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Author: tecunningham

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-Sep 22, 2025
+Sep 25, 2025
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-<a href="./posts/2025-06-14-model-of-chatgpt.html" class="no-external">A Model of ChatGPT</a>
+<a href="./posts/2025-06-14-model-of-chatgpt.html" class="no-external">A Model of Chatbots [==SUPERCEDED==]</a>
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docs/index.html

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-<lastBuildDate>Mon, 22 Sep 2025 07:00:00 GMT</lastBuildDate>
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 <item>
   <title>Too Much Good News is Bad News</title>
   <dc:creator>Tom Cunningham</dc:creator>
@@ -134,10 +134,10 @@ Here the expected wait time is uniformly decreasing in <img src="https://latex.c
 </ol>
 </section></div> ]]></description>
   <guid>tecunningham.github.io/posts/2024-12-26-heavy-tailed-noise.html</guid>
-  <pubDate>Mon, 22 Sep 2025 07:00:00 GMT</pubDate>
+  <pubDate>Thu, 25 Sep 2025 07:00:00 GMT</pubDate>
 </item>
 <item>
-  <title>A Model of ChatGPT</title>
+  <title>A Model of Chatbots [==SUPERCEDED==]</title>
   <dc:creator>Tom Cunningham</dc:creator>
   <link>tecunningham.github.io/posts/2025-06-14-model-of-chatgpt.html</link>
   <description><![CDATA[ 
@@ -146,6 +146,8 @@ Here the expected wait time is uniformly decreasing in <img src="https://latex.c
 
 
 
+<p>==SUPERCEDED==</p>
+<p>==MOVED TO .TEX==</p>
 <p>This paper develops a simple model of human and AI ability to answer questions. Each question <img src="https://latex.codecogs.com/png.latex?%5Cbm%7Bq%7D"> is a high-dimensional vector, with a true scalar answer <img src="https://latex.codecogs.com/png.latex?a">. An agent’s estimate of the answer is an interpolation based on previously-seen questions and answers <img src="https://latex.codecogs.com/png.latex?(%5Cbm%7Bq%7D%5Ei,a%5Ei)_%7Bi=1,%5Cldots,n%7D">. This framework extends an <a href="https://tecunningham.github.io/posts/2023-09-05-model-of-ai-imitation.html">earlier model</a> developed for a different purpose.</p>
 <p>The model yields several implications:</p>
 <ol type="1">
@@ -219,7 +221,7 @@ Here the expected wait time is uniformly decreasing in <img src="https://latex.c
 </tr>
 </tbody>
 </table>
-<p>We can make some conjectures about adoption by task: :</p>
+<p>We can make some conjectures about adoption by task:</p>
 <table class="caption-top table">
 <colgroup>
 <col style="width: 42%">
@@ -327,14 +329,14 @@ Here the expected wait time is uniformly decreasing in <img src="https://latex.c
 
 <div id="quarto-appendix" class="default"><section class="quarto-appendix-contents" id="quarto-citation"><h2 class="anchored quarto-appendix-heading">Citation</h2><div><div class="quarto-appendix-secondary-label">BibTeX citation:</div><pre class="sourceCode code-with-copy quarto-appendix-bibtex"><code class="sourceCode bibtex">@online{cunningham2025,
   author = {Cunningham, Tom},
-  title = {A {Model} of {ChatGPT}},
+  title = {A {Model} of {Chatbots} {{[}==SUPERCEDED=={]}}},
   date = {2025-06-14},
   url = {tecunningham.github.io/posts/2025-06-14-model-of-chatgpt.html},
   langid = {en}
 }
 </code></pre><div class="quarto-appendix-secondary-label">For attribution, please cite this work as:</div><div id="ref-cunningham2025" class="csl-entry quarto-appendix-citeas">
-Cunningham, Tom. 2025. <span>“A Model of ChatGPT.”</span> June 14, 2025.
-<a href="https://tecunningham.github.io/posts/2025-06-14-model-of-chatgpt.html">tecunningham.github.io/posts/2025-06-14-model-of-chatgpt.html</a>.
+Cunningham, Tom. 2025. <span>“A Model of Chatbots
+[==SUPERCEDED==].”</span> June 14, 2025. <a href="https://tecunningham.github.io/posts/2025-06-14-model-of-chatgpt.html">tecunningham.github.io/posts/2025-06-14-model-of-chatgpt.html</a>.
 </div></div></section></div> ]]></description>
   <guid>tecunningham.github.io/posts/2025-06-14-model-of-chatgpt.html</guid>
   <pubDate>Sat, 14 Jun 2025 07:00:00 GMT</pubDate>

docs/index.xml

@@ -10,7 +10,7 @@
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 <meta name="description" content="Tom Cunningham blog">
 
