sort of god-given.

Somehow it appears with all the rules and

productions, and so on.

And the difficulty, of course, has to do with even the

underlying string representation.

They just don't carry enough information to allow this

recovery of class representation.

Well here's just a simple example.

If you take two strings because they don't have

formative history embedded in them as a part of their

representation you can't really distinguish between

those two strings, even though, if you go to a little

bit more precise

representation, this is not tree.

This captured the formative history.

You will see that they are different.

And this is what is indicated with green and red, that you

had aba and aca applied where the second a was the context.

While in the second case the first a was the context, which

is very different situation.

OK.

I'm going to discuss a little bit vector

space in several minutes.

Well here is a formal definition, just to remind you

what a vector space is, you know, these famous eight

axioms. But basically you have two operations.

Now what does that mean from applied point of view where

you define vector space in this way?

This is standard, formal definition

of this as a structure.

So we must assume that representational structure is

the algebraic structure.

There's simply no other candidate for

representational structure.

So we must assume that it is this

operations that act on object.

And accordingly, here I'm just discussing why this was

systematically overlooked at.

But accordingly, what are we allowed, then, if we assume

that these are the operations on the data and that's what

mathematical description of that formal structure is?

We must demand that the class representation is expressible

via these operations.

The only candidates, then, become affine subspaces, just

shifted this linear subspaces, because they have to be

consistent with underlying structure.

Now from applied point of view, this linear

generativity, obviously, is going to capture--

AUDIENCE: So why can't you represent a class as a

half-space, for example?

AUDIENCE: Could you repeat the question please?

AUDIENCE: I'm sorry.

Why can't you represent a class as a half-space if you

choose a vector space representing a half-space.

LEV GOLDFARB: They do not feed this standard [? mass. ?]

You want to have class representation, every element

in the class be generative.

In other words, the class description must be of

generative type.

Every element must be expressible via basic

operations of class representation.

So if I give you a training set, and also here is

inductive, the second part comes in.

You want it to be recoverable uniquely from a finite

training set.

So you want to have this both things, generativity and this,

how would you define, then--

If I give you finite training set, and you would say the

class would be half-space, which

half-space would you choose?

AUDIENCE: I'd [UNINTELLIGIBLE] margin half-space.

Let's say the half-space that separates the training data.

LEV GOLDFARB: No.

Suppose I give you just one class, this training set from

that class.

How would you choose which class representation would be

reasonable for, if I give you whatever, 20 vectors?

AUDIENCE: [UNINTELLIGIBLE] of one class.

LEV GOLDFARB: How would you define because you want to

have those two properties, the generativity and everything

should be expressible via basic operation, this vector

addition and multiplication?

How would you define class elements?

How would you give me exact--

you have to generate every class element.

AUDIENCE: Why do you feel that this ability is

necessary for a--

LEV GOLDFARB: Well, because if you think about here is the

real classes and here is your formalism we want to have the

object mapping induces class mapping.

So if I have certain objects in the class I want to be able

to generate every object of this class only, and only this

object in the class using class representation.

I want to have this one-to-one mapping between real objects

and objects in my formalism.

AUDIENCE: So one thing that's been proposed for a one-class

classification is to find the half-space whose co-efficient

vector has the smallest [UNINTELLIGIBLE], or

something, that satisfies constraints of the--

enforce the fact that all members of your class are on

one side of the half-space, for example.

LEV GOLDFARB: But again, if you take, again--

let's go back to the real object in this mapping.

You remember this mapping from real

object into your formalism?

You want to ensure that after you do this that all object

that you can generate in your formalism, every object that

you can generate in your formalism, correspond to the

physical object that you are dealing with, with the class

you're dealing with.

I mean this mapping is very important because you are

mapping the actual object into objects in your formalism.

So you want to have a very tight link between the actual

object and the object that you have in your formalism.

So once you say it's a class representation you have to

then claim that every object that fall within this class

has a corresponding object in reality, which

will not be the case.

You want to have it a strong restriction.

It's a very strong restriction on what you want to have as a

representation of formalism.

AUDIENCE: Yeah.

