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_freeze/posts/2026-01-29-knowledge-creating-llms/execute-results/html.json

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<a href="./posts/2026-01-26-new-derivation.html" class="no-external">Formal derivations</a>
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<a href="./posts/2026-01-26-new-derivation.html" class="no-external">Summary</a>
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<dc:creator>Tom Cunningham</dc:creator>
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<li>TODO: Discuss the <em>separable</em> case.</li>
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<li>TODO: add discussion of bottlenecks, &amp; decreasing returns to scale.</li>
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<li>TODO: mention Amdahl’s law.</li>
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<li>TODO: what if you know t and t’, and know a single m changed.</li>
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docs/posts/2026-01-29-knowledge-creating-llms.html

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<dt>A visual explanation.</dt>
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Below we illustrate a set of humans, and their cost to do different tasks. Here each human has a speciality, i.e.&nbsp;a set of tasks at which they have the lowest cost. We can visualize a knowledge-sharing LLM as having the minimum-cost across all humans, while a knowledge-creating LLM achieves even lower costs.
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<p>Below we illustrate a set of humans, and their cost to do different tasks. Here each human has a speciality, i.e.&nbsp;a set of tasks at which they have the lowest cost.</p>
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<p>We can visualize a knowledge-sharing LLM assistant as equalizing knowledge, and therefore achieving the minimum-cost across all humans. However a knowledge-creating LLM achieves even lower costs.</p>
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<li>Create a movie</li>
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<dt>A simple model with recipes:</dt>
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<h1>Model</h1>
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<dt>Baseline: everyone buys from the person who knows the best recipe.</dt>
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<li><strong>Baseline: everyone buys from the person who knows the best recipe.</strong> Everyone has a unit of labor. There’s one consumption good, but various recipes for producing it, <span class="math inline">\(r\in R\)</span>, which determine the labor-cost of producing the good, <span class="math inline">\(c(r)\)</span>. In equilibrium the person who knows the lowest-cost recipe (<span class="math inline">\(c_1\)</span>) will sell the good in return for others’ labor. Their margins are equal to the difference to the next-lowest-cost recipe, <span class="math inline">\(c_2-c_1\)</span> (assume Bertrand competition).</li>
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<li><strong>Knowledge-sharing LLMs eliminate rents.</strong> Now you invent a knowledge-sharing LLM, which can reveal the lowest-cost known recipe, <span class="math inline">\(c_1\)</span>. You cannot make substantial profits from this knowledge: once two producers have the same cost then margins will be driven to zero. Assuming the recipe does diffuse, total output remains the same but the surplus is now distributed equally. If we additionally assumed some trade cost <span class="math inline">\(\delta\)</span> then the knowledge will have value equal to <span class="math inline">\(\delta\)</span>, but notably there’s no value to <em>exclusively</em> license your LLM. Also notably the returns to innovation fall: there’s much less incentive to discover a new low-cost recipe if that knowledge will be immediately shared.</li>
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<li><strong>Knowledge-creating LLMs generate additional surplus.</strong> Next we introduce a knowledge-creating LLM, which generates a new recipe <span class="math inline">\(c_0&lt;c_1\)</span>. The inventor can monetize this either by producing the good themselves or licensing the recipe to a single producer. Now exclusivity is important: if they sold the recipe to <em>two</em> producers then profits will be driven to zero, and the value of the recipe will be zero. In equilibrium total output increases, the extra surplus is split between consumers and the owner of the new recipe.</li>
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Everyone has a unit of labor. There’s one consumption good, but various recipes for producing it, <span class="math inline">\(r\in R\)</span>, which determine the labor-cost of producing the good, <span class="math inline">\(c(r)\)</span>. In equilibrium the person who knows the lowest-cost recipe (<span class="math inline">\(c_1\)</span>) will sell the good in return for others’ labor. Their margins are equal to the difference to the next-lowest-cost recipe, <span class="math inline">\(c_2-c_1\)</span> (assume Bertrand competition).
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<dt>Knowledge-sharing LLMs eliminate rents.</dt>
