literally

Author: tecunningham

_freeze/posts/2025-09-13-recursive-self-improvement-explosion-optimization-offcuts/execute-results/html.json

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-<lastBuildDate>Mon, 06 Apr 2026 12:00:00 GMT</lastBuildDate>
+<lastBuildDate>Tue, 07 Apr 2026 07:00:00 GMT</lastBuildDate>
 <item>
   <title>An Apple-Picking Model of AI R&amp;D</title>
   <dc:creator>Tom Cunningham</dc:creator>
@@ -528,7 +528,7 @@ Yuksekgonul, Mert, Daniel Koceja, Xinhao Li, Federico Bianchi, Jed McCaleb, Xiao
 </ol>
 </section></div> ]]></description>
   <guid>tecunningham.github.io/posts/2026-03-13-apple-picking-ai.html</guid>
-  <pubDate>Mon, 06 Apr 2026 12:00:00 GMT</pubDate>
+  <pubDate>Tue, 07 Apr 2026 07:00:00 GMT</pubDate>
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   <title>When You Overtake More Runners than You’re Overtaken by</title>
@@ -721,7 +721,7 @@ Yuksekgonul, Mert, Daniel Koceja, Xinhao Li, Federico Bianchi, Jed McCaleb, Xiao
 
  ]]></description>
   <guid>tecunningham.github.io/posts/2023-08-13-runner-percentile.html</guid>
-  <pubDate>Fri, 06 Mar 2026 11:00:00 GMT</pubDate>
+  <pubDate>Sat, 07 Mar 2026 08:00:00 GMT</pubDate>
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   <title>Knowledge-Creating LLMs</title>
@@ -940,7 +940,7 @@ Cunningham, Tom. 2026. <span>“Knowledge-Creating LLMs.”</span> February
 6, 2026. <a href="https://tecunningham.github.io/posts/2026-01-29-knowledge-creating-llms.html">tecunningham.github.io/posts/2026-01-29-knowledge-creating-llms.html</a>.
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   <guid>tecunningham.github.io/posts/2026-01-29-knowledge-creating-llms.html</guid>
-  <pubDate>Thu, 05 Feb 2026 11:00:00 GMT</pubDate>
+  <pubDate>Fri, 06 Feb 2026 08:00:00 GMT</pubDate>
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   <title>LLM verification</title>
@@ -1070,7 +1070,7 @@ You have one friend who is full of new ideas, you have another friend who can te
 
  ]]></description>
   <guid>tecunningham.github.io/posts/2025-12-30-llm-verification.html</guid>
-  <pubDate>Mon, 29 Dec 2025 11:00:00 GMT</pubDate>
+  <pubDate>Tue, 30 Dec 2025 08:00:00 GMT</pubDate>
 </item>
 <item>
   <title>Forecasts of AI &amp; Economic Growth</title>
@@ -1082,7 +1082,7 @@ You have one friend who is full of new ideas, you have another friend who can te
 
 
 
-<div id="265b553c" class="cell" data-results="asis" data-execution_count="1">
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 <li>❌ [15/18] Bib quotes present in local fulltext version (programmatic)</li>
 </ul>
-Last checked: 2026-03-18
+Last checked: 2026-04-12
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@@ -1560,7 +1560,7 @@ Cunningham, Tom. 2025. <span>“Forecasts of AI &amp; Economic
 Growth.”</span> November 6, 2025. <a href="https://tecunningham.github.io/posts/2025-10-19-forecasts-of-AI-growth.html">tecunningham.github.io/posts/2025-10-19-forecasts-of-AI-growth.html</a>.
 </div></div></section></div> ]]></description>
   <guid>tecunningham.github.io/posts/2025-10-19-forecasts-of-AI-growth.html</guid>
-  <pubDate>Wed, 05 Nov 2025 11:00:00 GMT</pubDate>
+  <pubDate>Thu, 06 Nov 2025 08:00:00 GMT</pubDate>
 </item>
 <item>
   <title>Economics and Transformative AI</title>
@@ -2073,7 +2073,7 @@ Cunningham, Tom. 2025. <span>“Economics and Transformative AI.”</span>
 October 2, 2025. <a href="https://tecunningham.github.io/posts/2025-09-19-transformative-AI-notes.html">tecunningham.github.io/posts/2025-09-19-transformative-AI-notes.html</a>.
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   <guid>tecunningham.github.io/posts/2025-09-19-transformative-AI-notes.html</guid>
-  <pubDate>Wed, 01 Oct 2025 11:00:00 GMT</pubDate>
+  <pubDate>Thu, 02 Oct 2025 07:00:00 GMT</pubDate>
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 <item>
   <title>On Deriving Things</title>
@@ -2305,7 +2305,7 @@ Suppose you’ll admitting a student to your PhD program only if they have a GRE
 
