Name: 講義3B：記号的微分；引用 (Lecture 3B: Symbolic Differentiation; Quotation)
Uploaded: 2021-01-14T10:26:49.000Z
Duration: 44 min 2 s
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PROFESSOR: Well, Hal just told us how you build robust

I'm sure that many of you don't really assimilate that

yet-- but the key idea is that in order to make a system

that's robust, it has to be insensitive to small changes,

that is, a small change in the problem should lead to only a

The space of solutions ought to be continuous in this space

The way he was explaining how to do that was instead of

solving a particular problem at every level of

decomposition of the problem at the subproblems, where you

solve the class of problems, which are a neighborhood of

the particular problem that you're trying to solve.

The way you do that is by producing a language at that

level of detail in which the solutions to that class of

problems is representable in that language.

Therefore when you makes more changes to the problem you're

trying to solve, you generally have to make only small local

changes to the solution you've constructed, because at the

level of detail you're working, there's a language

where you can express the various solutions to alternate

Well that's the beginning of a very important idea, the most

important perhaps idea that makes computer science more

powerful than most of the other kinds of engineering

What we've seen so far is sort of how to use

And, of course, the power of embedding languages partly

What you see here is the derivative program that we

It's a procedure that takes a procedure as an argument and

You can make things like push combinators and all that sort

of wonderful thing that you saw last time.

However, now I'm going to really muddy the waters.

See this confuses the issue of what's the procedure and what

What we really want to do is confuse it very badly.

And the best way to do that is to get involved with the

manipulation of the algebraic expressions that the

So at this point, I want to talk about instead of things

like on this slide, the derivative procedure being a

And what you're seeing is a representation of the

numerical approximation to the derivative.

In fact what I'd like to talk about is instead things that

And what we have here are rules from a calculus book.

These are rules for finding the derivatives of the

It says things like a derivative of a constant is 0.

The derivative of the valuable with respect to which you are

The derivative of a constant times the function is the

constant times the derivative of the function,

And, in fact, it's very easy to make programs that

Let's look at these rules in some detail.

You all have seen these rules in your elementary calculus

And you know from calculus that it's easy to produce

You also know from your elementary calculus that it's

Yet integrals and derivatives are opposites of each other.

What is special about these rules that makes it possible

for one to produce derivatives easily and

Every one of these rules, when used in the direction for

taking derivatives, which is in the direction of this

arrow, the left side is matched against your

expression, and the right side is the thing which is the

In each of these rules, the expressions on the right-hand

side of the rule that are contained within derivatives

are subexpressions, are proper subexpressions, of the

So here we see the derivative of the sum, with is the

expression on the left-hand side is the sum of the

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講義3B：記号的微分；引用 (Lecture 3B: Symbolic Differentiation; Quotation)

sort

constant

expression

structure