autosave: 2026-03-12 06:22:08

Author: tecunningham

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

@@ -9,7 +9,7 @@
 <link>tecunningham.github.io/</link>
 <atom:link href="tecunningham.github.io/index.xml" rel="self" type="application/rss+xml"/>
 <description>{{&lt; meta description-meta &gt;}}</description>
-<generator>quarto-1.8.25</generator>
+<generator>quarto-1.5.57</generator>
 <lastBuildDate>Sat, 07 Mar 2026 08:00:00 GMT</lastBuildDate>
 <item>
   <title>When You Overtake More Runners than You’re Overtaken by</title>

_freeze/posts/2025-09-13-recursive-self-improvement-explosion-optimization/figure-html/bernoulli-functions-1.png

@@ -4,7 +4,7 @@
     "href": "index.html",
     "title": "Blog Posts",
     "section": "",
-    "text": "When You Overtake More Runners than You’re Overtaken by\n\n\n\n\n\n\n\n\n\n\nMar 7, 2026\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\n\nKnowledge-Creating LLMs\n\n\n\n\n\n\n\n\n\n\nFeb 6, 2026\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\n\nLLM verification\n\n\n\n\n\n\n\n\n\n\nDec 30, 2025\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\n\nForecasts of AI & Economic Growth\n\n\n\n\n\n\n\n\n\n\nNov 6, 2025\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\n\nEconomics and Transformative AI\n\n\n\n\n\n\n\n\n\n\nOct 2, 2025\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\n\nOn Deriving Things\n\n\n\n\n\n\n\n\n\n\nJan 30, 2025\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\n\nToo Much Good News is Bad News\n\n\n\n\n\n\n\n\n\n\nDec 26, 2024\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\n\nPremature Optimization and the Valley of Confusion\n\n\n\n\n\n\n\n\n\n\nMay 10, 2024\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\n\nPeer Effects, Culture, and Taxes\n\n\n\n\n\n\n\n\n\n\nApr 28, 2024\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\n\nBloodhounds and Bulldogs\n\n\nOn Perception, Judgment, & Decision-Making\n\n\n\n\n\n\n\nApr 27, 2024\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\n\nThe Influence of AI on Content Moderation and Communication\n\n\n\n\n\n\n\n\n\n\nDec 11, 2023\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\n\nThe History of Automated Text Moderation\n\n\n\n\n\n\n\n\n\n\nNov 18, 2023\n\n\nIntegrity Institute collaborators: Alex Rosenblatt, Jeff Allen, Ejona Varangu, Dave Sullivan, Tom Cunningham\n\n\n\n\n\n\n\n\n\n\n\n\nThinking About Tradeoffs? Draw an Ellipse\n\n\n\n\n\n\n\n\n\n\nOct 25, 2023\n\n\nTom Cunningham, OpenAI.\n\n\n\n\n\n\n\n\n\n\n\n\nExperiment Interpretation and Extrapolation\n\n\n\n\n\n\n\n\n\n\nOct 17, 2023\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\n\nAn AI Which Imitates Humans Can Beat Humans\n\n\n\n\n\n\n\n\n\n\nOct 6, 2023\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\n\nSushi-Roll Model of Online Media\n\n\nPreviously: “pizza model”, “salami model”\n\n\n\n\n\n\n\nSep 8, 2023\n\n\nTom Cunningham, Integrity Institute\n\n\n\n\n\n\n\n\n\n\n\n\nHow Much has Social Media affected Polarization?\n\n\n\n\n\n\n\n\n\n\nAug 7, 2023\n\n\nTom Cunningham, Integrity Institute\n\n\n\n\n\n\n\n\n\n\n\n\nThe Paradox of Small Effects\n\n\n\n\n\n\n\n\n\n\nAug 2, 2023\n\n\nTom Cunningham, Integrity Institute\n\n\n\n\n\n\n\n\n\n\n\n\nRanking by Engagement\n\n\n\n\n\n\n\n\n\n\nMay 8, 2023\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\n\nSocial Media Suspensions of Prominent Accounts\n\n\n\n\n\n\n\n\n\n\nJan 31, 2023\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\n\nOptimal Coronavirus Policy Should be Front-Loaded\n\n\n\n\n\n\n\n\n\n\nApr 5, 2020\n\n\n\n\n\n\n\n\n\n\n\n\nOn Unconscious Influences (Part 1)\n\n\n\n\n\n\n\n\n\n\nDec 8, 2017\n\n\n\n\n\n\n\n\n\n\n\n\nThe Work of Art in the Age of Mechanical Production\n\n\n\n\n\n\n\n\n\n\nSep 27, 2017\n\n\n\n\n\n\n\n\n\n\n\n\nRepulsion from the Prior\n\n\n\n\n\n\n\n\n\n\nMay 26, 2017\n\n\n\n\n\n\n\n\n\n\n\n\nThe Repeated Failure of Laws of Behaviour\n\n\n\n\n\n\n\n\n\n\nApr 15, 2017\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\n\nEconomist Explorers\n\n\n\n\n\n\n\n\n\n\nFeb 25, 2017\n\n\n\n\n\n\n\n\n\n\n\n\nSamuelson & Expected Utility\n\n\n\n\n\n\n\n\n\n\nFeb 25, 2017\n\n\n\n\n\n\n\n\n\n\n\n\nWeber’s Law Doesn’t Imply Concave Representations or Concave Judgments\n\n\n\n\n\n\n\n\n\n\nFeb 25, 2017\n\n\n\n\n\n\n\n\n\n\n\n\nRelative Thinking\n\n\n\n\n\n\n\n\n\n\nApr 30, 2016\n\n\nTom Cunningham\n\n\n\n\n\nNo matching items"
