Robots again

From: Doug Yowza <yowza_at_yowza.com>
Date: Tue Mar 17 03:39:50 1998

On Mon, 16 Mar 1998, Lawrence Wilkinson wrote:

[1.0/3.0]
> But a digital computer can represent rational numbers exactly as you
> have (e.g. Smalltalk has a rational data type which behaves just like
> any other number) but irrational numbers cause problems.

That's interesting. How does SmallTalk deal with complex expressions?
Does it postpone evaluation until forced?

> But then can
> an analogue machine represent irrational numbers exactly?

Sure, values like pi and e are real-world analog constants, but "analog
machine" is pretty open-ended; at the lowest level, even digital machines
use analog processes.

It's been 10 years since I played with artificial neural nets, but the
basic goal was to define a neuron-like computing element that:

1) Could be arranged in networks that mapped arbitrary input sets to
arbitrary output sets.

2) Was simple enough to analyze mathematically.

3) Was trainable.

All of the ANNs ignored the distinctions between analog and digital,
as well as more obvious characteristics of real neurons.

The first try was the single-layer perceptron. A neuron simply summed
it's imputs and generated an output if the value exceeded a threshold.
You can make AND and OR maps with these, but not XOR, for example.

So, Minsky and Papert added a second layer, and showed that you could now
make XOR maps, but they couldn't find a way to train the net to build such
a map on its own.

Then Rummelhart (at UCSD) showed that by adding non-linearities (a
sigmoidal threshold function) and "back-propagating" errors through the
net, you could train a net to generate an XOR map (and many other maps).

For more complex mappings, there were lots of problems related to the time
it would take a net to converge, how to best layout the net, scalability
issues, how to model temporal associations, etc. Around this time, I had
to get a job, so I don't know the state of affairs today, but since today
there's more interest in Java than in neural nets, I assume they haven't
solved the problems yet.

-- Doug
Received on Tue Mar 17 1998 - 03:39:50 GMT