<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">sure, but a person can learn the idea for n-bits from a few examples with a small number of bits, generalizing it to large values of n. most current systems learn it for a certain number of bits and don’t generalize beyond that number of bits.<br class=""><div><br class=""><blockquote type="cite" class=""><div class="">On Jul 18, 2022, at 7:17 AM, Barak A. Pearlmutter <<a href="mailto:barak@pearlmutter.net" class="">barak@pearlmutter.net</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class=""><div dir="ltr" class=""><br class=""></div><br class=""><div class="gmail_quote"><div dir="ltr" class="">On Mon, 18 Jul 2022 at 14:43, Danko Nikolic <<a href="mailto:danko.nikolic@gmail.com" class="">danko.nikolic@gmail.com</a>> wrote:<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div class=""><span id="cid:ii_l5qskat80"><image.png></span><br class=""></div><div class=""><br class=""></div><div class="">It is a hard problem to learn for a connectionist network.</div></blockquote><div class=""><br class=""></div><div class="">We don't need to invent new terminology, like "inverters problem" or "generalized xor." This is parity. Four (4) bit parity.</div><div class=""><br class=""></div><div class=""><a href="https://urldefense.com/v3/__https://en.wikipedia.org/wiki/Parity_function__;!!BhJSzQqDqA!SymFAG_laXvyUDdhFw_r1ISi5nIQSZWSrOosRKtv9NMqcadSQYnFL016TNGGLHTyVZc8YnrrFxRtAyZTQLiE$" class="">https://en.wikipedia.org/wiki/Parity_function</a></div><div class=""><br class=""></div><div class="">Parity is *not* a hard function to learn. Even for a connectionist network.</div><div class=""><br class=""></div><div class="">It is an interesting function for historic reasons (n-bit parity cannot be loaded by a k-th order perceptron, for k<n, although there are loopholes if a random bits are available or if you are allowed to only almost load it) and because it's an interesting function for many mathematical constructions. See the above wikipedia page for some details. But it is not super difficult to learn.</div><br class=""><div class="">--Barak Pearlmutter.<br class=""></div></div></div></div>
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