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From: ranjit@grad2.cis.upenn.edu (Ranjit Bhatnagar)
Newsgroups: comp.sys.amiga
Subject: Re: blitting a neural net.
Keywords: Neural nets, blitter, life, pickled cumquats
Message-ID: <11269@netnews.upenn.edu>
Date: 20 May 89 04:17:38 GMT
References: <1082@altos86.UUCP> <10650@orstcs.CS.ORST.EDU> <3029@cps3xx.UUCP> <610@censor.UUCP> <730@wsu-cs.uucp>
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Reply-To: ranjit@grad2.cis.upenn.edu.UUCP (Ranjit Bhatnagar)
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Amazingly, it's been proven (statistically) that a network of McCullough-Pitts
neurons (see below) has nearly as much computational power after you restrict
it so that all the interconnection weights are 0, 1, or -1.  That is to say,
given a network with arbitrary weights that can recognize N inputs reliably,
a network with binary interconnection weights (0, 1, or -1 only) need only
be a few times larger to recognize N inputs just as reliably.  

Since the implementation of such a restricted network consists of
nothing but zillions of 1-bit adds and multiplies, and a relatively
small number of integer operations, and any network
that does anything reasonable is going to be very large, perhaps the
blitter would actually be able simulate such a network very efficiently
compared to a general purpose processor (like the 68000).  

	- Ranjit

A McCullough-Pitts neuron is the following function (approximately -
it shows up in slightly different forms): [it's easier to write
pseudo-code than math functions on a terminal!]

A function of n real numbers which returns one integer.
The array of n weights w[i] and threshold K are real values
associated with a particular neuron - it is these values that
are tweaked to make a network learn things.

	subtotal = 0;
	for i = 1 to n 
		subtotal = subtotal + w[i] * input[i];
	if subtotal > K then output = 1;
			else output = 0 (or -1, whichever you prefer)

In the binary approximation, the weight matrix only contains 1's or 0's
instead of arbitrary real numbers.  To simplify things, K is often
restricted to be 0, though this reduces the power of the neuron.




"Trespassers w"   ranjit@eniac.seas.upenn.edu	mailrus!eecae!netnews!eniac!...
	   "Such a brute that even his shadow breaks things." (Lorca)