Re: What is your philosophy? Tracking or Static?
Dan,
Thank you for the useful characterization. I, too, began assuming tracking, but I am coming more to the static view.
Early in AD, a frequently cited difficulty was scaling:
x is a vector
s = max(|x|)
x = x / s // Normalize
y = lots of computations
y = y * s // Rescale back
Is y a differentiable function of x? AD is forced to assume not. Intervals can help decide this question more precisely, but the analogy is whether we care about the history or only the result.
Or, suppose
x is a scalar
f(x) = sign(x)
y = 0 * f(x)
Is y a continuous function of x?
I am becoming a static-ist.
George
On May 25, 2011, at 6:17 AM, Dan Zuras Intervals wrote:
>> Date: Tue, 24 May 2011 19:05:38 -0500
>> From: Ralph Baker Kearfott <rbk@xxxxxxxxxxxx>
>> To: Nate Hayes <nh@xxxxxxxxxxxxxxxxx>
>> CC: John Pryce <j.d.pryce@xxxxxxxxxxxx>,
>> stds-1788 <stds-1788@xxxxxxxxxxxxxxxxx>
>> Subject: Re: Ar we succeeding?
>>
>> All,
>>
>> Does someone else also have an opinion concerning this (please)?
>>
>> Baker
>>
>
> Baker, et al,
>
> I find I do have an opinion on this. And as long as Nate's
> motion is in its discussion period, now is as good a time
> as any to discuss it.
>
> Let me put it in the form of a question I put to Nate:
>
> Is your philosophy about decorations a tracking approach or
> a static approach?
>
> There seem to be two schools of thought about the meaning
> of decorations.
>
> There is the TRACKING school in which decorations are the
> maximal (most pessimistic) result of the tree of evaluations
> that led up to the result to which they are attached. That
> is, every exceptional or noteworthy incident in that tree is
> recorded for all to see whether it is relevant to the final
> result or not.
>
> Then there is the STATIC school in which decorations are
> information concerning the current result only. Earlier
> decorations may pass through to this result if they still
> apply & may be discarded if they do not. In this case the
> decoration must be able to be interpreted in the context
> of the final result whatever happened before.
>
> (In either school, the decoration must be ordered WRT to
> subsets of arguments. I believe this is both necessary &
> sufficient for an FTDIA to be proved.)
>
> I asked this question of Nate because his motion seemed to
> be primarily of the tracking school but with some static
> features thrown in.
>
> I think we need to be consistent on this point. As much
> for our own understanding as to explain the meaning of
> decorations to the rest of the world.
>
> I will admit that I started out in the Tracking school.
> But some remarks I've heard in this forum & privately have
> suggested to me that the Static school might serve us better
> as a standard.
>
> So I ask of all of you: Which philosophy should we espouse?
> Tracking or Static?
>
> I believe that once we decide this many of our more
> difficult questions will fall out as obvious.
>
> Yours,
>
> Dan
Dr. George F. Corliss
Electrical and Computer Engineering
Marquette University
P.O. Box 1881
1515 W. Wisconsin Ave
Milwaukee WI 53201-1881 USA
414-288-6599; GasDay: 288-4400; Fax 288-5579
George.Corliss@xxxxxxxxxxxxx
www.eng.mu.edu/corlissg