So I guess depending on what you call a class, which I

guess is what we were talking about over lunch the would be

[INTERPOSING VOICES]

LEV GOLDFARB: Well, no, you don't want to call anything

artificial class.

You want to define class in such a way that this mapping

is validated.

Because representational formalism is something that

you're going to use to represent the actual objects,

whether it's a web page, it doesn't matter.

You're going to use that representational formalism to

map object.

So once you are in your representational formalism now

you have to live here.

But that means you cannot invent the concept of class

that is not meaningful over here.

So once you map the object you're done.

You are not allowed--

you don't have any other means--

to change what the class of actual objects over here on

the left-hand side.

Because you're dealing with real objects.

You just representing them in this formalism on the

right-hand side.

So once you map them that's it, you have no control.

So the whole point is that once you do this mapping,

realize you want it to be automatically induced the

mapping of this class onto this class.

It's a strong requirement but what I am suggesting that this

is sort of a necessary requirement.

You see, if you do not satisfy that condition you will be

defining classes here that has no reality over here, and

that's a problem.

AUDIENCE: It just seems to me that it's impossible to define

formalism like--

LEV GOLDFARB: You will see now.

That's what I am going been talking about.

This is most of the talk will be about.

AUDIENCE: But then the question might be, are there

things that we would call classes that are not captured

by this formalism as well?

If you define a class to be things that are captured by

this formalism?

LEV GOLDFARB: But you will see.

No you will see--

formalism is universally applicable because this

formalism all object can be encoded, therefore, it's very

easy to check if there are real classes that--

once you have that mapping and you use this formalism, then,

if you can find classes here that are not classes in your

formalism then you're done.

Then you know it's not good.

But you will see it is not like that.

So anyway, what I am suggesting that to compensate

for above paucity of, not classes, but this classes

according to that definition, and in violation of sort of

wisdom in mathematics.

One brings alien class representation and, therefore,

alien classes.

So you bring things like nonlinear functions and other

things to define class.

They have nothing to do with the structure of this vector

space, which is algebraic.

This is a representational structure.

That's the whole point, that if you want to treat objects

this way, if you want to take your representational

formalism seriously, you must take the operations on objects

also seriously.

So this is a typical picture.

Here is your class, and you have some nonlinear decision

surfaces here.

Now everybody got used to this.

It took me 10 years to ask this kind of question because

I also was used to these things, assuming that that's

OK, you know, this is how things look like.

But the question is how meaningful and informative

such class description, if you call this classes?

What do we learn when I draw these curves

in the vector space?

How much did I learn about anything real because this

class is going to respond to reality?

How much am I learning about reality when I am drawing

these kind of curves in a vector space or surfaces?

What am I learning?

Well, it's useful to ask this question because you want to

be able to say that when you've gotten class

representation that you learn a lot of things about reality

because that's sort of the purpose of induction.

And this is where the hidden induction--

this is what philosophers thought.

That we should be able, when we say we learn something,

class, we should get wiser.

What are we learning about actual objects

when we draw this?

But anyway, let me move on.

So there is no tight link between the training set and

the class representation.

And that's a big problem because we want to have a much

tighter link so it's things are uniquely deducible, the

class representation.

So what are we learning during the

learning process, basically?

So the problem is not with learning algorithms, that's

what I am saying.

It is a much deeper underlying problem with the

representational formalism itself because the structure

of this representational formalism is such that you

cannot remedy this deficiency to begin once you're there.

So I'm saying the more intransient in machine

learning is, again, these distances, kernels, and so on,

they don't change.

I'm just listing again, it doesn't change the basic

situation that we have been discussing.

You still don't have meaningful class a

representation, and that's a big problem.

So we've got to move-- as hard as it appears--

we've got to move on.

And the benefits are tremendous because once you

have that kind of formalism you are really doing--

it's not just important for information processing,

classifying web pages, but you also, from point of view of

biological--

when you have these protein data banks you have a good

description of these classes to meaningful description,

which it would be then very illuminating to biologists.

It won't be just something that one uses only for some

strange auxiliary purposes.

And of course as far as the search engines are concerned,

well, imagine if you have that formalism you'll represent

classes and you use it as a basis for

organizing search engine.