  ]]></description>
   <guid>tecunningham.github.io/posts/2020-10-02-on-deriving-things.html</guid>
-  <pubDate>Wed, 29 Jan 2025 11:00:00 GMT</pubDate>
+  <pubDate>Thu, 30 Jan 2025 08:00:00 GMT</pubDate>
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 <item>
   <title>Too Much Good News is Bad News</title>
@@ -2430,7 +2430,7 @@ Here the expected wait time is uniformly decreasing in <img src="https://latex.c
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   <guid>tecunningham.github.io/posts/2024-12-26-heavy-tailed-noise.html</guid>
-  <pubDate>Wed, 25 Dec 2024 11:00:00 GMT</pubDate>
+  <pubDate>Thu, 26 Dec 2024 08:00:00 GMT</pubDate>
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   <title>Premature Optimization and the Valley of Confusion</title>
@@ -2478,7 +2478,7 @@ Here the expected wait time is uniformly decreasing in <img src="https://latex.c
 
  ]]></description>
   <guid>tecunningham.github.io/posts/2024-05-10-premature-optimization.html</guid>
-  <pubDate>Thu, 09 May 2024 12:00:00 GMT</pubDate>
+  <pubDate>Fri, 10 May 2024 07:00:00 GMT</pubDate>
 </item>
 <item>
   <title>Peer Effects, Culture, and Taxes</title>
@@ -2841,7 +2841,7 @@ Cunningham, Tom. 2024. <span>“Peer Effects, Culture, and Taxes.”</span>
 April 28, 2024. <a href="https://tecunningham.github.io/posts/2023-01-23-peer-effects-norms-culture-sin-taxes.html">tecunningham.github.io/posts/2023-01-23-peer-effects-norms-culture-sin-taxes.html</a>.
 </div></div></section></div> ]]></description>
   <guid>tecunningham.github.io/posts/2023-01-23-peer-effects-norms-culture-sin-taxes.html</guid>
-  <pubDate>Sat, 27 Apr 2024 12:00:00 GMT</pubDate>
+  <pubDate>Sun, 28 Apr 2024 07:00:00 GMT</pubDate>
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 <item>
   <title>Bloodhounds and Bulldogs</title>
@@ -3194,7 +3194,7 @@ Cunningham, Tom. 2024. <span>“Bloodhounds and Bulldogs.”</span> April
 27, 2024. <a href="https://tecunningham.github.io/posts/2023-10-24-manifesto-perception-judgment-decision-making.html">tecunningham.github.io/posts/2023-10-24-manifesto-perception-judgment-decision-making.html</a>.
 </div></div></section></div> ]]></description>
   <guid>tecunningham.github.io/posts/2023-10-24-manifesto-perception-judgment-decision-making.html</guid>
-  <pubDate>Fri, 26 Apr 2024 12:00:00 GMT</pubDate>
+  <pubDate>Sat, 27 Apr 2024 07:00:00 GMT</pubDate>
 </item>
 <item>
   <title>The Influence of AI on Content Moderation and Communication</title>
@@ -3637,7 +3637,7 @@ Cunningham, Tom. 2023. <span>“The Influence of AI on Content Moderation
 and Communication.”</span> December 11, 2023. <a href="https://tecunningham.github.io/posts/2023-06-06-effect-of-ai-on-communication.html">tecunningham.github.io/posts/2023-06-06-effect-of-ai-on-communication.html</a>.
 </div></div></section></div> ]]></description>
   <guid>tecunningham.github.io/posts/2023-06-06-effect-of-ai-on-communication.html</guid>
-  <pubDate>Sun, 10 Dec 2023 11:00:00 GMT</pubDate>
+  <pubDate>Mon, 11 Dec 2023 08:00:00 GMT</pubDate>
 </item>
 <item>
   <title>The History of Automated Text Moderation</title>
@@ -3762,7 +3762,7 @@ Weng, Lilian, Vik Goel, and Andrea Vallone. 2023. <span>“Using GPT-4 for Conte
 </div>
 </div></section></div> ]]></description>
   <guid>tecunningham.github.io/posts/2023-11-18-history-automated-text-moderation.html</guid>
-  <pubDate>Fri, 17 Nov 2023 11:00:00 GMT</pubDate>
+  <pubDate>Sat, 18 Nov 2023 08:00:00 GMT</pubDate>
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 <item>
   <title>Thinking About Tradeoffs? Draw an Ellipse</title>
@@ -4020,7 +4020,7 @@ Simplify[First[%1]]</code></pre>
 