-<title>A Model of ChatGPT | Tom Cunningham – Tom Cunningham</title>
+<title>A Model of Chatbots [==SUPERCEDED==] | Tom Cunningham – Tom Cunningham</title>
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@@ -148,12 +148,12 @@
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-      <h1 class="title">A Model of ChatGPT</h1>
+      <h1 class="title">A Model of Chatbots [==SUPERCEDED==]</h1>
                       </div>
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@@ -228,7 +228,7 @@ <h1 class="title">A Model of ChatGPT</h1>
       <div>
       <div class="quarto-title-meta-heading">Modified</div>
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-        <p class="date-modified">June 14, 2025</p>
+        <p class="date-modified">September 24, 2025</p>
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@@ -237,33 +237,17 @@ <h1 class="title">A Model of ChatGPT</h1>
 
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-  <nav id="quarto-sidebar" class="sidebar collapse collapse-horizontal quarto-sidebar-collapse-item sidebar-navigation floating overflow-auto">
-    <nav id="TOC" role="doc-toc" class="toc-active">
-    <h2 id="toc-title">On this page</h2>
-   
-  <ul class="collapse">
-  <li><a href="#model" id="toc-model" class="nav-link active" data-scroll-target="#model">Model</a></li>
-  <li><a href="#propositions" id="toc-propositions" class="nav-link" data-scroll-target="#propositions">Propositions</a></li>
-  <li><a href="#related-literature" id="toc-related-literature" class="nav-link" data-scroll-target="#related-literature">Related Literature</a>
-  <ul class="collapse">
-  <li><a href="#agrawal-et-al.-2018-exploring-the-impact-of-artificial-intelligence-prediction-versus-judgment" id="toc-agrawal-et-al.-2018-exploring-the-impact-of-artificial-intelligence-prediction-versus-judgment" class="nav-link" data-scroll-target="#agrawal-et-al.-2018-exploring-the-impact-of-artificial-intelligence-prediction-versus-judgment">Agrawal et al.&nbsp;(2018) “Exploring the Impact of Artificial Intelligence: Prediction versus Judgment”</a></li>
-  <li><a href="#kleinberg-et-al.-2017-human-decisions-and-machine-predictions" id="toc-kleinberg-et-al.-2017-human-decisions-and-machine-predictions" class="nav-link" data-scroll-target="#kleinberg-et-al.-2017-human-decisions-and-machine-predictions">Kleinberg et al.&nbsp;(2017) “Human Decisions and Machine Predictions”</a></li>
-  </ul></li>
-  <li><a href="#references" id="toc-references" class="nav-link" data-scroll-target="#references">References</a></li>
-  </ul>
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+<p>==SUPERCEDED==</p>
+<p>==MOVED TO .TEX==</p>
 <p>This paper develops a simple model of human and AI ability to answer questions. Each question <span class="math inline">\(\bm{q}\)</span> is a high-dimensional vector, with a true scalar answer <span class="math inline">\(a\)</span>. An agent’s estimate of the answer is an interpolation based on previously-seen questions and answers <span class="math inline">\((\bm{q}^i,a^i)_{i=1,\ldots,n}\)</span>. This framework extends an <a href="https://tecunningham.github.io/posts/2023-09-05-model-of-ai-imitation.html">earlier model</a> developed for a different purpose.</p>
 <p>The model yields several implications:</p>
 <ol type="1">
@@ -337,7 +321,7 @@ <h2 id="toc-title">On this page</h2>
 </tr>
 </tbody>
 </table>
-<p>We can make some conjectures about adoption by task: :</p>
+<p>We can make some conjectures about adoption by task:</p>
 <table class="caption-top table">
 <colgroup>
 <col style="width: 42%">
@@ -483,14 +467,14 @@ <h1>References</h1>
 
 <div id="quarto-appendix" class="default"><section class="quarto-appendix-contents" id="quarto-citation"><h2 class="anchored quarto-appendix-heading">Citation</h2><div><div class="quarto-appendix-secondary-label">BibTeX citation:</div><pre class="sourceCode code-with-copy quarto-appendix-bibtex"><code class="sourceCode bibtex">@online{cunningham2025,
   author = {Cunningham, Tom},
-  title = {A {Model} of {ChatGPT}},
+  title = {A {Model} of {Chatbots} {{[}==SUPERCEDED=={]}}},
   date = {2025-06-14},
   url = {tecunningham.github.io/posts/2025-06-14-model-of-chatgpt.html},
   langid = {en}
 }
 </code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre><div class="quarto-appendix-secondary-label">For attribution, please cite this work as:</div><div id="ref-cunningham2025" class="csl-entry quarto-appendix-citeas" role="listitem">
-Cunningham, Tom. 2025. <span>“A Model of ChatGPT.”</span> June 14, 2025.
-<a href="https://tecunningham.github.io/posts/2025-06-14-model-of-chatgpt.html">tecunningham.github.io/posts/2025-06-14-model-of-chatgpt.html</a>.
+Cunningham, Tom. 2025. <span>“A Model of Chatbots
+[==SUPERCEDED==].”</span> June 14, 2025. <a href="https://tecunningham.github.io/posts/2025-06-14-model-of-chatgpt.html">tecunningham.github.io/posts/2025-06-14-model-of-chatgpt.html</a>.
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