And then the query will be either a class element or

description of a class, two things are possible.

So the user will be a certain interface, either will

specified class element or will specify

description of class.

And he will get, as a result of query, the class itself.

Well, here I am discussing where the origins of this

[? word ?] go back to 1990.

It's a long paper published in Pattern Recognition.

This is the website for the latest version.

It's a 70-page paper but it's well illustrated.

And its just 70 pages, I think we removed all the

[UNINTELLIGIBLE PHRASE].

Just the basic concept there, it takes 70 pages, but there

are a lot of illustrations.

There's a formal decision, here I'm just going to give

you informal, just intuitive feeling for what's going on.

So as a scientific view we would like to view the reality

as a multitude of interacting and evolving classes of

structural processes.

That's all.

Let's say let's view reality as this.

In fact, that's what it is, any bottle, any desk.

This actually is a process, and you will see next.

If you think about a chromosome, because it has

genes, this is a poor representation.

A string is a poor-- it doesn't correspond because, in

reality, it's a dynamic process.

This is how it was created, and this is how it gets

translated, and so on.

So there is a process involved and string doesn't capture

this kind of reality.

So--

pardon?

AUDIENCE: But a string captures a more abstract

concept because different chromosomes could share the

same DNA sequence, right?

[INTERPOSING VOICES] a chromosome in different

configurations.

LEV GOLDFARB: Yes, but you remember what I mentioned

about strings earlier.

That if I give you--

even never mind the sort of more pragmatic point of view,

but just doing learning--

if I give you finite set of strings why there are

infinitely many classes of strings currently, according

to the current concept, that contain this finite set?

That's not a palatable situation.

You don't want to have that situation.

Why?

Again because a string does not carry within itself

sufficient information for doing this adequate recovery.

AUDIENCE: But I think there are reasonable principles to

use to choose from among the infinitely many concepts that

are consistent with a finite set,

LEV GOLDFARB: They would be somewhat ad hoc principles

that would simply have to be put in in order to deal with

that big problem.

AUDIENCE: And there's a trade-off between how ad hoc

or principled a solution is and how useful it is.

LEV GOLDFARB: But the whole point, you see, of having a

good formalism for classification you don't want

to introduce this kind of assumptions.

You want to get into representation and you want to

move on with it and doing easily the job

that you need to do.

You don't want to introduce later on all kinds of ad hoc

assumptions.

AUDIENCE: It depend on what you want to do, I suppose.

LEV GOLDFARB: No, I mean, in general that's the idea of

representational formalism.

If you look back at these first two axioms, once you

represent the objects you want your

classes to emerge naturally.

You don't want to do any hocus pocus.

You want them to be sitting there.

AUDIENCE: But it depends, right?

If somebody has an engineering objective to build an

interface to a database where scientists can put their

sequence and it tells them something about the likely

function, let's say, of a tissue sample, or

something like that.

The representation depends on the DNA--

LEV GOLDFARB: I'm sorry, what are the classes here?

What would be the classes?

AUDIENCE: The class might be proteins with a given

function, I suppose.

LEV GOLDFARB: Proteins with a given function.

Right.

So that's precisely fit into this concept of class.

AUDIENCE: But a representation that depends on the DNA coding

for the protein might be a more convenient and effective

way to design an engineering [INTERPOSING VOICES].

LEV GOLDFARB: Not necessarily, If it is known that there are

proteins that have very similar DNA structure or RNA

structure but they have different function, quite

different function.

AUDIENCE: But the existence of those cases doesn't

necessarily mean that it isn't an effective engineering tool.

[INTERPOSING VOICES]

LEV GOLDFARB: No, it's an indication that you cannot

grasp effectively class of these.

The whole point is you want to have a reliable grasp of the

class that you are dealing with.

That is the purpose of classification.

You said yourself, you want to be able to say that this class

of proteins have very similar functions.

That's the purpose, I assume, you told me that would be the

definition of that class.

AUDIENCE: [INAUDIBLE]

LEV GOLDFARB: Right.

So if you want this, then you automatically want--

if I give you a small training sample, 5, 10, 15 proteins,

you want to be able later on reliably say whether other

proteins belongs to that class or not.