  ]]></description>
   <guid>tecunningham.github.io/posts/2023-10-23-pareto-frontiers-experiments-ranking.html</guid>
-  <pubDate>Tue, 24 Oct 2023 11:00:00 GMT</pubDate>
+  <pubDate>Wed, 25 Oct 2023 07:00:00 GMT</pubDate>
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   <title>Experiment Interpretation and Extrapolation</title>
@@ -4476,7 +4476,7 @@ Cunningham, T., 2023. Experiment Interpretation and Extrapolation [WWW
 Document]. URL <a href="https://tecunningham.github.io/posts/2023-04-18-experiment-interpretation-extrapolation.html">tecunningham.github.io/posts/2023-04-18-experiment-interpretation-extrapolation.html</a>
 </div></div></section></div> ]]></description>
   <guid>tecunningham.github.io/posts/2023-04-18-experiment-interpretation-extrapolation.html</guid>
-  <pubDate>Mon, 16 Oct 2023 11:00:00 GMT</pubDate>
+  <pubDate>Tue, 17 Oct 2023 07:00:00 GMT</pubDate>
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 <item>
   <title>An AI Which Imitates Humans Can Beat Humans</title>
@@ -4952,7 +4952,7 @@ Cunningham, Tom. 2023. <span>“An AI Which Imitates Humans Can Beat
 Humans.”</span> October 6, 2023. <a href="https://tecunningham.github.io/posts/2023-09-05-model-of-ai-imitation.html">tecunningham.github.io/posts/2023-09-05-model-of-ai-imitation.html</a>.
 </div></div></section></div> ]]></description>
   <guid>tecunningham.github.io/posts/2023-09-05-model-of-ai-imitation.html</guid>
-  <pubDate>Thu, 05 Oct 2023 11:00:00 GMT</pubDate>
+  <pubDate>Fri, 06 Oct 2023 07:00:00 GMT</pubDate>
 </item>
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   <title>Sushi-Roll Model of Online Media</title>
@@ -5098,7 +5098,7 @@ Anderson, Simon P., and Bruno Jullien. 2015. <span>“Chapter 2 - the Advertisin
 </div>
 </div></section></div> ]]></description>
   <guid>tecunningham.github.io/posts/2023-03-06-social-media-business-models-sushi-roll.html</guid>
-  <pubDate>Thu, 07 Sep 2023 12:00:00 GMT</pubDate>
+  <pubDate>Fri, 08 Sep 2023 07:00:00 GMT</pubDate>
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   <title>How Much has Social Media affected Polarization?</title>
@@ -5465,7 +5465,7 @@ Zhuravskaya, E., Petrova, M., Enikolopov, R., 2020. Political effects of the int
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 </div></section></div> ]]></description>
   <guid>tecunningham.github.io/posts/2023-07-27-meta-2020-elections-experiments.html</guid>
-  <pubDate>Sun, 06 Aug 2023 12:00:00 GMT</pubDate>
+  <pubDate>Mon, 07 Aug 2023 07:00:00 GMT</pubDate>
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   <title>The Paradox of Small Effects</title>
@@ -5551,7 +5551,7 @@ Tosh, Christopher, Philip Greengard, Ben Goodrich, Andrew Gelman, Aki Vehtari, a
 </div>
 </div></section></div> ]]></description>
   <guid>tecunningham.github.io/posts/2023-08-02-small-effects.html</guid>
-  <pubDate>Tue, 01 Aug 2023 12:00:00 GMT</pubDate>
+  <pubDate>Wed, 02 Aug 2023 07:00:00 GMT</pubDate>
 </item>
 <item>
   <title>Ranking by Engagement</title>
@@ -6235,7 +6235,7 @@ Cunningham, Tom. 2023. <span>“Ranking by Engagement.”</span> May 8,
 2023. <a href="https://tecunningham.github.io/posts/2023-04-28-ranking-by-engagement.html">tecunningham.github.io/posts/2023-04-28-ranking-by-engagement.html</a>.
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   <guid>tecunningham.github.io/posts/2023-04-28-ranking-by-engagement.html</guid>
-  <pubDate>Sun, 07 May 2023 12:00:00 GMT</pubDate>
+  <pubDate>Mon, 08 May 2023 07:00:00 GMT</pubDate>
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_freeze/posts/2025-09-13-recursive-self-improvement-explosion-optimization/execute-results/html.json