+    "text": "When You Overtake More Runners than You’re Overtaken by\n\n\n\n\n\n\n\n\n\n\n\nMar 7, 2026\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\nKnowledge-Creating LLMs\n\n\n\n\n\n\n\n\n\n\n\nFeb 6, 2026\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\nLLM verification\n\n\n\n\n\n\n\n\n\n\n\nDec 30, 2025\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\nForecasts of AI & Economic Growth\n\n\n\n\n\n\n\n\n\n\n\nNov 6, 2025\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\nEconomics and Transformative AI\n\n\n\n\n\n\n\n\n\n\n\nOct 2, 2025\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\nOn Deriving Things\n\n\n\n\n\n\n\n\n\n\n\nJan 30, 2025\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\nToo Much Good News is Bad News\n\n\n\n\n\n\n\n\n\n\n\nDec 26, 2024\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\nPremature Optimization and the Valley of Confusion\n\n\n\n\n\n\n\n\n\n\n\nMay 10, 2024\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\nPeer Effects, Culture, and Taxes\n\n\n\n\n\n\n\n\n\n\n\nApr 28, 2024\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\nBloodhounds and Bulldogs\n\n\nOn Perception, Judgment, & Decision-Making\n\n\n\n\n\n\n\n\nApr 27, 2024\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\nThe Influence of AI on Content Moderation and Communication\n\n\n\n\n\n\n\n\n\n\n\nDec 11, 2023\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\nThe History of Automated Text Moderation\n\n\n\n\n\n\n\n\n\n\n\nNov 18, 2023\n\n\nIntegrity Institute collaborators: Alex Rosenblatt, Jeff Allen, Ejona Varangu, Dave Sullivan, Tom Cunningham\n\n\n\n\n\n\n\n\n\n\n\nThinking About Tradeoffs? Draw an Ellipse\n\n\n\n\n\n\n\n\n\n\n\nOct 25, 2023\n\n\nTom Cunningham, OpenAI.\n\n\n\n\n\n\n\n\n\n\n\nExperiment Interpretation and Extrapolation\n\n\n\n\n\n\n\n\n\n\n\nOct 17, 2023\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\nAn AI Which Imitates Humans Can Beat Humans\n\n\n\n\n\n\n\n\n\n\n\nOct 6, 2023\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\nSushi-Roll Model of Online Media\n\n\nPreviously: “pizza model”, “salami model”\n\n\n\n\n\n\n\n\nSep 8, 2023\n\n\nTom Cunningham, Integrity Institute\n\n\n\n\n\n\n\n\n\n\n\nHow Much has Social Media affected Polarization?\n\n\n\n\n\n\n\n\n\n\n\nAug 7, 2023\n\n\nTom Cunningham, Integrity Institute\n\n\n\n\n\n\n\n\n\n\n\nThe Paradox of Small Effects\n\n\n\n\n\n\n\n\n\n\n\nAug 2, 2023\n\n\nTom Cunningham, Integrity Institute\n\n\n\n\n\n\n\n\n\n\n\nRanking by Engagement\n\n\n\n\n\n\n\n\n\n\n\nMay 8, 2023\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\nSocial Media Suspensions of Prominent Accounts\n\n\n\n\n\n\n\n\n\n\n\nJan 31, 2023\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\nOptimal Coronavirus Policy Should be Front-Loaded\n\n\n\n\n\n\n\n\n\n\n\nApr 5, 2020\n\n\n\n\n\n\n\n\n\n\n\nOn Unconscious Influences (Part 1)\n\n\n\n\n\n\n\n\n\n\n\nDec 8, 2017\n\n\n\n\n\n\n\n\n\n\n\nThe Work of Art in the Age of Mechanical Production\n\n\n\n\n\n\n\n\n\n\n\nSep 27, 2017\n\n\n\n\n\n\n\n\n\n\n\nRepulsion from the Prior\n\n\n\n\n\n\n\n\n\n\n\nMay 26, 2017\n\n\n\n\n\n\n\n\n\n\n\nThe Repeated Failure of Laws of Behaviour\n\n\n\n\n\n\n\n\n\n\n\nApr 15, 2017\n\n\nTom Cunningham\n\n\n\n\n\n\n\n\n\n\n\nEconomist Explorers\n\n\n\n\n\n\n\n\n\n\n\nFeb 25, 2017\n\n\n\n\n\n\n\n\n\n\n\nSamuelson & Expected Utility\n\n\n\n\n\n\n\n\n\n\n\nFeb 25, 2017\n\n\n\n\n\n\n\n\n\n\n\nWeber’s Law Doesn’t Imply Concave Representations or Concave Judgments\n\n\n\n\n\n\n\n\n\n\n\nFeb 25, 2017\n\n\n\n\n\n\n\n\n\n\n\nRelative Thinking\n\n\n\n\n\n\n\n\n\n\n\nApr 30, 2016\n\n\nTom Cunningham\n\n\n\n\n\n\nNo matching items"
   },
   {
     "objectID": "posts/2023-01-31-social-media-suspensions-data.html",