And more importantly, you won't be able to answer that

question unless your class representation contain some

nontrivial information related to the function of this

protein in some form.

AUDIENCE: Yeah, like the DNA sequence.

LEV GOLDFARB: No, but DNA sequence

AUDIENCE: Yeah, but he's talking about-- you're talking

about folding a protein.

The same sequence can fold in different ways under the

influence of other things in the system, which really ties

into his argument where the temporal process is the

folding and there are a lot of other elements involved in the

protein folding beside just the DNA sequence.

AUDIENCE: [INTERPOSING VOICES] chromosomes.

LEV GOLDFARB: No.

But this is again--

AUDIENCE: [INTERPOSING VOICES]

The chromosomes are the source code that describes the DNA

sequence, but the sequence has to be executed in the rest of

the system that causes the folding to occur that

eventually produces the behavior of the protein.

The behavior of the protein is really just determined by how

this folded and not just by the sequence itself.

AUDIENCE: But that fact doesn't necessarily imply that

one must design induction engines that are going to

reason about classes of proteins using representations

of proteins that involve all the details of the

evolutionary history of the protein and--

LEV GOLDFARB: No, no, no.

We are not talking about this yet.

AUDIENCE: It's not evolutionary history, it's

just an individual--

AUDIENCE: Process [INTERPOSING VOICES]

which protein involved.

[UNINTELLIGIBLE]

LEV GOLDFARB: No, no.

We're not we're not talking yet, I think this is what you

added yourself right now.

I haven't suggested that you have to plug in entire

information about protein.

I'm only telling you that your representation of formalism

should be reliable enough that it will capture the class in

the right way with this function.

And the string does not have enough information.

AUDIENCE: It depends.

It depends on the class that you're trying to describe.

LEV GOLDFARB: Well you gave me an example of a class, right?

So I'm assuming we're discussing that class.

AUDIENCE: There are some classes that can be described

very well by their DNA sequence.

LEV GOLDFARB: Well I don't know of any classes, except

very trivial ones, that would be described by DNA sequence.

AUDIENCE: A chionesis sequence, I suppose.

So chionesis have a protein sequence that highly conserved

the code spore region of the protein that attaches to a

particular type of molecule.

LEV GOLDFARB: Right.

But for example, I can give you a sequence very close to

the ones that you think belong to that class that will not be

doing this at all.

AUDIENCE: But for the engineering purpose of

classifying real proteins the scientists really encounter--

LEV GOLDFARB: No, no.

When you say real, but this would be real sequence because

I can manufacture you something that will have

exactly that sequence but will not behave in that way.

AUDIENCE: But the inability of my system to handle that

artificially created sequence--

LEV GOLDFARB: It's not artificially created, this is

a real thing.

I'm talking about create a real--

AUDIENCE: I mean that those type of circumstances will

arise infrequently enough that my engineering tool will,

nevertheless, be useful.

LEV GOLDFARB: Why are you so sure about this?

AUDIENCE: A tool of that type is being used as we speak.

LEV GOLDFARB: No, no.

It is being used because we don't have other tools.

It is not being used because it is superior to the tools I

want to discuss because these tools have not been around

yet, the ones that I want to discuss.

AUDIENCE: I guess what I'm arguing for is a possibility

that abstract representations, which leave out some aspects

of the items that we wish to classify can, nevertheless, be

useful engineering.

That's the only proposition--

LEV GOLDFARB: Yes.

But this is general enough statement.

What I want to discuss is I want to discuss, today, is

what is important to have in the representational formalism

that will give you a reliable way to deal with

specification, not that is what is possible to do.

Of course, if you are poor in the representational means,

yes. but why not, if you have a more powerful

representational means, why not to go for this because you

will have a much more precise picture everything?

AUDIENCE: But sometimes that structure can be powerful

because it can save you unnecessary effort on sorting

through the vast complexity--

LEV GOLDFARB: OK.

You will see, as we go down, you will see why it is true.

There is a certain hypothesis you will see coming up.

I just beginning to discuss this temporal process that is

very important.

First, I just want to remind you there were a few Nobel

Prizes even awarded in the last 15 years in the

evolutionary developmental biology.