@@ -7,7 +7,7 @@
 <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
 
 <meta name="author" content="Tom Cunningham">
-<meta name="dcterms.date" content="2026-04-07">
+<meta name="dcterms.date" content="2026-04-13">
 <meta name="description" content="Tom Cunningham blog">
 
 <title>AI Recursive Self-Improvement OFFCUTS | Tom Cunningham – Tom Cunningham</title>
@@ -238,7 +238,7 @@ <h1 class="title">AI Recursive Self-Improvement OFFCUTS</h1>
       <div>
       <div class="quarto-title-meta-heading">Published</div>
       <div class="quarto-title-meta-contents">
-        <p class="date">April 7, 2026</p>
+        <p class="date">April 13, 2026</p>
       </div>
     </div>
 
@@ -258,6 +258,36 @@ <h1 class="title">AI Recursive Self-Improvement OFFCUTS</h1>
 
 
 <p>==OFFCUTS FILE==</p>
+<p>Core model:</p>
+<p><span class="math display">\[\begin{aligned}
+    \utt{\dot{A}}{algorithmic}{progress}
+        &amp;=\utt{R^{\gamma}}{new}{research}
+            {\utt{A^{1-\beta}}{algorithms}{}}
+        &amp;&amp; \text{(progress)}\\
+    R&amp;=A^{\kappa}
+        &amp;&amp; \text{}\\
+    \dot{A}&amp;=A^{1-\beta+\kappa}\\
+\end{aligned}
+\]</span></p>
+<dl>
+<dt>The strength of the feedback depends on TH-&gt;uplift.</dt>
+<dd>
+<p>Historically algorithmic progress has been a function of human R&amp;D, but we now expect the AI to itself increase the rate of algorithmic progress, through increasing effective R&amp;D: <span class="math display">\[
+\xymatrix@C=1.4em@R=1.4em{
+    &amp; *++[F]{\text{R\&amp;D}_t}\ar[d]
+    &amp; *++[F]{\text{R\&amp;D}_{t+1}}\ar[d]
+    &amp; *++[F]{\text{R\&amp;D}_{t+2}}\ar[d]
+    &amp; \\
+    \ar[r]
+    &amp; *++[F]{\text{Algorithms}_t}\ar[r]
+    &amp; *++[F]{\text{Algorithms}_{t+1}}\ar[r]\ar[ur]|{??}
+    &amp; *++[F]{\text{Algorithms}_{t+2}}\ar[r]\ar[ur] &amp;
+}
+\]</span></p>
+<p>There is still no consensus on the key diminishing-returns parameter <span class="math inline">\(\beta\)</span>. The cleanest direct AI-domain estimates I found are Ho &amp; Whitfill’s computer-vision, RL, and NLP posteriors, which are around <span class="math inline">\(\beta \approx 1.3\)</span>-<span class="math inline">\(1.6\)</span> but very noisy. By contrast, several software-intelligence-explosion calibrations imply much lower values like <span class="math inline">\(\beta \approx 0.15\)</span>-<span class="math inline">\(0.25\)</span>, while Davidson et al.&nbsp;summarize the software evidence as roughly <span class="math inline">\(\beta_S \approx 1\)</span> <span class="citation" data-cites="ho2025explosionexperiments">Ho and Whitfill (<a href="#ref-ho2025explosionexperiments" role="doc-biblioref">2025</a>)</span>; <span class="citation" data-cites="davidson2021could">Davidson (<a href="#ref-davidson2021could" role="doc-biblioref">2021</a>)</span>; <span class="citation" data-cites="davidson2026automatingairesearch">Davidson et al. (<a href="#ref-davidson2026automatingairesearch" role="doc-biblioref">2026</a>)</span>.</p>
+<p>A lot of the nearby literature is actually written in terms of returns parameters like <span class="math inline">\(r=\lambda/\beta\)</span> or <span class="math inline">\(r=\lambda \alpha / \beta\)</span> rather than <span class="math inline">\(\beta\)</span> itself. That matters because <span class="math inline">\(r\)</span> is informative about long-run dynamics, but it does not separately identify <span class="math inline">\(\beta\)</span> unless the authors also pin down <span class="math inline">\(\lambda\)</span> and sometimes <span class="math inline">\(\alpha\)</span> <span class="citation" data-cites="erdil2024estimating">Erdil, Besiroglu, and Ho (<a href="#ref-erdil2024estimating" role="doc-biblioref">2024</a>)</span>; <span class="citation" data-cites="davidson2025howquickandbigwo">Davidson and Houlden (<a href="#ref-davidson2025howquickandbigwo" role="doc-biblioref">2025</a>)</span>.</p>