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Now you invent a knowledge-sharing LLM, which can reveal the lowest-cost known recipe, <span class="math inline">\(c_1\)</span>. You cannot make substantial profits from this knowledge: once two producers have the same cost then margins will be driven to zero. Assuming the recipe does diffuse, total output remains the same but the surplus is now distributed equally. If we additionally assumed some trade cost <span class="math inline">\(\delta\)</span> then the knowledge will have value equal to <span class="math inline">\(\delta\)</span>, but notably there’s no value to <em>exclusively</em> license your LLM. Also notably the returns to innovation fall: there’s much less incentive to discover a new low-cost recipe if that knowledge will be immediately shared.
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<dt>Knowledge-creating LLMs generate additional surplus.</dt>
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Next we introduce a knowledge-creating LLM, which generates a new recipe <span class="math inline">\(c_0&lt;c_1\)</span>. The inventor can monetize this either by producing the good themselves or licensing the recipe to a single producer. Now exclusivity is important: if they sold the recipe to <em>two</em> producers then profits will be driven to zero, and the value of the recipe will be zero. In equilibrium total output increases, the extra surplus is split between consumers and the owner of the new recipe.
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<h1>More to Do</h1>
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<dt>There are obvious implications for intellectual property.</dt>
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<p>A specific worry: if we maintain the same intellectual property law then there will be a land-grab, firms will rush to be the first to discover new technologies, and will then get an exclusive license, but that exclusivity will be inefficient (i.e.&nbsp;it wasn’t necessary to motivate the research, the technology would’ve been discovered anyway).</p>
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<dt>It would be more satisfying to have a generative model.</dt>
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I’d really like to sketch out a very simple model in which both humans and LLMs learn recipes from experimenting against the real world.
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<h1>Recent Examples of Knowledge-Advancing AI [UNFINISHED]</h1>
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<dt><span class="citation" data-cites="yuksekgonul2026learning">Yuksekgonul et al. (<a href="#ref-yuksekgonul2026learning" role="doc-biblioref">2026</a>)</span>, “Learning to Discover at Test Time”</dt>
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<p>“We report results for every problem we attempted, across mathematics, GPU kernel engineering, algorithm design, and biology. TTT-Discover sets the new state of the art in almost all of them: (i) Erdős’ minimum overlap problem and an autocorrelation inequality; (ii) a GPUMode kernel competition (up to 2×faster than prior art); (iii) past AtCoder algorithm competitions; and (iv) denoising problem in single-cell analysis. Our solutions are reviewed by experts or the organizers.”</p>
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If “new LLMs” reliably generate <em>valuable, appropriable</em> new recipes, then the equilibrium object may be closer to exclusive licensing / restricted access (or secrecy) than to wide diffusion of a general-purpose tool.
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<dt>There are obvious implications for intellectual property.</dt>
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<p>A specific worry: if we maintain the same intellectual property law then there will be a land-grab, firms will rush to be the first to discover new technologies, and will then get an exclusive license, but that exclusivity will be inefficient (i.e.&nbsp;it wasn’t necessary to motivate the research, the technology would’ve been discovered anyway).</p>
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I’d really like to sketch out a very simple model in which both humans and LLMs learn recipes from experimenting against the real world.
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<h1>Related Notes</h1>
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<dt><span class="citation" data-cites="yuksekgonul2026learning">Yuksekgonul et al. (<a href="#ref-yuksekgonul2026learning" role="doc-biblioref">2026</a>)</span>, “Learning to Discover at Test Time”</dt>
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<p>“We report results for every problem we attempted, across mathematics, GPU kernel engineering, algorithm design, and biology. TTT-Discover sets the new state of the art in almost all of them: (i) Erdős’ minimum overlap problem and an autocorrelation inequality; (ii) a GPUMode kernel competition (up to 2×faster than prior art); (iii) past AtCoder algorithm competitions; and (iv) denoising problem in single-cell analysis. Our solutions are reviewed by experts or the organizers.”</p>
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<div id="quarto-appendix" class="default"><section class="quarto-appendix-contents" role="doc-bibliography" id="quarto-bibliography"><h2 class="anchored quarto-appendix-heading">References</h2><div id="refs" class="references csl-bib-body hanging-indent" data-entry-spacing="0" role="list">

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