If it look at the body plan, it turns out that all animals

have roughly, what, 500 million years ago there is a

regulatory genes that organize during the

development the body plan.

And you go from mammals, and you go to flies, and they're

very similar.

Of course, there were some modifications.

So I'll come back to this.

I just want you to keep in mind this sort of regular

proteins that organize things.

So what is a body plan?

You can think about each segment as a class.

And this class is being modified evolutionarily.

But think of each body segment also as a class, and you build

larger classes out of the smaller body segments.

But we will come back to this one.

Well, what about other data?

OK.

Let's look at web pages.

Web pages should not be treated as static.

So what we are talking about is not whether you can

represent-- you can always represent something

in a very poor way.

We want to understand what means a reliable

representation for the purposes of classification.

What is a good representation for the purposes of

classification?

That's what we haven't discussed.

We are not discussing whether--

we can always go into poor

representations for various reasons.

But to do classification, that's what we are discussing,

which kind of representation.

So the web page, we are interacting with the web page,

so it is not a static object.

If you think about it, even the way we represent web page

we are sort of interacting, and here is the time element,

so there is a process involved.

So I'm preparing you towards objects as processes view.

This is what will be done.

So if you're talking about classes of objects, we are

talking about now about classes of processes.

So each object kind of will be-- you will see now, I

haven't defined this formally yet, it's just

something like that.

So what is the basic formal units here?

They are called primitives, more fully, primitive

transformations.

This circle, now, this is an abstract primitive.

What it defines is this.

Each of these figures on the top correspond to a class of

processes that are coming in.

Then they interact and something, other classes, are

being produced, sometimes similar.

So this is the unit of representation.

This is atomic units of representation.

And what do they capture?

They capture a set of events because everything now

processes, so we use events to represent things.

Events understood as interaction of classes.

So this is a concrete primitive.

Unfortunately the figures are the same but now you're

talking about concrete process that belongs to the class, so

you can think of concrete object.

So those [? c1, ?]

1 and cj2, and so on, these are the concrete processes in

our concrete elements of the class.

So this is a concrete primitive.

And this is a label, if you see that.

What is the label?

Label is a way, because we are not going to be writing those

processes on the top, so this label b capture the sequence

of processes.

And well, when you observe it, your sequence of events, it

just happened that this process turn into the terminal

process, so-called, for one primitive became an initial

process for another primitive.

Now primitives are events, they're just encapsulating

events that you observe during the interaction, whatever.

So just some very light examples.

Car collision, OK?

You have an event, right?

Two processes come in and two processes come out.

Two cars were driving, this is the two

processes, two objects.

And this sentence.

Take a sentence, John fell in love with Susan, OK?

Well if I tell you that John fall in love with Susan, as

far as you're concerned, you're representation is just

an event to you.

That two processes, one of the way of modeling it.

Two initials and two terminals, because you change

your perception of those two people, so

something happened to them.

It's not the same John and it's not the same Susan,

something was added.

This event added something to this.

But you continue, John is still John, but it's a

slightly different.

This is what is shown.

So Alice and Bob had a baby.

Again, having a baby, two initials three terminals

because you knew Alice and Bob, now, there are three of

them, and so you have three processes.

Let's go more scientific example, so to

speak, is into physics.

This was inspired by Feynman diagrams but

they are less precise.

They are capturing this situation less--

you will see now.

You will see several examples related to this.

So you have primal processes, this are the processes that

come in and come out.

They're called primal processes.

You see, you don't know at the basic level, you don't know

yet the structure of the process.

So the structure is suppressed and you just see lines.

That's all what you see.

Later on, you will see that this structure will become

available for transform once we learn something.

So this is the primal processes and this is the

events, this is the basic events.

Now let's take a look at hydrogen atom.

Well, I guess, no.

Before this we still have to take a look at that view.

This is just an encapsulation how to think, how to translate

everything into this formalism in ETS.

So here you observe state one, you observe something abc.

Then state two, you observe d and c, and what you saw that a

and b merged to form d.

Here is an event.

So normally, conventionally, you would represent them as

sequence of this state.

Here what you are representing is this.

That's a representation of the situation where time

is going this way.