+</dd>
+</dl>
 <section id="distinction" class="level1">
 <h1>distinction</h1>
 <ol type="1">
@@ -353,18 +383,18 @@ <h1>offcuts</h1>
 </ol>
 <table class="caption-top table">
 <colgroup>
-<col style="width: 32%">
-<col style="width: 22%">
-<col style="width: 13%">
-<col style="width: 18%">
-<col style="width: 13%">
+<col style="width: 30%">
+<col style="width: 21%">
+<col style="width: 20%">
+<col style="width: 16%">
+<col style="width: 12%">
 </colgroup>
 <thead>
 <tr class="header">
 <th></th>
 <th style="text-align: center;">annual growth (log)</th>
-<th style="text-align: center;">worker exp.</th>
-<th style="text-align: center;">experiment exp.</th>
+<th style="text-align: center;">worker expenditure</th>
+<th style="text-align: center;">experiment expenditure</th>
 <th style="text-align: center;">scale-free?</th>
 </tr>
 </thead>
@@ -895,6 +925,21 @@ <h1>Kwa diagram</h1>
 <div id="ref-agrawal2019needles" class="csl-entry" role="listitem">
 Agrawal, Ajay, John McHale, and Alexander Oettl. 2019. <span>“Finding Needles in Haystacks: Artificial Intelligence and Recombinant Growth.”</span> In <em>The Economics of Artificial Intelligence: An Agenda</em>, edited by Ajay Agrawal, Joshua Gans, and Avi Goldfarb, 149–74. Chicago, IL: University of Chicago Press. <a href="https://doi.org/10.7208/9780226613475-007">https://doi.org/10.7208/9780226613475-007</a>.
 </div>
+<div id="ref-davidson2021could" class="csl-entry" role="listitem">
+Davidson, Tom. 2021. <span>“Could Advanced AI Drive Explosive Economic Growth.”</span> <em>Open Philanthropy</em> 25. <a href="https://www.openphilanthropy.org/research/could-advanced-ai-drive-explosive-economic-growth">https://www.openphilanthropy.org/research/could-advanced-ai-drive-explosive-economic-growth</a>.
+</div>
+<div id="ref-davidson2026automatingairesearch" class="csl-entry" role="listitem">
+Davidson, Tom, Basil Halperin, Thomas Houlden, and Anton Korinek. 2026. <span>“When Does Automating AI Research Produce Explosive Growth?”</span> <a href="https://www.basilhalperin.com/papers/shs.pdf">https://www.basilhalperin.com/papers/shs.pdf</a>.
+</div>
+<div id="ref-davidson2025howquickandbigwo" class="csl-entry" role="listitem">
+Davidson, Tom, and Tom Houlden. 2025. <span>“How Quick and Big Would a Software Intelligence Explosion Be?”</span> <a href="https://www.forethought.org/research/how-quick-and-big-would-a-software-intelligence-explosion-be">https://www.forethought.org/research/how-quick-and-big-would-a-software-intelligence-explosion-be</a>.
+</div>
+<div id="ref-erdil2024estimating" class="csl-entry" role="listitem">
+Erdil, Ege, Tamay Besiroglu, and Anson Ho. 2024. <span>“Estimating Idea Production: A Methodological Survey,”</span> May. <a href="https://doi.org/10.2139/ssrn.4814445">https://doi.org/10.2139/ssrn.4814445</a>.
+</div>
+<div id="ref-ho2025explosionexperiments" class="csl-entry" role="listitem">
+Ho, Anson, and Parker Whitfill. 2025. <span>“The Software Intelligence Explosion Debate Needs Experiments.”</span> <a href="https://epoch.ai/gradient-updates/the-software-intelligence-explosion-debate-needs-experiments">https://epoch.ai/gradient-updates/the-software-intelligence-explosion-debate-needs-experiments</a>.
+</div>
 <div id="ref-jones2023recipes" class="csl-entry" role="listitem">
 Jones, Charles I. 2023. <span>“Recipes and Economic Growth: A Combinatorial March down an Exponential Tail.”</span> <em>Journal of Political Economy</em> 131 (8): 1994–2031. <a href="https://doi.org/10.1086/723631">https://doi.org/10.1086/723631</a>.
 </div>