docs/index.html

@@ -2,7 +2,7 @@
 <urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">
   <url>
     <loc>tecunningham.github.io/index.html</loc>
-    <lastmod>2025-10-29T15:46:32.992Z</lastmod>
+    <lastmod>2023-07-26T14:50:16.883Z</lastmod>
   </url>
   <url>
     <loc>tecunningham.github.io/posts/2023-01-31-social-media-suspensions-data.html</loc>

docs/index.xml

@@ -172,11 +172,13 @@ Apple Tree Optimization
 2. But the critical question is whether the fruit that it's picking are low-hanging. If all the optimizations are routine, then it'll run out pretty quickly.
 
 
-##              Apple-Picking Model
+##              Bernoulli Apple-Picking Model
 
 **Motivation:**
 
-- Agents are starting to autonomously optimize real-world functions, beating the human state-of-the-art.
+- Agents are showing the ability to autonomously optimize AI training, beating the human state-of-the-art.
+- Where does this end? If you can pay some tokens to improve the training function by $x$% better, then ....
+
 - In most models of RSI, agents only automate subtasks in R&D, but now they seem to be doing the whole thing autonomously.
 - Intuitively they're only doing *shallow* optimizations, not deep optimizations.
 - We want a model so that we can define what it means to only do shallow optimizations, and test whether agents obey these predictions.
@@ -190,7 +192,7 @@ Apple Tree Optimization
 
 **We can then derive apples found:**
 
-   $$\text{share apples found}= 1-\left(\underbrace{\lambda e^{-p(t_H+t_A)}}_{\text{agent+human search}}+\underbrace{(1-\lambda)e^{-p t_H}}_{\text{human-only search}}\right).$$
+   $$\text{share apples found}= 1-\left(\underbrace{\lambda e^{-p(t_H+t_A)}}_{\text{bottom of tree}}+\underbrace{(1-\lambda)e^{-p t_H}}_{\text{top of tree}}\right).$$
 
 **Implication: agents asymptote to a lower level than humans.** Here we compare agent-only to human-only. Note that agents might reasonably have a higher rate of finding apples ($p_H>p_A$) per unit time (or money), in which case the agent curve would rise quicker but still asymptote lower.