So time become a very important factor.

Time and structural representation now become

interlinked.

First of all, you cannot go back.

Once you're here, that's it.

Time is going down, you cannot back, so

everything going one way.

It's irreversible processes.

So by the way, this is what we will call formative history,

and I'm going to be using often this term regularly.

Hopefully we will get to the meaning of that.

So biology gives a very good example of science to suggest

how to think about objects, I think, for our purposes, for

purposes of classes and classification.

So what is a struct in this model?

Well, here is a struct sequence of events.

Some of the events, of course, you didn't see they were not

temporally arranged.

So that's OK.

They are not temporally order.

This is still representation of the process, oa, a small

segment of the process.

By the way, this is nothing to do with graphs, now, because

of the temporal thing.

It was inspired, of course, by natural numbers because,

according to [UNINTELLIGIBLE]

axioms, this is how the numbers are built.

Have a success sort of operation, and numbers are

built that way.

Now with numbers you can collapse them.

You don't need this initially primitive [? tribes ?]

stored actually this sort of [? not. ?]

But then they started to write three, so the temporal part

sort of disappeared.

But if you look at this, you can see now you cannot

collapse it because each one has a structure.

Each event now has a structure.

and you keep it as part of the representation.

So this is the fundamental distinction because you cannot

collapse it because each event is possibly structurally

different from the other and you have a temporal sequence.

But it was inspired by numbers, of course, this

representation.

Well here's is a hydrogen atom.

You have one proton and one electron.

And you can see the sequence of events that correspond.

This is, you can think of it as a hydrogen process.

They're going on this interactions.

So that's a representation would be of hydrogen process.

By the way, this is a structural representation.

In contrast to Feynman diagrams,

this was just drawings.

This is interpreted as a formal structural

representation because this events is a formal entities.

This is lithium process, slightly more complex.

And you can see when

[? periodicity ?], because, of course--

yes, I have to move on faster--

So struct relabeling.

There is a formal concept of struct relabeling.

So when you relabel the struct it's just a mapping so each

struct, each class has a set of labels associated with it.

So you can take all the labels of one class and map it.

So you allowed relabeling that preserve class belonging.

But what will happen it we will reveal-- see, here are

the two structs.

One is obtained simply by relabeling the other one.

But now you can see that they share something which you

couldn't see before, you see here.

So relabeling plays an important role even though

it's a simple operation.

AUDIENCE: So what are you classifying as an entire

[INTERPOSING VOICES]

LEV GOLDFARB: That's right.

That's an object now.

Everything becomes a object.

That's at a representation of an object.

AUDIENCE: How do you separate out

objects because one could--

LEV GOLDFARB: No.

This is a representation would be of a single object.

It's a process.

AUDIENCE: But one could imagine one giant object, the

universe, or something, as one humongous process

[INTERPOSING VOICES]

LEV GOLDFARB: No, no.

There's nothing to classify.

If you take the whole universe,

there's nothing to classify.

You're talking about now object, conventional web page,

whatever you want to deal with classes, that would be

represented like this.

AUDIENCE: But how do you decide what's part of one

object and not?

LEV GOLDFARB: No, no.

You are modeling that object and this process.

So you choose you primitives, you chose it, and then you

encode it in this format.

AUDIENCE: So the same real life objects could be modeled

differently?

LEV GOLDFARB: They could be modeled differently but the

whole point here is, as example from physics suggests,

that you want to choose events that would be most appropriate

for modeling a like chunk of the domain you

want to deal with.

It is true.

Initially it will not be easy to do.

So you would choose certain events but eventually you

would settle.

If you want model certain class of web pages set

reasonably wide you will fix the set of events which you

will find reliably, and you will use that set of events.

It's interaction events in terms of the user.

AUDIENCE: Right.

For example, you have chemistry.

In chemistry you deal with molecules.

And molecules consist of data, atoms. How do you decide in a

particular situation do we want to view this as

collection of molecules or collection of atoms?

LEV GOLDFARB: You will see in this formalism, it allows the

stages of representation.

So you will see, in fact in this talk, how you--

when the lithium and the hydrogen will interact and

form lithium hydride, you will see how it

can become a primitive.

