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<p class="MsoNormal"><span style="font-size:11.0pt">Some have difficulty accepting findings that were rewarded with Nobel prizes. These scientists were rewarded for finding “meaning” in the activations of single neurons. That flies in the face of population
coding. And, in science, you can repeat these experiments and verify these findings again and again. Some see lots of activations and think that must be population coding.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Asim Roy<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Professor, Information Systems<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Arizona State University<o:p></o:p></span></p>
<p class="MsoNormal"><a href="https://search.asu.edu/profile/9973">Asim Roy | ASU Search</a><o:p></o:p></p>
<p class="MsoNormal"><a href="https://lifeboat.com/ex/bios.asim.roy">Lifeboat Foundation Bios: Professor Asim Roy</a><o:p></o:p></p>
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<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">From:</span></b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif"> Connectionists <connectionists-bounces@mailman.srv.cs.cmu.edu>
<b>On Behalf Of </b>Weng, Juyang<br>
<b>Sent:</b> Saturday, June 15, 2024 7:28 AM<br>
<b>To:</b> Gabriele Scheler <gscheler@gmail.com>; connectionists@mailman.srv.cs.cmu.edu<br>
<b>Subject:</b> Re: Connectionists: Ensemble computing<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black">Dear Gabriele Scheler,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"> You wrote, "Each symbol stands for one pattern". This is an invalid statement, meaningless in mathematics and computer science. <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"> (1) I suggest that you review the term One-to-One correspondence required for symbolic representations in discrete mathematics and computer science (like Turing machines). <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"> (2) Counter Example 1: While my brain senses your face, many neurons in my brain will fire. Do they stand for the same pattern (your face)? This means one-to-many mapping, defeating the one-to-one correspondence
in (1). <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"> (3) Counter Example 2: While my brain senses your face at different viewing angles, distances, and lighting conditionss, my motor neurons will fire to produce Gabriele Scheler. Any of motor neurons stand for
many patterns of your face, not only "one pattern". This means many-to-one mapping, defeating the one-to-one correspondence in (1). <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"> With the above proof, "Each symbol stands for one pattern" is meaningless in mathematics and computer science.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"> Best regards,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black">-John Weng<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="color:black">On Sat, Jun 15, 2024 at 9:46</span><span style="font-family:"Arial",sans-serif;color:black"> </span><span style="color:black">PM Gabriele Scheler <<a href="mailto:gscheler@gmail.com">gscheler@gmail.com</a>> wrote:<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black">Oh st simpkicissismus.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="color:black">Symbolic neurons have connections with each other. Each symbol stands for one pattern. They also have connections with their feature patterns. But we compute with the symbolic neurons alone. There are no examples
given for that.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="color:black">So by computing with symbolic neurons we can use exact reasoning. But when we want to know the meaning of a symbol we can then turn to their features. The clever part - since you have trouble reading - is that
we can use only the symbolic neurons, we do not ha e to stimulate them in a way that their feature parts become active. In that case, 1 symbol, 1 neuron. <o:p></o:p></span></p>
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<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:black">From:</span></b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:black"> Connectionists <<a href="mailto:connectionists-bounces@mailman.srv.cs.cmu.edu">connectionists-bounces@mailman.srv.cs.cmu.edu</a>>
on behalf of Gabriele Scheler <<a href="mailto:gscheler@gmail.com">gscheler@gmail.com</a>><br>
<b>Sent:</b> Monday, June 10, 2024 8:03 AM<br>
<b>To:</b> <a href="mailto:connectionists@mailman.srv.cs.cmu.edu">connectionists@mailman.srv.cs.cmu.edu</a> <<a href="mailto:connectionists@mailman.srv.cs.cmu.edu">connectionists@mailman.srv.cs.cmu.edu</a>><br>
<b>Subject:</b> Connectionists: Ensemble computing</span> <o:p></o:p></p>
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<p class="MsoNormal"> <o:p></o:p></p>
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<p class="MsoNormal">This paper may be relevant to the discussion on symbolic computing in the brain. <br clear="all">
<o:p></o:p></p>
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<p class="MsoNormal"><a href="https://urldefense.com/v3/__https:/www.biorxiv.org/content/10.1101/2023.12.22.573036v2__;!!HXCxUKc!3XvVBOS7Ewzj9hEc7LIS4jJ1KaOBIEg96-dgQQoFBKgSXwmbWIv9bbBw_q5aEBIrkXofN97mq1r_Tw$">https://www.biorxiv.org/content/10.1101/2023.12.22.573036v2</a><o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">It leverages ideas about ensembles in the brain and outlines a basic scheme for symbolic abstraction .<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Gabriele<o:p></o:p></p>
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<p class="MsoNormal"><span class="xgmailsignatureprefix">-- </span><o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Dr. Gabriele Scheler<br>
Carl Correns Foundation for Mathematical Biology <o:p></o:p></p>
<p class="MsoNormal">1030 Judson Dr<br>
Mountain View, CA 94040 <o:p></o:p></p>
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<p class="MsoNormal"><a href="https://urldefense.com/v3/__http:/www.theoretical-biology.org__;!!HXCxUKc!3XvVBOS7Ewzj9hEc7LIS4jJ1KaOBIEg96-dgQQoFBKgSXwmbWIv9bbBw_q5aEBIrkXofN95zer6I-w$" target="_blank">https://www.theoretical-biology.org</a><o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Please re-send an email if I fail to respond.<o:p></o:p></p>
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