Because this is a natural, no special tricks are necessary.

It's just a part of the

representational formalism now.

So structurally identical structs you notice that the

labels are different here but their structure is the same.

So you can think of it, when you strip them of labels, the

real object, this is abstract struct, you can call it.

Well, there is a struct assembly because here they are

depicted separately, but if you will notice that they

share some of the primitive.

So when you put them together this is

called struct assembly.

What it means is that you observe them separately but,

of course, some primitive, for example this primitive, is

shared, of course, by this struct and buy that struct.

So when you just picture them together that's

called struct assembly.

So in other words, when I am observing a face or a web page

I may have noticed only part of it, and I

represent it as a part.

But later on I looked at another part of the web page

and then I will put a picture of it.

But then eventually I have to put things together because

I'm looking at different parts.

AUDIENCE: Lev, I think someone will come to get the room in a

few minutes, so you probably want to move

on to the main points.

LEV GOLDFARB: All right.

So here is an example of how to model Bubble Sort here.

Here you can do both model architect.

Architecture is static for the array, and

you have a data flow.

So there are primitives--

this just a simple example because it's

an array, very simple.

But it could illustrate some points.

Sorry.

So here is the model, here is one comparison how it would be

modeled, a single comparison.

Now we will see this is a single internal loop.

So what you do you bubble four,

bubble up to its location.

This is how representation look.

The architecture doesn't change.

This is just says this marks the boundary of [? cell ?] of

these events.

But you can have a dynamic architecture, it would be more

complex than picture.

So--

just a bit slow--

so here is sorting of this 4, 2, 3, 1.

So you see here is the struct

corresponding to actual process.

So 3:00 someone may come in?

AUDIENCE: Yeah.

I believe there's the service being used

[INTERPOSING VOICES]

AUDIENCE: I also had another talk at 3:00 I have to go to.

[INTERPOSING VOICES]

We've got about four more minutes before I have to start

packing up.

LEV GOLDFARB: OK.

So here is an example of two structs.

Now here is the class description.

Class description, you need constraints.

Class is defined with constraints, and here is how

you generate elements of the class.

You allow environment to make a move, so to speak,

environment is whatever the process is that participate.

The white lines represent the events that you

[UNINTELLIGIBLE] that becomes class element.

So here is the picture.

Here is your class element.

So class representation consists of a struct plus this

generating system that actually build class elements,

and is specified via those constraints

So here is the same example with web

pages, you know, just--

Here is the simulation.

This is constraints for Bubble Sort, and you will see now

simulation of what happens, how you generate because this

is a class description.

So this is sort of description.

This is how that struct is being generated.

And, of course, this class description could be used for

construction of any struck that belongs to so-called

Bubble Sort.

Now, it turns out that there are levels.

You see, if you take a struct, and if you learn some classes,

the whole thing could be partitioned then, and you have

a more information.

So you could call it a level one struct because it contains

this partitioning based on the classes that you have learned.

So there is a formal description how to build next

level classes because there are constraints, now,

associated how they interact class elements.

So still the same kind of language.

And here is a class element construction.

Now you use larger chunks because now you are not using

single primitive you're using class elements to build this

level 1 class.

The same sort of a picture, but you're building out with

larger chunks.

So this is just some example how you can build.

So here, you see this is a level 1 class but

it's built out of--

here is a description of classes of previous level.

This is one element of a level 1 class.

And just very similar here to what you have here.

Here is a transformations.

Here is a process, something happens here.

Now at this level, you can see the processes.

Before the processes were not visible.

So this is how you go to the next level, it's is

compressed.

Now here is an example with this lithium hydride.

This is what you have seen, but you can shrink it and it

becomes primitive, and you can use it for

description of other.

So that's the last slide.

This is the encapsulation of what picture.

You have various level classes here, then you move to the

next stage.

This is when this transformation appear, when

you see this interactions, larger chunks, and so on.

This is how this representation--

So the basic idea is this, that I don't think we can do

classification without adequate

representation of formalism.

In spite of the fact that there are so many people

engaged in classification I think that it has to do with

the right representational formalism that will have an

important impact, a major impact on this activity.